Logics for Epistemic Actions: Completeness, Decidability, Expressivity

IF 0.4 Q4 LOGIC Journal of Applied Logics Pub Date : 2023-06-12 DOI:10.3390/logics1020006
Alexandru Baltag, Lawrence S. Moss, Sławomir Solecki
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Abstract

We build and study dynamic versions of epistemic logic. We study languages parameterized by an action signature that allows one to express epistemic actions such as (truthful) public announcements, completely private announcements to groups of agents, and more. The language L(Σ) is modeled on dynamic logic. Its sentence-building operations include modalities for the execution of programs, and for knowledge and common knowledge. Its program-building operations include action execution, composition, repetition, and choice. We consider two fragments of L(Σ). In L1(Σ), we drop action repetition; in L0(Σ), we also drop common knowledge. We present the syntax and semantics of these languages and sound proof systems for the validities in them. We prove the strong completeness of a logical system for L0(Σ) and the weak completeness of one for L1(Σ). We show the finite model property and, hence, decidability of L1(Σ). We translate L1(Σ) into PDL, obtaining a second proof of decidability. We prove results on expressive power, comparing L1(Σ) with modal logic together with transitive closure operators. We prove that a logical language with operators for private announcements is more expressive than one for public announcements.
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认知行为的逻辑:完备性、可决性、可表达性
我们建立和研究动态版本的认知逻辑。我们研究由动作签名参数化的语言,该签名允许人们表达认知行为,例如(真实的)公开公告,向代理组发布完全私有的公告等等。语言L(Σ)是基于动态逻辑建模的。它的造句操作包括执行程序的方式,以及知识和常识的方式。它的程序构建操作包括动作执行、组合、重复和选择。我们考虑L的两个片段(Σ)。在L1(Σ)中,我们放弃动作重复;在L0(Σ)中,我们也省略了常识。我们提出了这些语言的语法和语义,以及它们有效性的可靠系统。证明了一个逻辑系统对于L0(Σ)的强完备性和一个逻辑系统对于L1(Σ)的弱完备性。我们展示了有限模型性质,因此,L1的可判决性(Σ)。我们将L1(Σ)翻译成PDL,得到了第二个可决性证明。我们将L1(Σ)与模态逻辑以及传递闭包算子进行比较,证明了结果的表达能力。我们证明了带有私有公告运算符的逻辑语言比带有公共公告运算符的逻辑语言更具表现力。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Applied Logics
Journal of Applied Logics Mathematics-Logic
CiteScore
1.20
自引率
0.00%
发文量
0
期刊最新文献
Graph Algebras and Derived Graph Operations Carnap’s Problem for Intuitionistic Propositional Logic Bilateral Connexive Logic Why Logics? Logics for Epistemic Actions: Completeness, Decidability, Expressivity
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