A logic for reasoning about the probability of fuzzy events
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 Pi 1/2) allowing to reason about conditional states. (C) 2006 Elsevier B.V. All rights reserved.
fuzzy events lukasiewicz logic state and conditional states on mv-algebras standard completeness