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Pure General Logic Programming (PGLP) (Intro/Overview) Rensselaer AI & Reasoning (RAIR) Lab Department of Cognitive Science Department of Computer Science Lally School of Management Rensselaer Polytechnic Institute (RPI) Troy, New York 12180 USA Intro to Logic 2/7/2019 Selmer Bringsjord

Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

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Page 1: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Pure General Logic Programming(PGLP)

(Intro/Overview)

Rensselaer AI & Reasoning (RAIR) LabDepartment of Cognitive ScienceDepartment of Computer Science

Lally School of ManagementRensselaer Polytechnic Institute (RPI)

Troy, New York 12180 USA

Intro to Logic2/7/2019

Selmer Bringsjord

Page 2: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

A computer program and its execution in PGLP (@ level of propositional calculus):

Page 3: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

A computer program and its execution in PGLP (@ level of propositional calculus):

PC ⊢ ✓

GIVEN. φ ∧ ¬φ{GIVEN} Assume ✓

GOAL. ψ{GIVEN}

Page 4: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

A computer program and its execution in PGLP (@ level of propositional calculus):

PC ⊢ ✓

GIVEN. φ ∧ ¬φ{GIVEN} Assume ✓

GOAL. ψ{GIVEN}

Program:

Page 5: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

A computer program and its execution in PGLP (@ level of propositional calculus):

PC ⊢ ✓

GIVEN. φ ∧ ¬φ{GIVEN} Assume ✓

GOAL. ψ{GIVEN}

Program:

Query:

Page 6: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

A computer program and its execution in PGLP (@ level of propositional calculus):

PC ⊢ ✓

GIVEN. φ ∧ ¬φ{GIVEN} Assume ✓

GOAL. ψ{GIVEN}

Program:

Query:

Automated Reasoner:

Page 7: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

A computer program and its execution in PGLP (@ level of propositional calculus):

PC ⊢ ✓

GIVEN. φ ∧ ¬φ{GIVEN} Assume ✓

GOAL. ψ{GIVEN}

Program:

Query:

Automated Reasoner:

Checker

Page 8: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

A computer program and its execution in PGLP (@ level of propositional calculus):

PC ⊢ ✓

GIVEN. φ ∧ ¬φ{GIVEN} Assume ✓

GOAL. ψ{GIVEN}

Program:

Query:

Automated Reasoner:

Checker

Page 9: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Logistics …

Page 10: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Logistics …

Any questions?

Page 11: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Some Brief Polling (redux) …

Page 12: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Some Brief Polling (redux) …How many have taken a programming course?

Page 13: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Some Brief Polling (redux) …How many have taken a programming course?

How many have learned a functional-programming language?

Page 14: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Some Brief Polling (redux) …How many have taken a programming course?

How many have learned a logic-programming language?

How many have learned a functional-programming language?

Page 15: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Pure General Logic Programming (Intro/Overview)

Rensselaer AI & Reasoning (RAIR) LabDepartment of Cognitive ScienceDepartment of Computer Science

Lally School of ManagementRensselaer Polytechnic Institute (RPI)

Troy, New York 12180 USA

Intro to Logic3/7/2019

Selmer Bringsjord

Page 16: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Entscheidungsproblem

20191666

Leibniz

“Universal Computational Logic”

20201854

Organon

Intro to Logic @ RPI

300 BC350 BC

Euclid

The Singularity?

1956

Logic Theorist(birth of modern logicist AI)

Simon

?

Page 17: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Entscheidungsproblem

20191666

Leibniz

“Universal Computational Logic”

20201854

Organon

Intro to Logic @ RPI

300 BC350 BC

Euclid

The Singularity?

1956

Logic Theorist(birth of modern logicist AI)

Simon

?

Page 18: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Entscheidungsproblem

20191666

Leibniz

“Universal Computational Logic”

20201854

Organon

Intro to Logic @ RPI

300 BC350 BC

Euclid

The Singularity?

1956

Logic Theorist(birth of modern logicist AI)

Simon

?

Frege

Page 19: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Entscheidungsproblem

20191666

Leibniz

“Universal Computational Logic”

20201854

Organon

Intro to Logic @ RPI

300 BC350 BC

Euclid

The Singularity?

1956

Logic Theorist(birth of modern logicist AI)

Simon

?

Exceeds Leibniz & de-mystifies Euclid: the “compellingness” of these proofs consists in their being, at bottom, formal proofs in first-order logic (FOL).Frege

Page 20: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Entscheidungsproblem

20191666

Leibniz

“Universal Computational Logic”

20201854

Organon

Intro to Logic @ RPI

300 BC350 BC

Euclid

The Singularity?

1956

Logic Theorist(birth of modern logicist AI)

Simon

?

Exceeds Leibniz & de-mystifies Euclid: the “compellingness” of these proofs consists in their being, at bottom, formal proofs in first-order logic (FOL).Frege

Church

Page 21: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Entscheidungsproblem

20191666

Leibniz

“Universal Computational Logic”

20201854

Organon

Intro to Logic @ RPI

300 BC350 BC

Euclid

The Singularity?

