一个极小直觉主义公开宣告逻辑
A minimal intuitionistic public announcement logic
Philippe Balbiani, Hans van Ditmarsch, Cigdem Gencer, Clara Lerouvillois
AI 速读 基于摘要
作者提出不要求传统合流条件的直觉主义公开宣告逻辑 Lmin 与 Lequ，并报告其相对于相应双关系框架类的可靠性与完全性。
cs.LO
查看原文摘要
We introduce intuitionistic public announcement logics Lmin and Lequ determined by classes of birelational frames where the intuitionistic preorder and the modal accessibility relation do not need to satisfy the confluence conditions traditionally considered within the framework of IPAL. Our logics can be seen as generalisations of IPAL seeing that their language is based on a binary epistemic modality of "relativised knowledge" that allows us to define valid reduction axioms. Our main results are the soundness and completeness of Lmin with respect to the class of all birelational frames and the soundness and completeness of Lequ with respect to the class of all birelational frames where the modal accessibility relation is an equivalence relation.