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An Epistemic Separation Logic with Action Models
Journal of Logic, Language and Information ( IF 0.8 ) Pub Date : 2022-08-10 , DOI: 10.1007/s10849-022-09372-z
Hans van Ditmarsch , Didier Galmiche , Marta Gawek

In this paper we present an extension of (bunched) separation logic, Boolean BI, with epistemic and dynamic epistemic modalities. This logic, called action model separation logic (\(\mathrm {AMSL}\)), can be seen as a generalization of public announcement separation logic in which we replace public announcements with action models. Then we not only model public information change (public announcements) but also non-public forms of information change, such as private announcements. In this context the semantics for the connectives \(*\) and \(\mathrel {-*}\) from separation logic are epistemic versions of their usual semantics. This is because formulas are interpreted in states, not in resources, and agents may be uncertain between different states representing the same resource. We present the logic \(\mathrm {AMSL}\) and its semantics, with a detailed case study that highlights its interest for modeling. We also prove the elimination of the dynamics modalities and discuss some alternative epistemic semantics for the separation connectives.



中文翻译:

具有行动模型的认知分离逻辑

在本文中,我们提出了(束)分离逻辑的扩展,布尔 BI,具有认知和动态认知模态。这种逻辑称为动作模型分离逻辑(\(\mathrm {AMSL}\)),可以看作是公告分离逻辑的概括,其中我们用动作模型替换公告。然后我们不仅对公共信息变更(公开公告)进行建模,而且对非公开形式的信息变更进行建模,例如私下公告。在这种情况下,连接词\(*\)\(\mathrel {-*}\)的语义从分离逻辑是它们通常语义的认知版本。这是因为公式是在状态中解释的,而不是在资源中,并且代理可能在代表相同资源的不同状态之间不确定。我们介绍了逻辑\(\mathrm {AMSL}\)及其语义,并通过详细的案例研究突出了其对建模的兴趣。我们还证明了动态模态的消除,并讨论了分离连接词的一些替代认知语义。

更新日期:2022-08-12
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