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Introduction to formal semantics 1 / 25Enrico Leonhardt
Introduction toformal semantics
-Enrico Leonhardt
Introduction to formal semantics 2 / 25Enrico Leonhardt
structure• Motivation - Philosophy
– paradox– antinomy– division in object und Meta language
• Semiotics– syntax– semantics– Pragmatics
• Formal semantics in Computer Science
| Motivation | Semiotics | Formal semantics in CS |
Introduction to formal semantics 3 / 25Enrico Leonhardt
Motivation - Philosophy
• Problem of truth– is sentence or statement true?
– (intuitive) TARSKI scheme: “X is true if and only if p”
– definition of the ‘true’ predicate in S
“I”, “we”, “now”… different meaning in different situations
investigate only statements
name of p statement
colloquial language
| Motivation | Semiotics | Formal semantics in CS |
Introduction to formal semantics 4 / 25Enrico Leonhardt
paradox
• Paradox definition
• Paradox act commandment
No logical problems
A suicide murderer kills all that do not kill themselves.
Give somebody a shed of paper with“please turn around” on both sites.
| Motivation | Semiotics | Formal semantics in CS |
Introduction to formal semantics 5 / 25Enrico Leonhardt
antinomy
• Logical paradox or antinomy
if there is a prove that such person exists
• Antinomy by TARSKI (“X is true if and only if p” )
A suicide murderer kills all that do not kill themselves.
This statement is not true.
| Motivation | Semiotics | Formal semantics in CS |
Introduction to formal semantics 6 / 25Enrico Leonhardt
antinomy
• Conditions to create an antinomy
1. Language is semantically closed– statements in the language can contain
its own ‘true’ predicate
2. Basic laws of logic
| Motivation | Semiotics | Formal semantics in CS |
Introduction to formal semantics 7 / 25Enrico Leonhardt
division in object und meta language
• To solve antinomies divide natural language
Object language: to describe anything (‘true’, ‘false’,…)
Meta language: Object language + ‘true’, ‘false’…
Order one
Order two…
The sun is shining today.The statement above is true.The second statement here is true.
Order one
Order two
Order three
| Motivation | Semiotics | Formal semantics in CS |
Introduction to formal semantics 8 / 25Enrico Leonhardt
division in object und meta language
• To solve antinomies divide natural language
The statement on slide 8 is not true.The statement of order one on slide 8 is not true.
There is a statement of order one on slide 8 that is false.
| Motivation | Semiotics | Formal semantics in CS |
The statement of order one on slide 8 is not true.
Introduction to formal semantics 9 / 25Enrico Leonhardt
structure• Motivation - Philosophy
– paradox– antinomy– division in object und meta language
• Semiotics– syntax– semantics– pragmatics
• Formal semantics in Computer Science
“X is true if and only if p”
| Motivation | Semiotics | Formal semantics in CS |
This statement is not true.The color is late.
Introduction to formal semantics 10 / 25Enrico Leonhardt
Semiotics
• The study of signs and symbols• Study of how meaning is constructed and understood• Can be empirical or ‘pure’
– syntax– semantics– pragmatics
historical languages artificial languages
| Motivation | Semiotics | Formal semantics in CS |
Introduction to formal semantics 11 / 25Enrico Leonhardt
syntax
• Study of the rules, or “patterned relations”
historical languages
The color is late.
subject verb adjective
| Motivation | Semiotics | Formal semantics in CS |
Introduction to formal semantics 12 / 25Enrico Leonhardt
semantics
• Study of the aspects of meaning
• the relation that a sign has to other signs sense
• the relation that a sign has to objects andobjective situations, actual or possible reference
historical languages
| Motivation | Semiotics | Formal semantics in CS |
The color is late.
