A fuzzy modal logic for belief functions

Authors:
Lluís Godo;Petr Hájek;Francesc Esteva
Affiliations:
AI Research Institute, IIIA-CSIC, Bellaterra, Spain;Institute of Computer Science, Academy of Sciences, Prague, Czech Republic;AI Research Institute, IIIA-CSIC, Bellaterra, Spain
Venue:
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Year:
2001

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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 Bφ 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 ŁΠ1/2 which puts Lukasiewicz and Product logics together.