Tommaso Flaminio
Abstract
In this paper we present the logic FP(L"n,L) which allows to reason about the probability of fuzzy events formalized by means of the notion of state in a MV-algebra. This logic is defined starting from a basic idea exposed by Hajek [Metamathematics of Fuzzy Logic, Kluwer, Dordrecht, 1998]. Two kinds of semantics have been introduced, namely the class of weak and strong probabilistic models. The main result of this paper is a completeness theorem for the logic FP(L"n,L) w.r.t. both weak and strong models. We also present two extensions of FP(L"n,L): the first one is the logic FP(L"n,RPL), obtained by expanding the FP(L"n,L)-language with truth-constants for the rationals in [0,1], while the second extension is the logic FCP(L"n,L@P12) allowing to reason about conditional states.
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Index Terms
- A logic for reasoning about the probability of fuzzy events
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