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Combinatorial Semantics: Semantics for Frequent Validity
Author(s) -
Kyburg Henry E.
Publication year - 1997
Publication title -
computational intelligence
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.353
H-Index - 52
eISSN - 1467-8640
pISSN - 0824-7935
DOI - 10.1111/0824-7935.00039
Subject(s) - inference , probabilistic logic , semantics (computer science) , computer science , artificial intelligence , bayesian inference , operator (biology) , natural language processing , bayesian probability , mathematics , theoretical computer science , programming language , biochemistry , chemistry , repressor , transcription factor , gene
In ordinary first–order logic, a valid inference in a language L is one in which the conclusion is true in every model of the language in which the premises are true. To accommodate inductive/uncertain/probabilistic/nonmonotonic inference, we weaken that demand to the demand that the conclusion be true in a large proportion of the models in which the relevant premises are true. More generally, we say that an inference is [p,q] valid if its conclusion is true in a proportion lying between p and q of those models in which the relevant premises are true. If we include a statistical variable binding operator “%” in our language, there are many quite general (and useful) things we can say about uncertain validity. A surprising result is that some of these things may conflict with Bayesian conditionalization.