David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Journal of Philosophical Logic 27 (2):109-142 (1998)
In many logics dealing with information one needs to make statements not only about cognitive states, but also about transitions between them. In this paper we analyze a dynamic modal logic that has been designed with this purpose in mind. On top of an abstract information ordering on states it has instructions to move forward or backward along this ordering, to states where a certain assertion holds or fails, while it also allows combinations of such instructions by means of operations from relation algebra. In addition, the logic has devices for expressing whether in a given state a certain instruction can be carried out, and whether that state can be arrived at by carrying out a certain instruction.This paper deals mainly with technical aspects of our dynamic modal logic. It gives an exact description of the expressive power of this language; it also contains results on decidability for the language with arbitrary structures and for the special case with a restricted class of admissible structures. In addition, a complete axiomatization is given. The paper concludes with a remark about the modal algebras appropriate for our dynamic modal logic, and some questions for further work.
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References found in this work BETA
Carlos E. Alchourrón, Peter Gärdenfors & David Makinson (1985). On the Logic of Theory Change: Partial Meet Contraction and Revision Functions. Journal of Symbolic Logic 50 (2):510-530.
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Citations of this work BETA
Patrick Blackburn & Yde Venema (1995). Dynamic Squares. Journal of Philosophical Logic 24 (5):469 - 523.
Philippe Balbiani & Dimiter Vakarelov (2003). PDL with Intersection of Programs: A Complete Axiomatization. Journal of Applied Non-Classical Logics 13 (3-4):231-276.
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