1956

Logic Theorist(birth of modern logicist AI)

Simon

?

Exceeds Leibniz & de-mystifies Euclid: the “compellingness” of these proofs consists in their being, at bottom, formal proofs in first-order logic (FOL).Frege

Church Turing

Page 22: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Entscheidungsproblem

20191666

Leibniz

“Universal Computational Logic”

20201854

Organon

Intro to Logic @ RPI

300 BC350 BC

Euclid

The Singularity?

1956

Logic Theorist(birth of modern logicist AI)

Simon

?

Exceeds Leibniz & de-mystifies Euclid: the “compellingness” of these proofs consists in their being, at bottom, formal proofs in first-order logic (FOL).Frege

Church Turing Post

Page 23: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Entscheidungsproblem

20191666

Leibniz

“Universal Computational Logic”

20201854

Organon

Intro to Logic @ RPI

300 BC350 BC

Euclid

The Singularity?

1956

Logic Theorist(birth of modern logicist AI)

Simon

?

Exceeds Leibniz & de-mystifies Euclid: the “compellingness” of these proofs consists in their being, at bottom, formal proofs in first-order logic (FOL).Frege

Church Turing Post

Here’s what a computer is, and given that, sorry, the Entscheidungsproblem can’t be solved by such a machine!

Page 24: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Entscheidungsproblem

20191666

Leibniz

“Universal Computational Logic”

20201854

Organon

Intro to Logic @ RPI

300 BC350 BC

Euclid

The Singularity?

1956

Logic Theorist(birth of modern logicist AI)

Simon

?

Exceeds Leibniz & de-mystifies Euclid: the “compellingness” of these proofs consists in their being, at bottom, formal proofs in first-order logic (FOL).Frege

Church Turing Post

Here’s what a computer is, and given that, sorry, the Entscheidungsproblem can’t be solved by such a machine!

New: Functional = Church; Procedural = Turing. Where is logicist computation?

Page 25: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Entscheidungsproblem

20191666

Leibniz

“Universal Computational Logic”

20201854

Organon

Intro to Logic @ RPI

300 BC350 BC

Euclid

The Singularity?

1956

Logic Theorist(birth of modern logicist AI)

Simon

?

Exceeds Leibniz & de-mystifies Euclid: the “compellingness” of these proofs consists in their being, at bottom, formal proofs in first-order logic (FOL).Frege

Church Turing Post

Here’s what a computer is, and given that, sorry, the Entscheidungsproblem can’t be solved by such a machine!

New: Functional = Church; Procedural = Turing. Where is logicist computation?

Page 26: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Entscheidungsproblem

20191666

Leibniz

“Universal Computational Logic”

20201854

Organon

Intro to Logic @ RPI

300 BC350 BC

Euclid

The Singularity?

1956

Logic Theorist(birth of modern logicist AI)

Simon

?

Exceeds Leibniz & de-mystifies Euclid: the “compellingness” of these proofs consists in their being, at bottom, formal proofs in first-order logic (FOL).Frege

Church Turing Post

Here’s what a computer is, and given that, sorry, the Entscheidungsproblem can’t be solved by such a machine!

New: Functional = Church; Procedural = Turing. Where is logicist computation?

Page 27: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Entscheidungsproblem

20191666

Leibniz

“Universal Computational Logic”

20201854

Organon

Intro to Logic @ RPI

300 BC350 BC

Euclid

The Singularity?

1956

Logic Theorist(birth of modern logicist AI)

Simon

?

Exceeds Leibniz & de-mystifies Euclid: the “compellingness” of these proofs consists in their being, at bottom, formal proofs in first-order logic (FOL).Frege

Church Turing Post

Here’s what a computer is, and given that, sorry, the Entscheidungsproblem can’t be solved by such a machine!

New: Functional = Church; Procedural = Turing. Where is logicist computation?

Page 28: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Entscheidungsproblem

20191666

Leibniz

“Universal Computational Logic”

20201854

Organon

Intro to Logic @ RPI

300 BC350 BC

Euclid

The Singularity?

1956

Logic Theorist(birth of modern logicist AI)

Simon

?

Exceeds Leibniz & de-mystifies Euclid: the “compellingness” of these proofs consists in their being, at bottom, formal proofs in first-order logic (FOL).Frege

Church Turing Post

Here’s what a computer is, and given that, sorry, the Entscheidungsproblem can’t be solved by such a machine!

New: Functional = Church; Procedural = Turing. Where is logicist computation?

Page 29: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Two Logicist Branches; B1:

Page 30: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Two Logicist Branches; B1:Frege (remember him?), 1893:“Aha! Currying! I recast multiple-arity operations with functions into a unary affair!”

Page 31: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Two Logicist Branches; B1:Frege (remember him?), 1893:“Aha! Currying! I recast multiple-arity operations with functions into a unary affair!”

Schönfinkel, 1920’s:“Aha! I can do this stuff using combinatory logic!”

