Possibilistic Logic, Preferential Models, Non-monotonicity and Related Issues

Abstract

The links between Shoham's preference logic and possibilistic logic, a numerical logic of uncertainty based on Zadeh's possibility measures, are investigated. Starting from a fuzzy set of preferential interpretations of a propositional theory, we prove that the notion of preferential entailment is closely related to a previously introduced notion of conditional possibility. Conditional possibility is then shown to possess all properties (originally stated by Gabbay) of a well-behaved non-mo~~t?n~c consequence relation. We obtain the possibihstic counterpart of Adams' E-sem.antics of condi~i?n~l probabilities which is the basis of the probabilistic model of non-monotonic logic proposed by Geffner and Pearl. Lastly we prove that our notion of possibilistic entailment is the one at work ~n possibilistic logic, a logic that ha~dle~ uncertam propositional formulas, where uncertainty IS model~ed by degrees of necessity, and where partial inconsistency is allowed. Considering the formerly established close links between Gru-denfors'epistemic entrenchment and necessity·measures, what this paper proposes is a new way of relating belie~ revisi~n. a!'d non-monotonic inference, namely via possibility theory.