论文标题
通过Belnap的信念功能推理 - Dunn逻辑
Reasoning with belief functions over Belnap--Dunn logic
论文作者
论文摘要
我们设计了Belnap- dunn逻辑的扩展，具有信念和合理性函数，允许具有不一致且不完整的概率信息的非平凡推理。我们还以两种方式使用非标准的概率和信念功能正式推理。首先，使用线性不平等的演算，类似于〜\ cite {faginhalpernmegiddo1990}中呈现的分节。其次，作为两层模态逻辑，其中证据（外层）的推理利用了lukasiewicz逻辑的paracensistent膨胀。第二种方法的灵感来自〜\ cite {baldicintulanoguera2020}。我们证明了这两种微积分的完整性，并通过在两个方向上建立忠实的翻译来展示它们的等价性。
We design an expansion of Belnap--Dunn logic with belief and plausibility functions that allow non-trivial reasoning with inconsistent and incomplete probabilistic information. We also formalise reasoning with non-standard probabilities and belief functions in two ways. First, using a calculus of linear inequalities, akin to the one presented in~\cite{FaginHalpernMegiddo1990}. Second, as a two-layered modal logic wherein reasoning with evidence (the outer layer) utilises paraconsistent expansions of Łukasiewicz logic. The second approach is inspired by~\cite{BaldiCintulaNoguera2020}. We prove completeness for both kinds of calculi and show their equivalence by establishing faithful translations in both directions.
