Combinatorial Semantics: Semantics for Frequent Validity
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 t...
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Veröffentlicht in: | Computational intelligence 1997-05, Vol.13 (2), p.215-257 |
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Sprache: | eng |
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Zusammenfassung: | 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. |
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ISSN: | 0824-7935 1467-8640 |
DOI: | 10.1111/0824-7935.00039 |