A concurrent dynamic logic of knowledge, belief and certainty for multi-agent systems

This paper extends the logic of Knowledge, Belief and Certainty from one agent to multi-agent systems, and gives a good combination between logic of knowledge, belief, certainty in multi-agent systems and actions that have concurrent and dynamic properties. Based on it, we present a concurrent dynamic logic of knowledge, belief and certainty for MAS, which is called CDKBC logic. Furthermore, a CDKBC model is given for interpreting this logic. We construct a CDKBC proof system for the logic and show the proof system is sound and complete, and prove the validity problem for the system is EXPTIME-complete.

[1]  Richard E. Ladner,et al.  Propositional Dynamic Logic of Regular Programs , 1979, J. Comput. Syst. Sci..

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

[3]  J. C. M. Baeten,et al.  Process Algebra: Bibliography , 1990 .

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

[5]  Jerzy Tiuryn,et al.  Dynamic logic , 2001, SIGA.

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

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

[8]  David Peleg,et al.  Concurrent dynamic logic , 1987, JACM.

[9]  Johan van Benthem.  Logics for information update , 2001 .

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

[11]  David Peleg,et al.  Communication in Concurrent Dynamic Logic , 1987, J. Comput. Syst. Sci..

[12]  Wolfgang Lenzen,et al.  Recent work in epistemic logic , 1978 .

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

[14]  Yde Venema,et al.  Dynamic Logic by David Harel, Dexter Kozen and Jerzy Tiuryn. The MIT Press, Cambridge, Massachusetts. Hardback: ISBN 0–262–08289–6, $50, xv + 459 pages , 2002, Theory and Practice of Logic Programming.

[15]  Michael Wooldridge,et al.  Completeness and Complexity of Multi-modal CTL , 2009, M4M.

[16]  Guido Governatori,et al.  A computationally grounded logic of knowledge, belief and certainty , 2005, AAMAS '05.

[17]  R. Aumann,et al.  Epistemic Conditions for Nash Equilibrium , 1995 .

[18]  Hans van Ditmarsch,et al.  Descriptions of Game Actions , 2002, J. Log. Lang. Inf..

[19]  Hector J. Levesque,et al.  Foundations for the Situation Calculus , 1998, Electron. Trans. Artif. Intell..

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

[21]  Wiebe van der Hoek,et al.  Concurrent dynamic epistemic logic for MAS , 2003, AAMAS '03.