Page 32: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Two Logicist Branches; B1:Frege (remember him?), 1893:“Aha! Currying! I recast multiple-arity operations with functions into a unary affair!”

Schönfinkel, 1920’s:“Aha! I can do this stuff using combinatory logic!”

Church, 1920’s & 30’s:“Aha! The lambda calculus!

Page 33: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Two Logicist Branches; B1:Frege (remember him?), 1893:“Aha! Currying! I recast multiple-arity operations with functions into a unary affair!”

Schönfinkel, 1920’s:“Aha! I can do this stuff using combinatory logic!”

Church, 1920’s & 30’s:“Aha! The lambda calculus!

Page 34: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Two Logicist Branches; B1:Frege (remember him?), 1893:“Aha! Currying! I recast multiple-arity operations with functions into a unary affair!”

Schönfinkel, 1920’s:“Aha! I can do this stuff using combinatory logic!”

Church, 1920’s & 30’s:“Aha! The lambda calculus!

Haskell

Page 35: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Two Logicist Branches; B2:

Page 36: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Two Logicist Branches; B2:The AI Branch: Automated Reasoning

Page 37: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Two Logicist Branches; B2:

Leibniz

The AI Branch: Automated Reasoning

Page 38: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Two Logicist Branches; B2:

Leibniz

Simon & Newell @ Dawn of Modern AI: LT & GPS

The AI Branch: Automated Reasoning

Page 39: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Two Logicist Branches; B2:

Leibniz

Simon & Newell @ Dawn of Modern AI: LT & GPS

The AI Branch: Automated Reasoning

Page 40: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Two Logicist Branches; B2:

Leibniz

Simon & Newell @ Dawn of Modern AI: LT & GPS

The AI Branch: Automated Reasoning

Prolog?

Page 41: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Two Logicist Branches; B2:

Leibniz

Simon & Newell @ Dawn of Modern AI: LT & GPS

The AI Branch: Automated Reasoning

Page 42: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Two Logicist Branches; B2:

Leibniz

Simon & Newell @ Dawn of Modern AI: LT & GPS

The AI Branch: Automated Reasoning

PGLP

Page 43: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Single-Slide Encapsulation …

Page 44: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

�10

L := hL, Ii

P Lq L

R : hP, qi �! hY|N|U, �,⇡(s)|↵(s)iC : ⇡(s)|↵(s) �! hY|N|U, �i

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Page 45: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

�11

L := hL, Ii

P Lq L

R : hP, qi �! hY|N|U, �,⇡(s)|↵(s)iC : ⇡(s)|↵(s) �! hY|N|U, �i

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query

program

reasoner

checker

degree of “confidence”

proof(s)

argument(s)

Page 46: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

The “British Track” (Procedural) …

Page 47: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

The Track

Page 48: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

The TrackComputational thinking is … Computer programming is … A computer program is …

Page 49: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

The Track

Page 50: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

The Track

Page 51: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

The Track

Page 52: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

The Track

Page 53: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

The Track

Teach computer programming!(procedural, o-o, functional)

Page 54: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

The Track

Teach computer programming!(procedural, o-o, functional)

Page 55: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

The Track

Teach computer programming!(procedural, o-o, functional)

Page 56: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

The Track

Teach computer programming!(procedural, o-o, functional)

– Rapaport, “phics" book

Page 57: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

The Track

Teach computer programming!(procedural, o-o, functional)

– Rapaport, “phics" book

What about Turner?!?

Page 58: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

1. A Hard Question …

Page 59: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Easy Question

Page 60: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

What is pure procedural programming?

Easy Question

Page 61: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Another Easy Question

Page 62: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

What is pure functional programming?

Another Easy Question

Page 63: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

A Hard Question

Page 64: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

What is pure logic programming?

A Hard Question

Page 65: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

What is pure logic programming?

A Hard Question

Page 66: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

What is pure logic programming?

A Hard Question

A: …

B: …

C: …

Naveen: “Using automated theorem provers …”

Page 67: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

3. The Space of Particular Logical Calculi …

Page 68: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Logical Calculi

Infinitary Finitary

Intensional ExtensionalDeductive InductiveDeductive Inductive

Symbolic Diagram Symbolic Diagram Symbolic Diagram Symbolic Diagram

Page 69: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Logical Calculi

Infinitary Finitary

Intensional ExtensionalDeductive InductiveDeductive Inductive

Symbolic Diagram Symbolic Diagram Symbolic Diagram Symbolic Diagram

“textbook” AI (≤ FOL)

Page 70: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Logical Calculi

Infinitary Finitary

Intensional ExtensionalDeductive InductiveDeductive Inductive

Symbolic Diagram Symbolic Diagram Symbolic Diagram Symbolic Diagram“textbook” AI (≤ FOL)

Page 71: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Logical Calculi

Infinitary Finitary

Intensional ExtensionalDeductive InductiveDeductive Inductive

Symbolic Diagram Symbolic Diagram Symbolic Diagram Symbolic Diagram“textbook” AI (≤ FOL)