Introduction to formal semantics 13 / 25Enrico Leonhardt
semantics
• Semantic levels:– each word (lexical semantics)– relationship between words (structural semantics)– combination of sentences– texts of different persons (dialog)
• Connection between semantic levels:
historical languages
MEANING(the color is late)
= f(MEANING(the), MEANING(color), MEANING(is), MEANING(late))
Frege principle
| Motivation | Semiotics | Formal semantics in CS |
Introduction to formal semantics 14 / 25Enrico Leonhardt
pragmatics
• Considers the environment
• Sentence meaning speaker's meaning
• Interested in sentences
• Empirical factors:– Psychological activity by speaker– Historical identifiable language habit
historical languages
| Motivation | Semiotics | Formal semantics in CS |
Introduction to formal semantics 15 / 25Enrico Leonhardt
Semiotics
• The study of signs and symbols• Study of how meaning is constructed and understood• Can be empirical or ‘pure’
– syntax– semantics– pragmatics
historical languages artificial languages
| Motivation | Semiotics | Formal semantics in CS |
– syntax– semantics– pragmatics
Introduction to formal semantics 16 / 25Enrico Leonhardt
syntax
• defines a formal grammar, or simply grammar
• sets of rules for how strings in a language can begenerated
• rules for how a string can be analyzed to determinewhether it is a member of the language
artificial languages
| Motivation | Semiotics | Formal semantics in CS |
Introduction to formal semantics 17 / 25Enrico Leonhardt
semantics
• defines a mathematical model
– describes the possible computations
– three major classes:• Denotational semantics• Operational semantics• Axiomatic semantics
artificial languages
| Motivation | Semiotics | Formal semantics in CS |
Introduction to formal semantics 18 / 25Enrico Leonhardt
pragmatics artificial languages
| Motivation | Semiotics | Formal semantics in CS |
• defines the behavior in environments
• Compiler• OS• Machine
Introduction to formal semantics 19 / 25Enrico Leonhardt
structure• Motivation - Philosophy
– paradox– antinomy– division in object und meta language
• Semiotics– syntax– semantics– pragmatics
• Formal semantics in Computer Science
“X is true if and only if p”
(empirical + ‘pure’)
| Motivation | Semiotics | Formal semantics in CS |
The color is late.
Introduction to formal semantics 20 / 25Enrico Leonhardt
Formal semantics in CS
• mathematical model of programming language by
Denotational semantics– each phrase in the language is translated into a denotation,
i.e. a phrase in some other language
| Motivation | Semiotics | Formal semantics in CS |
Introduction to formal semantics 21 / 25Enrico Leonhardt
Formal semantics in CS
• mathematical model of programming language by
Denotational semantics– each phrase in the language is translated into a denotation,
i.e. a phrase in some other language
Operational semantics– execution of the language is described directly
(rather than by translation)
| Motivation | Semiotics | Formal semantics in CS |
Introduction to formal semantics 22 / 25Enrico Leonhardt
Formal semantics in CS
• mathematical model of programming language by
Denotational semantics– each phrase in the language is translated into a denotation,
i.e. a phrase in some other language
Operational semantics– execution of the language is described directly
(rather than by translation)
Axiomatic semantics– rules of inferences to reason from meaning of input
to meaning of output
| Motivation | Semiotics | Formal semantics in CS |
Introduction to formal semantics 23 / 25Enrico Leonhardt
Formal semantics in CS
• mathematical model of programming language by
Static semantics– properties that cannot change during execution
Dynamic semantics– properties that may change
| Motivation | Semiotics | Formal semantics in CS |
Var a : integer;…If a THEN…ELSE…
Var a : boolean;…If a THEN…ELSE…
Introduction to formal semantics 24 / 25Enrico Leonhardt
Conclusion• Motivation - Philosophy
– paradox– antinomy– division in object und Meta language
• Semiotics– syntax
– semantics– Pragmatics
• Formal semantics in Computer Science
| Motivation | Semiotics | Formal semantics in CS |
“X is true if and only if p”
(empirical + ‘pure’)
The color is late.
Introduction to formal semantics 25 / 25Enrico Leonhardt
Conclusion| Motivation | Semiotics | Formal semantics in CS |
Questions?