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.
Abstract (translated)
非累加性不确定性理论，通常称为可能性理论，信念函数和不确定的概率与模态逻辑有共同的特征：可能性和必要性测量之间的双对称性性质、信念和可能性函数以及上界和下界概率之间的双对称性性质将可能性和必要性模态扩展到梯度环境中。已经证明，可能性理论的无备选方案版本可以完全被一个最小知识逻辑(MEL)所捕捉，该逻辑使用KD模态逻辑的一个非常小的片段，而无需使用关系语义。此外，信念函数的案例也已经独立地研究了，并通过使用Łukasiewicz逻辑将模态逻辑S5扩展为梯度模态，虽然使用关系语义。这篇论文表明，通过在MEL之上添加Łukasiewicz逻辑，可以设计出更简单的信念函数逻辑。这允许在Shafer基本概率 assignments 方面实现更加自然语义。
URL
https://arxiv.org/abs/2303.13168