Mathematics (classical, classroom)

Page 72: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Logical Calculi

Infinitary Finitary

Intensional ExtensionalDeductive InductiveDeductive Inductive

Symbolic Diagram Symbolic Diagram Symbolic Diagram Symbolic Diagram“textbook” AI (≤ FOL)

Mathematics (classical, classroom)

Page 73: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Logical Calculi

Infinitary Finitary

Intensional ExtensionalDeductive InductiveDeductive Inductive

Symbolic Diagram Symbolic Diagram Symbolic Diagram Symbolic Diagram“textbook” AI (≤ FOL)

Mathematics (classical, classroom)

Page 74: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Logical Calculi

Infinitary Finitary

Intensional ExtensionalDeductive InductiveDeductive Inductive

Symbolic Diagram Symbolic Diagram Symbolic Diagram Symbolic Diagram“textbook” AI (≤ FOL)

Mathematics (classical, classroom)

Analogical Inductive Reasoning (formal & hence suitable for automation & verification)

Page 75: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Logical Calculi

Infinitary Finitary

Intensional ExtensionalDeductive InductiveDeductive Inductive

Symbolic Diagram Symbolic Diagram Symbolic Diagram Symbolic Diagram“textbook” AI (≤ FOL)

Mathematics (classical, classroom)

Analogical Inductive Reasoning (formal & hence suitable for automation & verification)

Page 76: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Space of Some Logical Calculi in Five Dimensions

……

Page 77: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Sub-Part of the CC Space

CC

CEC

DCEC

µC

DCEC⇤

DCEC⇤e

Page 78: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

Sub-Part of the CC Space

CC

CEC

DCEC

µC

DCEC⇤

DCEC⇤e

Inductive Logic, IJCAI 2017

Page 79: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

4. Ingredients for Making a PGLP Program …

Page 80: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

On the Anatomy of a PGLP Program

Page 81: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

On the Anatomy of a PGLP Program

object-level languageL<latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit>

meta-level1 languageLµ1

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Lµ2

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meta-level2 language

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9x rank(�) = x {�} ` U |= �<latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit>

�<latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit>

({�} ` ^ { } ` �) `µ2 {�} ` �<latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">AAACbXicbVHLSgMxFE3Hd31VxZUiwSLqpswUQZeiG5cKVkVThjuZO21o5kGSUcrQf/M3/AG3+gEuzNRZaOuBwMk59yY3J0EmhTau+1ZzZmbn5hcWl+rLK6tr642NzTud5opjh6cyVQ8BaJQiwY4RRuJDphDiQOJ9MLgs/ftnVFqkya0ZZtiNoZeISHAwVvIbj0esYFlfsBFlzyHoPmWZFpS9YNhDWnr6txeiNHBcbf2CxbnfHtGpI8ZlfqPpttwx6DTxKtIkFa79xhcLU57HmBguQesnz81MtwBlBJc4qrNcYwZ8AD18sjSBGHW3GGcwogdWCWmUKrsSQ8fq744CYq2HcWArYzB9PemV4r9eqSgd6T/3F5hHCgYTM5norFuIJMsNJvxnpCiX1KS0jJ6GQiE3cmgJcCXsqyjvgwJu7AfVbVzeZDjT5K7d8tyWd3PSPL+oglskO2SfHBGPnJJzckWuSYdw8kreyQf5rH04286us/dT6tSqni3yB87hN4yEv1A=</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit>

...<latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit>

Linguistics

Page 82: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

On the Anatomy of a PGLP Program

object-level languageL<latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit>

meta-level1 languageLµ1

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Lµ2

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meta-level2 language

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9x rank(�) = x {�} ` U |= �<latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">AAACbnicbVHLahtBEBxtXo7ysJxALiZkiAgoF7EbAsnFYJxLjg5EtkEjRO9srzVoHpvpWSOx6OPyGfkCX517DpmVFbDlNAwUVd10dU1eaUUhTX91knv3Hzx8tPO4++Tps+e7vb0XJ+RqL3EknXb+LAdCrSyOggoazyqPYHKNp/n8S6ufXqAn5ez3sKxwYuDcqlJJCJGa9sYCF3EL8YXgwuRu0Xiw89VAVDP1nh/wBRc/aii4aFpGrLi4KIBmXFSk/kkGwqz0MG9GUTauQE287Z72+ukwXRe/C7IN6LNNHU97f0ThZG3QBqmBaJylVZg04IOSGlddURNWIOdwjuMILRikSbMOYcXfRabgpfPx2cDX7M2JBgzR0uSxszVM21pL/ldrGU8l3drfYN2evOUplJ8njbJVHdDKa0tlrXlwvM2eF8qjDHoZAUiv4lVczsCDDPGHujGubDucu+DkwzBLh9m3j/3Do01wO2yfvWUDlrFP7JB9ZcdsxCT7yS7ZFfvduUpeJa+TN9etSWcz85LdqmTwF0XKv58=</latexit>

�<latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit>

({�} ` ^ { } ` �) `µ2 {�} ` �<latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit>

...<latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit>

Linguistics

InferenceA collection of inference schemata. (For economy, see coming Example 1.)

