DagSemProc.07351.15.pdf
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Optimal Regression for Reasoning about Knowledge and Actions
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Dagstuhl Seminar Proceedings, Volume 7351
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2007-11-20
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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)
https://doi.org/10.4230/DagSemProc.07351.15
https://doi.org/10.4230/DagSemProc.07351.15
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.
Keywords
- Reasoning about action and change
- reasoning about knowledge
- situation calculus
- frame problem
- dynamic epistemic logic
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