An Information-Based Theory of Conditionals
Wayne Wobcke
Source: Notre Dame J. Formal Logic Volume 41, Number 2
(2000), 95-141.
Abstract
We present an approach to combining three areas of
research which we claim are all based on information theory: knowledge
representation in Artificial Intelligence and Cognitive Science using
prototypes, plans, or schemata; formal semantics in natural language,
especially the semantics of the `if-then' conditional construct; and the logic
of subjunctive conditionals first developed using a possible worlds
semantics by Stalnaker and Lewis. The basic premise of the paper is that
both schema-based inference and the semantics of conditionals are based on
Dretske's notion of information flow and Barwise and Perry's notion of a
constraint in situation semantics. That is, the connection between
antecedent and consequent
of a conditional `if
were the case
then
would be the case' is an informational relation holding with respect
to a pragmatically determined utterance situation. The bridge between AI
and conditional logic is that a prototype or planning schema represents a
situation type, and the background assumptions underlying the application of
a schema in a situation correspond to channel conditions on the flow of
information. Adapting the work of Stalnaker and Lewis, the semantics of
conditionals is modeled by a refinement ordering on situations: a
conditional `if
then
' holds with respect to a situation if all the
minimal refinements of the situation that support
also support
. We
present new logics of situations, information flow, and subjunctive
conditionals based on three-valued partial logic that formalizes our
approach, and conclude with a discussion of the resulting theory of
conditionals, including the "paradoxes" of conditional implication, the
difference between truth conditions and assertability conditions for
subjunctive conditionals, and the relationship between subjunctive and
indicative conditionals.
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Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1038234607
Digital Object Identifier: doi:10.1305/ndjfl/1038234607
Mathematical Reviews number (MathSciNet): MR1932225
Zentralblatt MATH identifier: 1025.03014
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