Page 83: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

On the Anatomy of a PGLP Program

SemanticsReasoning-semantic; wholly inferentialist (after all, what’s the semantics of deduction over meta-level1 formulae??).

object-level languageL<latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit>

meta-level1 languageLµ1

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Lµ2

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meta-level2 language

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9x rank(�) = x {�} ` U |= �<latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">AAACbnicbVHLahtBEBxtXo7ysJxALiZkiAgoF7EbAsnFYJxLjg5EtkEjRO9srzVoHpvpWSOx6OPyGfkCX517DpmVFbDlNAwUVd10dU1eaUUhTX91knv3Hzx8tPO4++Tps+e7vb0XJ+RqL3EknXb+LAdCrSyOggoazyqPYHKNp/n8S6ufXqAn5ez3sKxwYuDcqlJJCJGa9sYCF3EL8YXgwuRu0Xiw89VAVDP1nh/wBRc/aii4aFpGrLi4KIBmXFSk/kkGwqz0MG9GUTauQE287Z72+ukwXRe/C7IN6LNNHU97f0ThZG3QBqmBaJylVZg04IOSGlddURNWIOdwjuMILRikSbMOYcXfRabgpfPx2cDX7M2JBgzR0uSxszVM21pL/ldrGU8l3drfYN2evOUplJ8njbJVHdDKa0tlrXlwvM2eF8qjDHoZAUiv4lVczsCDDPGHujGubDucu+DkwzBLh9m3j/3Do01wO2yfvWUDlrFP7JB9ZcdsxCT7yS7ZFfvduUpeJa+TN9etSWcz85LdqmTwF0XKv58=</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit>

�<latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit>

({�} ` ^ { } ` �) `µ2 {�} ` �<latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit>

...<latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit>

Linguistics

InferenceA collection of inference schemata. (For economy, see coming Example 1.)

Page 84: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

On the Anatomy of a PGLP Program

SemanticsReasoning-semantic; wholly inferentialist (after all, what’s the semantics of deduction over meta-level1 formulae??).

object-level languageL<latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit>

meta-level1 languageLµ1

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Lµ2

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meta-level2 language

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9x rank(�) = x {�} ` U |= �<latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit>

�<latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit>

({�} ` ^ { } ` �) `µ2 {�} ` �<latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit>

...<latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit>

Linguistics

InferenceA collection of inference schemata. (For economy, see coming Example 1.)

Page 85: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

On the Anatomy of a PGLP Program

SemanticsReasoning-semantic; wholly inferentialist (after all, what’s the semantics of deduction over meta-level1 formulae??).

object-level languageL<latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit>

meta-level1 languageLµ1

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Lµ2

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meta-level2 language

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9x rank(�) = x {�} ` U |= �<latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit>

�<latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit>

({�} ` ^ { } ` �) `µ2 {�} ` �<latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit>

...<latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit>

Linguistics

InferenceA collection of inference schemata. (For economy, see coming Example 1.)

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Page 86: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

On the Anatomy of a PGLP Program

SemanticsReasoning-semantic; wholly inferentialist (after all, what’s the semantics of deduction over meta-level1 formulae??).

object-level languageL<latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit>

meta-level1 languageLµ1

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Lµ2

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meta-level2 language

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9x rank(�) = x {�} ` U |= �<latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit>

�<latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit>

({�} ` ^ { } ` �) `µ2 {�} ` �<latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">AAACbXicbVHLSgMxFE3Hd31VxZUiwSLqpswUQZeiG5cKVkVThjuZO21o5kGSUcrQf/M3/AG3+gEuzNRZaOuBwMk59yY3J0EmhTau+1ZzZmbn5hcWl+rLK6tr642NzTud5opjh6cyVQ8BaJQiwY4RRuJDphDiQOJ9MLgs/ftnVFqkya0ZZtiNoZeISHAwVvIbj0esYFlfsBFlzyHoPmWZFpS9YNhDWnr6txeiNHBcbf2CxbnfHtGpI8ZlfqPpttwx6DTxKtIkFa79xhcLU57HmBguQesnz81MtwBlBJc4qrNcYwZ8AD18sjSBGHW3GGcwogdWCWmUKrsSQ8fq744CYq2HcWArYzB9PemV4r9eqSgd6T/3F5hHCgYTM5norFuIJMsNJvxnpCiX1KS0jJ6GQiE3cmgJcCXsqyjvgwJu7AfVbVzeZDjT5K7d8tyWd3PSPL+oglskO2SfHBGPnJJzckWuSYdw8kreyQf5rH04286us/dT6tSqni3yB87hN4yEv1A=</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit>

...<latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit>

Linguistics

InferenceA collection of inference schemata. (For economy, see coming Example 1.)

