A logic for reasoning about the probability of fuzzy events
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- 作者：Tommaso Flaminio ; Lluí ; s Godo
- 关键词：Ł ; ukasiewicz logic ; State and conditional states on MV-algebras ; Fuzzy events ; Standard completeness
- 刊名：Fuzzy Sets and Systems
- 出版年：2007
- 出版时间：16 March 2007
- 年：2007
- 卷：158
- 期：6
- 页码：625-638
- 全文大小：237 K
文摘
In this paper we present the logic itle=""Click to view the MathML source"">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 itle=""Click to view the MathML source"">FP(Łn,Ł) w.r.t. both weak and strong models. We also present two extensions of itle=""Click to view the MathML source"">FP(Łn,Ł): the first one is the logic itle=""Click to view the MathML source"">FP(Łn,RPL), obtained by expanding the itle=""Click to view the MathML source"">FP(Łn,Ł)-language with truth-constants for the rationals in itle=""Click to view the MathML source"">[0,1], while the second extension is the logic allowing to reason about conditional states.