Dynamic Epistemic Logic and Knowledge Puzzles

We briefly give an overview of Dynamic Epistemic Logic (DEL), mainly in semantic terms. We focus on the simplest of epistemic actions in DEL, called public announcements. We also sketch the effect of more complex epistemic actions, and briefly show how als factual change can be modelled in the same framework. We then apply the logic of public announcements in DEL to the analysis of a knowledge puzzle, called `What Sum'.

[1]  Wiebe van der Hoek,et al.  Dynamic epistemic logic with assignment , 2005, AAMAS '05.

[2]  Danny Dolev,et al.  Cheating husbands and other stories: A case study of knowledge, action, and communication , 1986, Distributed Computing.

[3]  Vladimir Lifschitz,et al.  Formalizing Common Sense: Papers by John McCarthy , 1998 .

[4]  A. Baltag,et al.  Dynamic Belief Revision over Multi-Agent Plausibility Models , 2006 .

[5]  W. van der Hoek,et al.  Epistemic logic for AI and computer science , 1995, Cambridge tracts in theoretical computer science.

[6]  Jan van Eijck,et al.  Logics of communication and change , 2006, Inf. Comput..

[7]  J. Armstrong Knowledge and Belief , 1953 .

[8]  Peter Gärdenfors,et al.  On the logic of theory change: Partial meet contraction and revision functions , 1985, Journal of Symbolic Logic.

[9]  R. Aumann Agreeing to disagree. , 1976, Nature cell biology.

[10]  H. V. Ditmarsch The semantics of actions in knowledge games , 1999 .

[11]  Lawrence S. Moss,et al.  The Logic of Public Announcements and Common Knowledge and Private Suspicions , 1998, TARK.

[12]  Ji Ruan,et al.  Model Checking Logic Puzzles , 2007 .

[13]  J. McCarthy Formalization of two Puzzles Involving Knowledge , 1987 .

[14]  J. Gerbrandy Bisimulations on Planet Kripke , 1999 .

[15]  H. V. Ditmarsch Prolegomena to Dynamic Logic for Belief Revision , 2005 .

[16]  David Lewis Convention: A Philosophical Study , 1986 .

[17]  Wundt William 100 PRISONERS AND A LIGHT BULB , 2009 .

[18]  Jelle Gerbrandy,et al.  Dynamic epistemic logic , 1998 .

[19]  Jan van Eijck,et al.  Dynamic epistemic modelling , 2004 .

[20]  Ronald Fagin,et al.  Reasoning about knowledge , 1995 .

[21]  C. E. Alchourrón,et al.  On the logic of theory change: Partial meet contraction and revision functions , 1985 .

[22]  Barteld P. Kooi,et al.  Expressivity and completeness for public update logics via reduction axioms , 2007, J. Appl. Non Class. Logics.

[23]  Jan A. Plaza,et al.  Logics of public communications , 2007, Synthese.

[24]  Guillaume Aucher,et al.  A Combined System for Update Logic and Belief Revision , 2004, PRIMA.