| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 391129 | Fuzzy Sets and Systems | 2007 | 14 Pages |
In this paper we present the logic FP(Łn,Ł) 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 Hájek [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(Łn,Ł) w.r.t. both weak and strong models. We also present two extensions of FP(Łn,Ł): the first one is the logic FP(Łn,RPL), obtained by expanding the FP(Łn,Ł)-language with truth-constants for the rationals in [0,1], while the second extension is the logic allowing to reason about conditional states.
