Optimal regression for reasoning about knowledge and actions

Authors:
Hans Van Ditmarsch;Andreas Herzig;Tiago De Lima
Affiliations:
Department of Computer Science, University of Otago, Dunedin, New Zealand;Université Paul Sabatier, IRIT-Équipe LILaC, Toulouse Cedex, France;Université Paul Sabatier, IRIT-Équipe LILaC, Toulouse Cedex, France
Venue:
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
Year:
2007

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Abstract

We show how in the propositional case both Reiter's and Scherl & Levesque's solutions to the frame problem can be modelled in dynamic epistemic logic (DEL), and provide an optimal regression algorithm for the latter. Our method is as follows: we extend Reiter's framework by integrating observation actions and modal operators of knowledge, and encode the resulting formalism in DEL with announcement and assignment operators. By extending Lutz' recent satisfiability-preserving reduction to our logic, we establish optimal decision procedures for both Reiter's and Scherl & Levesque's approaches: satisfiability is NP-complete for one agent, PSPACE-complete for multiple agents and EXPTIME-complete when common knowledge is involved.