TitleA logic for reasoning about the probability of fuzzy events
Publication TypeJournal Article
Year of Publication2007
AuthorsFlaminio T, Godo L
JournalFuzzy Sets and Systems
Volume158
Number6
Pagination625 – 638
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 Hájek in \cite{H98}. Two kinds of semantics have been introduced, namely the class of {\em weak} and {\em 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 $FCP(\L_n,\LΠ\half)$ allowing to reason about conditional states.