Synthese 190 (S1) (2013)

Authors
Yanjing Wang
Peking University
Abstract
In the literature, different axiomatizations of Public Announcement Logic (PAL) have been proposed. Most of these axiomatizations share a “core set” of the so-called “reduction axioms”. In this paper, by designing non-standard Kripke semantics for the language of PAL, we show that the proof system based on this core set of axioms does not completely axiomatize PAL without additional axioms and rules. In fact, many of the intuitive axioms and rules we took for granted could not be derived from the core set. Moreover, we also propose and advocate an alternative yet meaningful axiomatization of PAL without the reduction axioms. The completeness is proved directly by a detour method using the canonical model where announcements are treated as merely labels for modalities as in normal modal logics. This new axiomatization and its completeness proof may sharpen our understanding of PAL and can be adapted to other dynamic epistemic logics
Keywords Public announcement logic  Reduction axioms  Composition axiom  Dynamic epistemic logic  Completeness  Epistemic temporal logic
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DOI 10.1007/s11229-012-0233-5
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References found in this work BETA

Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2002 - Cambridge University Press.
Logics of Public Communications.Jan Plaza - 2007 - Synthese 158 (2):165 - 179.
Dynamic Logic for Belief Revision.Johan van Benthem - 2007 - Journal of Applied Non-Classical Logics 17 (2):129-155.

View all 16 references / Add more references

Citations of this work BETA

Contingency and Knowing Whether.Jie Fan, Yanjing Wang & Hans van Ditmarsch - 2015 - Review of Symbolic Logic 8 (1):75-107.
A Logic for Diffusion in Social Networks.Zoé Christoff & Jens Ulrik Hansen - 2015 - Journal of Applied Logic 13 (1):48-77.
Are There No Things That Are Scientific Theories?S. French & P. Vickers - 2011 - British Journal for the Philosophy of Science 62 (4):771-804.
Formal Learning Theory.Oliver Schulte - 2008 - Stanford Encyclopedia of Philosophy.

View all 19 citations / Add more citations

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