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Resolution principles in possibilistic logic. (English) Zbl 0697.68083
Summary: An extension of the resolution principle was recently proposed by Dubois and Prade for logical clauses weighted by certainty degrees and was used in theorem proving under uncertainty. These certainty degrees were lower bounds on necessity measures. In the case considered here, the available information may also be an upper bound on a necessity measure, or, if one prefers, a lower bound on the dual possibility measure. It leads to a second resolution principle for clauses weighted in terms of possibility or necessity degrees. The formal analogy between these two resolution principles and the ones existing in modal logic is stressed. Finally, the case where the uncertain clauses include fuzzy predicates, to which the excluded-middle law no longer applies, is studied, and a suitable adaptation of the extended resolution principles is proposed.

MSC:
68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
03B48 Probability and inductive logic
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