The paper introduces a basic logic of knowledge and abduction by extending Levesque logic of only-knowing with an abduction modal operator defined via the combination of basic epistemic concepts. The upshot is an alternative approach to abduction that employs a modal vocabulary and explores the relation between abductive reasoning and epistemic states of only knowing. Furthermore, by incorporating a preferential relation into modal frames, we provide a non-monotonic extension of our basic framework capable of expressing different selection methods for abductive explanations. Core metatheoretic properties of non-monotonic consequence relations are explored within this setting and shown to provide a well-behaved foundation for abductive reasoning.

翻译：本文通过扩展Levesque的仅知逻辑，引入一个由基本认知概念组合定义的溯因模态算子，从而提出一种关于知识与溯因的基础逻辑。其核心成果是提供了一种采用模态词汇的溯因研究新路径，并深入探讨了溯因推理与仅知认知状态之间的关联。进一步地，通过在模态框架中引入优先关系，我们构建了基础框架的非单调扩展，该扩展能够表达针对溯因解释的不同选择方法。在此框架下，本文探究了非单调后承关系的核心元理论性质，并证明其为溯因推理提供了具有良好性质的逻辑基础。