Selection of language, inference schemata, plus formulae/meta-formulae = PL<latexit sha1_base64="opHgzZEoXSE0vAJ0tWgLP/3xO8o=">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</latexit><latexit 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Page 87: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

On the Anatomy of a PGLP Program

SemanticsReasoning-semantic; wholly inferentialist (after all, what’s the semantics of deduction over meta-level1 formulae??).

object-level languageL<latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit>

meta-level1 languageLµ1

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Lµ2

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meta-level2 language

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9x rank(�) = x {�} ` U |= �<latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">AAACbnicbVHLahtBEBxtXo7ysJxALiZkiAgoF7EbAsnFYJxLjg5EtkEjRO9srzVoHpvpWSOx6OPyGfkCX517DpmVFbDlNAwUVd10dU1eaUUhTX91knv3Hzx8tPO4++Tps+e7vb0XJ+RqL3EknXb+LAdCrSyOggoazyqPYHKNp/n8S6ufXqAn5ez3sKxwYuDcqlJJCJGa9sYCF3EL8YXgwuRu0Xiw89VAVDP1nh/wBRc/aii4aFpGrLi4KIBmXFSk/kkGwqz0MG9GUTauQE287Z72+ukwXRe/C7IN6LNNHU97f0ThZG3QBqmBaJylVZg04IOSGlddURNWIOdwjuMILRikSbMOYcXfRabgpfPx2cDX7M2JBgzR0uSxszVM21pL/ldrGU8l3drfYN2evOUplJ8njbJVHdDKa0tlrXlwvM2eF8qjDHoZAUiv4lVczsCDDPGHujGubDucu+DkwzBLh9m3j/3Do01wO2yfvWUDlrFP7JB9ZcdsxCT7yS7ZFfvduUpeJa+TN9etSWcz85LdqmTwF0XKv58=</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">AAACbnicbVHLahtBEBxtXo7ysJxALiZkiAgoF7EbAsnFYJxLjg5EtkEjRO9srzVoHpvpWSOx6OPyGfkCX517DpmVFbDlNAwUVd10dU1eaUUhTX91knv3Hzx8tPO4++Tps+e7vb0XJ+RqL3EknXb+LAdCrSyOggoazyqPYHKNp/n8S6ufXqAn5ez3sKxwYuDcqlJJCJGa9sYCF3EL8YXgwuRu0Xiw89VAVDP1nh/wBRc/aii4aFpGrLi4KIBmXFSk/kkGwqz0MG9GUTauQE287Z72+ukwXRe/C7IN6LNNHU97f0ThZG3QBqmBaJylVZg04IOSGlddURNWIOdwjuMILRikSbMOYcXfRabgpfPx2cDX7M2JBgzR0uSxszVM21pL/ldrGU8l3drfYN2evOUplJ8njbJVHdDKa0tlrXlwvM2eF8qjDHoZAUiv4lVczsCDDPGHujGubDucu+DkwzBLh9m3j/3Do01wO2yfvWUDlrFP7JB9ZcdsxCT7yS7ZFfvduUpeJa+TN9etSWcz85LdqmTwF0XKv58=</latexit>

�<latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit>

({�} ` ^ { } ` �) `µ2 {�} ` �<latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit>

...<latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit>

Linguistics

InferenceA collection of inference schemata. (For economy, see coming Example 1.)

+ ShadowReasonerSelection of language, inference schemata, plus formulae/meta-formulae = PL<latexit sha1_base64="opHgzZEoXSE0vAJ0tWgLP/3xO8o=">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</latexit><latexit sha1_base64="opHgzZEoXSE0vAJ0tWgLP/3xO8o=">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</latexit><latexit 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Page 88: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

On the Anatomy of a PGLP Program

SemanticsReasoning-semantic; wholly inferentialist (after all, what’s the semantics of deduction over meta-level1 formulae??).

object-level languageL<latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit>

meta-level1 languageLµ1

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Lµ2

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meta-level2 language

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...<latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit>

Linguistics

InferenceA collection of inference schemata. (For economy, see coming Example 1.)

+ ShadowReasoner

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Page 89: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

On the Anatomy of a PGLP Program

SemanticsReasoning-semantic; wholly inferentialist (after all, what’s the semantics of deduction over meta-level1 formulae??).

