Baltag, Moss, and Solecki proposed an expansion of classical modal logic, called logic of epistemic actions and knowledge (EAK), in which one can reason about knowledge and change of knowledge. Kurz and Palmigiano showed how duality theory provides a flexible framework for modeling such epistemic changes, allowing one to develop dynamic epistemic logics on a weaker propositional basis than classical logic (for example an intuitionistic basis). In this paper we show how the techniques of Kurz and Palmigiano can be further extended to define and axiomatize a bilattice logic of epistemic actions and knowledge (BEAK). Our propositional basis is a modal expansion of the well-known four-valued logic of Belnap and Dunn, which is a system designed for handling inconsistent as well as potentially conflicting information. These features, we believe, make our framework particularly promising from a computer science perspective.

Baltag，Moss和Solecki提出了经典模态逻辑的扩展，称为认知行为和知识逻辑（EAK），在其中人们可以推理知识和知识变化。Kurz和Palmigiano展示了对偶理论如何为建模这种认知变化提供灵活的框架，从而使人们能够在比经典逻辑（例如直觉主义基础）更弱的命题基础上发展动态的认知逻辑。在本文中，我们展示了如何进一步扩展Kurz和Palmigiano的技术，以定义和公理认知行动和知识的双唇逻辑（BEAK）。我们的命题基础是Belnap和Dunn的众所周知的四值逻辑的模态扩展，该系统是为处理不一致和潜在冲突的信息而设计的系统。我们相信，从计算机科学的角度来看，这些功能使我们的框架特别有希望。