AGI 08 March 1-3, University of Memphis Hybrid Reasoning and the Future of Iconic Representations Catherine RECANATI LIPN UMR 7030 Université Paris 13

AGI 08March 1-3, University of Memphis

Hybrid Reasoning and the Future of Iconic Representations

Catherine RECANATI

LIPN UMR 7030 Université Paris 13

1. Icons or diagrammatic objects can be used as first class citizens (=normal syntactical objects) in safe inferential systems

2. Diagrammatic representations have a limited power of abstraction but are computationally very efficient

3. Diagrammatic and logico-linguistic representations having dual and complementary properties, their combining in HRS is very promising

Three points




Three points

Closure under constraints

“ Homer is on the left of Lisa ”


“ Homer is on the left of Lisa ” “ Lisa is on the left of Bart ”

The fact that Homer is on the left of Bart is directly accessible (explicit) on the diagrammatic representation

Barwise and Etchemendy (1990)Logic as a theory of valid inferences

independent of the modes

of representation

Shin (1991) : two graphical systems inspired by those of Venn and Peirce (for solving syllogisms)

Euler

“ All A is B ”

A

B

1768

Euler

“ All B is C ”

B

C

1768

Euler

… therefore “ All A is C ”

A

B

C

1768

Venn

“ All A is B ”

A B

1894

Peirce

“ All A is B ” and“ There is a B which is not an A ”

A B o x

1933

Peirce

“ All A is B ” or“ There is a B which is not an A ”

A B o x

1933

1991-94 Shin (Venn-Peirce)

A1A2 A3

D1 D2

A6

A4

A5

D3

Properties of diagrammatic systems

for Barwise and Etchemendy the main properties of diagrammatic systems are derived from the existence of

a syntactical homomorphismbetween icons (and icons types) used

and the properties of the objects

In paradigmatic cases, these systems exhibit the property of

Closure under constraintsrequiring that all logical consequences of

requiring that all logical consequences of the represented situation be explicit in the representation.


Easy treatment of conjunctions But difficulties with disjunctions

and abstract relations (negation, implication …)

Contradictions cannot be represented and each representation corresponds to a genuine situation





Three points


“ Homer is on the left of Lisa ” “ Lisa is on the left of Bart ”

The fact that Homer is on the left of Bart is directly accessible (explicit) on the diagrammatic representation

A linguistic representation

“ Homer is-on-the-left-of Lisa ” “ Lisa is-on-the-left-of Bart ”

needs a supplementary step and the use of a rule of transitivity to get that “Homer is-on-the-left-of Bart ”. Transitivity rule:if A is-on-the-left-of B, and if B is-on-the-left-of C, then A is-on-the-left-of C.

Linguistic reasoning

requires

(1) the representation of initial facts (2) an explicit representation of the

abstract properties of the objects(3) a computational mechanism

linking the two sources of information

Diagrammatic reasoning

(2) No explicit representation of the abstract properties of the objects

these properties are automatically taken into account by syntactic constraints on the representation of the objects

(3) No computational mechanism the representations have only to be inspected to

check whether the new fact is or not represented there

This makes these systems computationally very efficient

What is Closure under constraints ?

• Stenning and Oberlander (1995)(C) = Specificity

requires information of a certain kind to be specified in all interpretable representation

Classes of Representational SystemsMARS < LARS < UARS

diagrammatic systems are LARS

Minimum Abstraction Representational System

In a MARS a representation corresponds to a unique model of the world.

P1 P2 P3

Obj 1 0 1 1

Obj 2 1 1 0

[ B B Y Y R ]

Limited Abstraction Representational System

You can abstract on a minimal representation to quantify over the dimensions, by adding new symbols

P1 P2 P3

Obj 1 -- -- 1

Obj 2 1 1 0

[ B _ Y _ R ]

Specificity and limited abstraction

for Stenning and Oberlander

Specificity requires information of a certain kind to be specified in all interpretable representation

=

closure under constraints of B&E

What is Closure under constraints ?

• Perry and Macken (1996) only Berkeley’s notion of determined

character is required – the representation of an object as having a

particular property requires a specified value for this property. Ex: colored objects

(C) = Localization (or unique token property) + Iconicity + a constraint and systematic homomorphism

Iconicity and Richly Grounded Meaning

Iconic symbols have richly grounded meanings :

RIM – Readily Inferable Meaning

ERM – Easily Remembered Meaning

IMM – Internally Modifiable Meaning

Partially implicit

Situation

Explicit consequences

Algorithm in a particular

language

Evaluation

Mapping Syntax to Semantics




Three points

Z

X, y => z

O(x)G(y)annotated aspects

Hybrid Representation Systems

No need of inter-lingua

What makes these systems correctly tied together

is just that They denote the same objects

in the world.

New computational perspectivesthrough the

“diagonalization” of proofs

computations reputed to be bounded by a minimal cost may be turned out to be less costly in a hybrid system

P1 cost 1

P2

2

P3

7

P4

P1 cost 8

Q2 2

Q3 1

P4

2

HRS : new perspectives in AI and Cognitive Science

Reasoning Semantics Natural Language

Documents

AGI 08 March 1-3, University of Memphis Hybrid Reasoning and the Future of Iconic Representations Catherine RECANATI LIPN UMR 7030 Université Paris 13