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 {\L}ukasiewicz logic, albeit using relational semantics. This paper shows that a simpler belief function logic can be devised by adding {\L}ukasiewicz logic on top of MEL. It allows for a more natural semantics in terms of Shafer basic probability assignments.

翻译：非可加不确定性理论，典型的有可能性理论、信度函数和精确概率，它们与模态逻辑共享一个共同特征：可能性测度与必然性测度之间、信度函数与似然函数之间以及上概率与下概率之间的对偶性质，将可能性模态与必然性模态之间的对偶推广到了分级环境中。已有研究表明，可能性理论的全有或全无版本可以精确地被一种最小认知逻辑（MEL）所刻画，该逻辑使用了KD模态逻辑的一个非常小的片段，而无需借助关系语义。此外，信度函数的情况已被独立研究，通过使用Łukasiewicz逻辑将模态逻辑S5扩展到分级模态，得到了一种信度函数逻辑，尽管它仍使用了关系语义。本文表明，通过在MEL之上添加Łukasiewicz逻辑，可以设计出一种更简单的信度函数逻辑。该逻辑在Shafer基本概率赋值的意义上允许更自然的语义。