ICLA 2015: Logic and Its Applications pp 218-231 | Cite as
Representing Imperfect Information of Procedures with Hyper Models
Abstract
When reasoning about knowledge of procedures under imperfect information, the explicit representation of epistemic possibilities blows up the S5-like models of standard epistemic logic. To overcome this drawback, in this paper, we propose a new logical framework based on compact models without epistemic accessibility relations for reasoning about knowledge of procedures. Inspired by the 3-valued abstraction method in model checking, we introduce hyper models which encode the imperfect procedural information. We give a highly non-trivial 2-valued semantics of epistemic dynamic logic on such models while validating all the usual S5 axioms. Our approach is suitable for applications where procedural information is ‘learned’ incrementally, as demonstrated by various examples.
Keywords
Model Check Regular Expression Imperfect Information Label Transition System Kripke ModelPreview
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References
- 1.Chen, T., van de Pol, J., Wang, Y.: PDL over accelerated labeled transition systems. In: Proceedings of TASE 2009, pp. 193–200. IEEE Computer Society Press, Los Alamitos (2008)Google Scholar
- 2.van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic (Synthese Library), 1st edn. Springer (2007)Google Scholar
- 3.Espada, M., van de Pol, J.: Accelerated modal abstractions of labelled transition systems. In: Johnson, M., Vene, V. (eds.) AMAST 2006. LNCS, vol. 4019, pp. 338–352. Springer, Heidelberg (2006)CrossRefGoogle Scholar
- 4.Fagin, R., Halpern, J., Moses, Y., Vardi, M.: Reasoning about knowledge. MIT Press (1995)Google Scholar
- 5.Grumberg, O.: 2-valued and 3-valued abstraction-refinement in model checking. In: Logics and Languages for Reliability and Security, pp. 105–128 (2010)Google Scholar
- 6.Grumberg, O., Lange, M., Leucker, M., Shoham, S.: When not losing is better than winning: Abstraction and refinement for the full mu-calculus. Information and Computation 205(8), 1130–1148 (2007)CrossRefMATHMathSciNetGoogle Scholar
- 7.Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. The MIT Press (2000)Google Scholar
- 8.Huth, M.: Abstraction and probabilities for hybrid logics. ENTCS 112, 61–76 (2005)Google Scholar
- 9.Kuhn, H.W.: Extensive games and the problem of information. In: Kuhn, H.W., Tucker, A.W. (eds.) Contributions to the Theory of Games, pp. 196–216. Princeton University Press (1953)Google Scholar
- 10.Moore, R.C.: A formal theory of knowledge and action. Tech. rep., DTIC Document (1984)Google Scholar
- 11.Parikh, R., Ramanujam, R.: Distributed processes and the logic of knowledge. In: Proceedings of Conference on Logic of Programs, pp. 256–268. Springer, London (1985)CrossRefGoogle Scholar
- 12.Pratt, V.R.: Semantical considerations on floyd-hoare logic. Tech. rep., Cambridge, MA, USA (1976)Google Scholar
- 13.Shoham, S., Grumberg, O.: 3-valued abstraction: More precision at less cost. Information and Computation 206(11), 1313–1333 (2008)CrossRefMATHMathSciNetGoogle Scholar
- 14.Wang, Y., Cao, Q.: On axiomatizations of public announcement logic. Synthese 190, 103–134 (2013)CrossRefMathSciNetGoogle Scholar
- 15.Wang, Y., Li, Y.: Not all those who wander are lost: Dynamic epistemic reasoning in navigation. In: Advances in Modal Logic, pp. 559–580 (2012)Google Scholar