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A Fuzzy Modal Logic for Belief Functions

Godo L., Hájek P., Esteva F.

Fundamenta Informaticae

2003

Vol. 57, nr 2-4

127--146

In this paper we introduce a new logical approach to reason explicitly about Dempster-Shafer belief functions. We adopt the following view: one just starts with Boolean formulas j and a belief function on them; the belief of j is taken to be the truth degree of the (fuzzy) proposition Bj standing for ``j is believed''. For our complete axiomatization (Hylbert-style) we use one of the possible definitions of belief, namely as probability of (modal) necessity. This enables us to define a logical system combining the modal logic S5 with an already proposed fuzzy logic approach to reason about probabilities. In particular, our fuzzy logic is the logic P[ 1/2] which puts Lukasiewicz and Product fuzzy logics together.