Changing Modalities

The dynamic modal logic DML is presented, featuring actions that change the interpretation of a propositional variable ora modality. The semantics is defined both in terms of modal structures and of labelled transition systems (Kripke models). The extension µDML with recursively defined actions aims to unify and extend dynamic epistemic logics proposed by Plaza, Gerbrandy, Baltag, Van Ditmarsch and others. The main technical result is the completeness and decidability of µDML.

[1]  Ronald Fagin,et al.  A model-theoretic analysis of knowledge , 1991, JACM.

[2]  Lawrence S. Moss,et al.  The Undecidability of Iterated Modal Relativization , 2005, Stud Logica.

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

[4]  Kit Fine,et al.  Normal forms in modal logic , 1975, Notre Dame J. Formal Log..

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

[6]  Alexandru Baltag,et al.  A Logic for Suspicious Players: Epistemic Actions and Belief-Updates in Games , 2000 .

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

[8]  Ronald Fagin,et al.  An Internal Semantics for Modal Logic: Preliminary Report , 1985, STOC 1985.

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

[10]  Johan van Benthem,et al.  Exploring logical dynamics , 1996, Studies in logic, language and information.

[11]  Vaughan R. Pratt,et al.  SEMANTICAL CONSIDERATIONS ON FLOYD-HOARE LOGIC , 1976, FOCS 1976.

[12]  Ronald Fagin,et al.  A quantitative analysis of modal logic , 1994, Journal of Symbolic Logic.

[13]  Jelle Gerbrandy,et al.  Reasoning about Information Change , 1997, J. Log. Lang. Inf..