A fuzzy Modal Logic for Belief Functions
From Mathfuzzlog
Authors: |
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Title: | A fuzzy Modal Logic for Belief Functions | |||
Journal: | Fundamenta Informaticae | |||
Volume | 57 | |||
Number | ||||
Pages: | 127-146 | |||
Year: | 2003 |
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 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.