A Fuzzy Modal Logic for Belief Functions

Issue title: The 1st International Workshop on Knowledge Representation and Approximate Reasoning (KR&AR)

Article type: Research Article

Authors: Godo, Lluís | Hájek, Petr | Esteva, Francesc

Affiliations: Institut d'Investigació en Intelligencia Artificial, Spanish Research Council, CSIC, 08193 Bellaterra, Catalunya, Spain | Institute of Computer Science, Academy of Sciences of the Czech Republic, AV ČR, 182 07 Prague, Czech Republic

Abstract: 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 B φ standing for φ 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 ŁΠ½ which puts Lukasiewicz and Product fuzzy logics together.

Keywords: fuzzy logic, Dempster–Shafer belief functions, probability logic, probability logic, completeness

Journal: Fundamenta Informaticae, vol. 57, no. 2-4, pp. 127-146, 2003