Logics for Epistemic Actions: Completeness, Decidability, Expressivity-Reference-Cited by-同舟云学术

Logics for Epistemic Actions: Completeness, Decidability, Expressivity

Published:2023-06-12 Issue:2 Volume:1 Page:97-147
ISSN:2813-0405
Container-title:Logics
language:en
Short-container-title:Logics

Author:

Baltag Alexandru¹,Moss Lawrence S.²^ORCID,Solecki Sławomir³

Affiliation:

1. Institute for Logic, Language and Computation (ILLC), University of Amsterdam, 1090 GE Amsterdam, The Netherlands

2. Mathematics Department, Indiana University, Bloomington, IN 47405-7106, USA

3. Mathematics Department, Cornell University, Ithaca, NY 14853, USA

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.

Funder

Simons Foundation

Publisher

MDPI AG

Link

https://www.mdpi.com/2813-0405/1/2/6/pdf

Reference21 articles.

1. Plaza, J. (1989, January 12–14). Logics of public communications. Proceedings of the 4th International Symposium on Methodologies for Intelligent Systems, Charlotte, NC, USA.

2. Moss, L.S. (1999). Logic, Language, and Information, CSLI Publications, Stanford University.

3. Gerbrandy, J. (1999). Bisimulations on Planet Kripke. [Ph.D. Thesis, University of Amsterdam].

4. Reasoning about information change;Gerbrandy;J. Logic Lang. Inf.,1997

5. Baltag, A., Moss, L.S., and Solecki, S. (1998, January 22–24). The logic of common knowledge, public announcements, and private suspicions. Proceedings of the TARK-VII (Theoretical Aspects of the Rationality and Knowledge) Conference, Evanston, IL, USA.