A fuzzy Modal Logic for Belief Functions

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Lluís Godo
Petr Hájek
Francesc Esteva
Title: A fuzzy Modal Logic for Belief Functions
Journal: Fundamenta Informaticae
Volume 57
Pages: 127-146
Year: 2003


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 φ and a belief function on them; the belief of φ is taken to be the truth degree of the (fuzzy) proposition Bφ standing for “φ is believed”. For our complete axiomatizacion (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 ŁΠ1/2 which puts Lukasiewicz and Product fuzzy logics together.