object-level languageL<latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit><latexit sha1_base64="DVjxmbXnl7kH97AgGICPWjTuOKE=">AAACEnicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sbBIwMRAEsLs5G4yZHZ2mZkVwpIvsI0/Yye2/oD/YuFssoVJPDBwOOde7pnjx4Jr47rfTmFjc2t7p7hb2ts/ODwqH5+0dJQohk0WiUi1fapRcIlNw43AdqyQhr7AZ398n/nPL6g0j+STmcTYC+lQ8oAzaqzUeOyXK27VnYOsEy8nFchR75d/uoOIJSFKwwTVuuO5semlVBnOBE5L3URjTNmYDrFjqaQh6l46DzolF1YZkCBS9klD5urfjZSGWk9C306G1Iz0qpeJ/3qZonSgl+6nmASKjlcymeC2l3IZJwYlW0QKEkFMRLJ+yIArZEZMLKFMcfsrwkZUUWZsiyVbl7dazjppXVU9t+o1riu1u7y4IpzBOVyCBzdQgweoQxMYILzCDN6cmfPufDifi9GCk++cwhKcr186aZ6g</latexit>

meta-level1 languageLµ1

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Lµ2

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meta-level2 language

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9x rank(�) = x {�} ` U |= �<latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit><latexit sha1_base64="J2mQVl8uG3tvccG2H38vvCgaatQ=">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</latexit>

�<latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit><latexit sha1_base64="x9i+wxnXsY7RnyChVM+l1/GJza0=">AAACF3icbVDLSsNAFJ3UV62vqks3wSK4KokIuiy6cVnBPqAN5WZy046dTMLMRCih/+C2/ow7cevSf3HhpM3Cth4YOJxzL/fM8RPOlHacb6u0sbm1vVPereztHxweVY9P2ipOJcUWjXksuz4o5ExgSzPNsZtIhMjn2PHH97nfeUGpWCye9CRBL4KhYCGjoI3U7gfINQyqNafuzGGvE7cgNVKgOaj+9IOYphEKTTko1XOdRHsZSM0ox2mlnypMgI5hiD1DBUSovGyedmpfGCWww1iaJ7Q9V/9uZBApNYl8MxmBHqlVLxf/9XJFqlAt3c8wDSWMVzLp8NbLmEhSjYIuIoUpt3Vs5yXZAZNINZ8YAlQy8yubjkAC1abKiqnLXS1nnbSv6q5Tdx+va427orgyOSPn5JK45IY0yANpkhah5Jm8khl5s2bWu/VhfS5GS1axc0qWYH39AoGCoOw=</latexit>

({�} ` ^ { } ` �) `µ2 {�} ` �<latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">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</latexit><latexit sha1_base64="cyNccFDYAwPVFMsXguGtp3RIcs4=">AAACbXicbVHLSgMxFE3Hd31VxZUiwSLqpswUQZeiG5cKVkVThjuZO21o5kGSUcrQf/M3/AG3+gEuzNRZaOuBwMk59yY3J0EmhTau+1ZzZmbn5hcWl+rLK6tr642NzTud5opjh6cyVQ8BaJQiwY4RRuJDphDiQOJ9MLgs/ftnVFqkya0ZZtiNoZeISHAwVvIbj0esYFlfsBFlzyHoPmWZFpS9YNhDWnr6txeiNHBcbf2CxbnfHtGpI8ZlfqPpttwx6DTxKtIkFa79xhcLU57HmBguQesnz81MtwBlBJc4qrNcYwZ8AD18sjSBGHW3GGcwogdWCWmUKrsSQ8fq744CYq2HcWArYzB9PemV4r9eqSgd6T/3F5hHCgYTM5norFuIJMsNJvxnpCiX1KS0jJ6GQiE3cmgJcCXsqyjvgwJu7AfVbVzeZDjT5K7d8tyWd3PSPL+oglskO2SfHBGPnJJzckWuSYdw8kreyQf5rH04286us/dT6tSqni3yB87hN4yEv1A=</latexit>

...<latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit><latexit sha1_base64="2ef91jK/96qH7hB3WIqViyvsgT4=">AAACF3icbVDLSgMxFM34rPVVdekmWARXZUYEXRbduKxgH9AOJZPJtLGZZEjuFMrQf3Bbf8aduHXpv7gw087Cth4IHM65l3tygkRwA6777Wxsbm3v7Jb2yvsHh0fHlZPTllGppqxJlVC6ExDDBJesCRwE6ySakTgQrB2MHnK/PWbacCWfYZIwPyYDySNOCVip1RuHCky/UnVr7hx4nXgFqaICjX7lpxcqmsZMAhXEmK7nJuBnRAOngk3LvdSwhNARGbCupZLEzPjZPO0UX1olxJHS9knAc/XvRkZiYyZxYCdjAkOz6uXiv16uaBOZpfsZSyNNRiuZILrzMy6TFJiki0hRKjAonJeEQ64ZBTGxhFDN7a8wHRJNKNgqy7Yub7WcddK6rnluzXu6qdbvi+JK6BxdoCvkoVtUR4+ogZqIohf0imbozZk5786H87kY3XCKnTO0BOfrF8GhoRI=</latexit>

Linguistics

InferenceA collection of inference schemata. (For economy, see coming Example 1.)

