Logics for belief functions on MV-algebras

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Logics for belief functions on MV-algebras

Belief Functions
Fuzzy Events
Lukasiewicz Logic
Modal Logics

Publication Type:

Journal Article

Authors:

Tommaso Flaminio; Lluís Godo; Enrico Marchioni

Source:

International Journal of Approximate Reasoning (0)

Keywords:

Belief Functions; Lukasiewicz Logic; Modal Logics; Fuzzy Events

Abstract:

In this paper we present a generalization of belief functions over fuzzy events. In particular we focus on belief functions defined in the algebraic framework of finite MV-algebras of fuzzy sets. We introduce a fuzzy modal logic to formalize reasoning with belief functions on many-valued events. We prove, among other results, that several different notions of belief functions can be characterized in a quite uniform way, just by slightly modifying the complete axiomatization of one of the modal logics involved in the definition of our formalism.