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Optimal Regression for Reasoning about Knowledge and Actions

Authors: Hans van Ditmarsch, Andreas Herzig, and Tiago de Lima

Published in: Dagstuhl Seminar Proceedings, Volume 7351, Formal Models of Belief Change in Rational Agents (2007)

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.

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Hans van Ditmarsch, Andreas Herzig, and Tiago de Lima. Optimal Regression for Reasoning about Knowledge and Actions. In Formal Models of Belief Change in Rational Agents. Dagstuhl Seminar Proceedings, Volume 7351, pp. 1-22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{vanditmarsch_et_al:DagSemProc.07351.15,
  author =	{van Ditmarsch, Hans and Herzig, Andreas and de Lima, Tiago},
  title =	{{Optimal Regression for Reasoning about Knowledge and Actions}},
  booktitle =	{Formal Models of Belief Change in Rational Agents},
  pages =	{1--22},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7351},
  editor =	{Giacomo Bonanno and James Delgrande and J\'{e}r\^{o}me Lang and Hans Rott},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07351.15},
  URN =		{urn:nbn:de:0030-drops-12077},
  doi =		{10.4230/DagSemProc.07351.15},
  annote =	{Keywords: Reasoning about action and change, reasoning about knowledge, situation calculus, frame problem, dynamic epistemic logic}
}

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Optimal Regression for Reasoning about Knowledge and Actions

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