AGI 08 March 1-3, University of Memphis Hybrid Reasoning and the Future of Iconic Representations...
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Transcript of AGI 08 March 1-3, University of Memphis Hybrid Reasoning and the Future of Iconic Representations...
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
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
Closure under constraints
“ 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)
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.
Properties of diagrammatic systems
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
Properties of diagrammatic systems
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
Closure under constraints
“ 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
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
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