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Optimal Regression for Reasoning about Knowledge and Actions

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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.


BibTeX - Entry

@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/opus/volltexte/2007/1207},
  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}
}

Keywords: Reasoning about action and change, reasoning about knowledge, situation calculus, frame problem, dynamic epistemic logic
Seminar: 07351 - Formal Models of Belief Change in Rational Agents
Issue date: 2007
Date of publication: 20.11.2007


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