L<latexit sha1_base64="hAEDu4GQ6b/8ewm9yW25yL+8xc0=">AAACHHicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiGxcuKtgHtEPJpJk2NJMMSUYoQz/Dbf0Zd+JW8F9cmJnOwrYeCBzOuZd7coKYM21c99spbWxube+Udyt7+weHR9Xjk7aWiSK0RSSXqhtgTTkTtGWY4bQbK4qjgNNOMLnP/M4LVZpJ8WymMfUjPBIsZAQbK/X6ETZjTVT6OBtUa27dzYHWiVeQGhRoDqo//aEkSUSFIRxr3fPc2PgpVoYRTmeVfqJpjMkEj2jPUoEjqv00jzxDF1YZolAq+4RBufp3I8WR1tMosJN5xFUvE//1MkXpUC/dT2kSKjxZyWTCWz9lIk4MFWQRKUw4MhJlTaEhU5QYPrUEE8XsrxAZY4WJsX1WbF3eajnrpH1V99y693Rda9wVxZXhDM7hEjy4gQY8QBNaQEDCK8zhzZk7786H87kYLTnFzikswfn6BfHPo0o=</latexit><latexit sha1_base64="hAEDu4GQ6b/8ewm9yW25yL+8xc0=">AAACHHicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiGxcuKtgHtEPJpJk2NJMMSUYoQz/Dbf0Zd+JW8F9cmJnOwrYeCBzOuZd7coKYM21c99spbWxube+Udyt7+weHR9Xjk7aWiSK0RSSXqhtgTTkTtGWY4bQbK4qjgNNOMLnP/M4LVZpJ8WymMfUjPBIsZAQbK/X6ETZjTVT6OBtUa27dzYHWiVeQGhRoDqo//aEkSUSFIRxr3fPc2PgpVoYRTmeVfqJpjMkEj2jPUoEjqv00jzxDF1YZolAq+4RBufp3I8WR1tMosJN5xFUvE//1MkXpUC/dT2kSKjxZyWTCWz9lIk4MFWQRKUw4MhJlTaEhU5QYPrUEE8XsrxAZY4WJsX1WbF3eajnrpH1V99y693Rda9wVxZXhDM7hEjy4gQY8QBNaQEDCK8zhzZk7786H87kYLTnFzikswfn6BfHPo0o=</latexit><latexit sha1_base64="hAEDu4GQ6b/8ewm9yW25yL+8xc0=">AAACHHicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiGxcuKtgHtEPJpJk2NJMMSUYoQz/Dbf0Zd+JW8F9cmJnOwrYeCBzOuZd7coKYM21c99spbWxube+Udyt7+weHR9Xjk7aWiSK0RSSXqhtgTTkTtGWY4bQbK4qjgNNOMLnP/M4LVZpJ8WymMfUjPBIsZAQbK/X6ETZjTVT6OBtUa27dzYHWiVeQGhRoDqo//aEkSUSFIRxr3fPc2PgpVoYRTmeVfqJpjMkEj2jPUoEjqv00jzxDF1YZolAq+4RBufp3I8WR1tMosJN5xFUvE//1MkXpUC/dT2kSKjxZyWTCWz9lIk4MFWQRKUw4MhJlTaEhU5QYPrUEE8XsrxAZY4WJsX1WbF3eajnrpH1V99y693Rda9wVxZXhDM7hEjy4gQY8QBNaQEDCK8zhzZk7786H87kYLTnFzikswfn6BfHPo0o=</latexit><latexit sha1_base64="hAEDu4GQ6b/8ewm9yW25yL+8xc0=">AAACHHicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiGxcuKtgHtEPJpJk2NJMMSUYoQz/Dbf0Zd+JW8F9cmJnOwrYeCBzOuZd7coKYM21c99spbWxube+Udyt7+weHR9Xjk7aWiSK0RSSXqhtgTTkTtGWY4bQbK4qjgNNOMLnP/M4LVZpJ8WymMfUjPBIsZAQbK/X6ETZjTVT6OBtUa27dzYHWiVeQGhRoDqo//aEkSUSFIRxr3fPc2PgpVoYRTmeVfqJpjMkEj2jPUoEjqv00jzxDF1YZolAq+4RBufp3I8WR1tMosJN5xFUvE//1MkXpUC/dT2kSKjxZyWTCWz9lIk4MFWQRKUw4MhJlTaEhU5QYPrUEE8XsrxAZY4WJsX1WbF3eajnrpH1V99y693Rda9wVxZXhDM7hEjy4gQY8QBNaQEDCK8zhzZk7786H87kYLTnFzikswfn6BfHPo0o=</latexit>

Page 90: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

�27

L := hL, Ii

P Lq L

R : hP, qi �! hY|N|U, �,⇡(s)|↵(s)iC : ⇡(s)|↵(s) �! hY|N|U, �i

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Page 91: Pure General Logic Programming PGLP · Entscheidungsproblem 1666 2019 Leibniz “Universal Computational Logic” 1854 2020 Organon Intro to Logic @ RPI 350 BC 300 BC Euclid T h e

�28

L := hL, Ii

P Lq L

R : hP, qi �! hY|N|U, �,⇡(s)|↵(s)iC : ⇡(s)|↵(s) �! hY|N|U, �i

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query

program

reasoner

checker

degree of “confidence”

proof(s)

argument(s)

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�29

finis