An elementary belief function logic

Abstract

Non-additive uncertainty theories, typically possibility theory, belief functions and imprecise probabilities share a common feature with modal logic: the duality properties between possibility and necessity measures, belief and plausibility functions as well as between upper and lower probabilities extend the duality between possibility and necessity modalities to the graded environment. It has been shown that the all-or-nothing version of possibility theory can be exactly captured by a minimal epistemic logic (MEL) that uses a very small fragment of the KD modal logic, without resorting to relational semantics. Besides, the case of belief functions has been studied independently, and a belief function logic has been obtained by extending the modal logic S5 to graded modalities using Łukasiewicz logic, albeit using relational semantics. This paper shows that a simpler belief function logic can be devised by adding Łukasiewicz logic on top of MEL. It allows for a more natural semantics in terms of Shafer basic probability assignments.