Dynamic Epistemic Logic and Logical Omniscience

Mattias Skipper Rasmussen

DOI: http://dx.doi.org/10.12775/LLP.2015.014

Abstract


Epistemic logics based on the possible worlds semantics suffer from the problem of logical omniscience, whereby agents are described as knowing all logical consequences of what they know, including all tautologies. This problem is doubly challenging: on the one hand, agents should be treated as logically non-omniscient, and on the other hand, as moderately logically competent. Many responses to logical omniscience fail to meet this double challenge because the concepts of knowledge and reasoning are not properly separated. In this paper, I present a dynamic logic of knowledge that models an agent’s epistemic state as it evolves over the course of reasoning. I show that the logic does not sacrifice logical competence on the altar of logical non-omniscience.


Keywords


epistemic logic; dynamic epistemic logic; logical omniscience; resource-bounded reasoning

Full Text:

PDF

References


Anderson, A., and N. Belnap, Entailment. The Logic of Relevance and Necessity, Princeton University Press, 1975.

Ågotnes, T., “A logic of finite syntactic epistemic states”, 2004.

Ågotnes, T., and N. Alechina, “The dynamics of syntactic knowledge”, Journal of Logic and Computation, (2006): 1–34. DOI: 10.1093/logcom/exl019

Belnap, N., A Useful Four-Valued Logic, D. Reichel: Dordrecht, 1977.

Bjerring, J.C., “Non-ideal epistemic spaces”, 2010.

Bjerring, J.C., “Impossible worlds and logical omniscience: An impossibility result”, Synthese, 190, 13 (2013): 2505–2524. DOI: 10.1007/s11229-011-0038-y

Bjerring, J.C., “Problems in epistemic space”, Journal of Philosophical Logic, 43 (2014): 153–170. DOI: 10.1007/s10992-012-9257-z

Bostock, D., Intermediate Logic, Oxford University Press: Oxford, 1997.

Chalmers, D., “The nature of epistemic space”, pages 60–107 in Epistemic Modality, Oxford University Press: New York, 2011. DOI: 10.1093/acprof:oso/9780199591596.003.0003

Cresswell, M. J, “Classical intensional logic”, Theoria, 36, 3 (1970): 347–372. DOI: 10.1111/j.1755-2567.1970.tb00433.x

Cresswell, M. J, “Intensional logics and logical truth”, Journal of Philosophical Logic, 1, 1 (1972): 2–15. DOI: 10.1007/BF00649986

Cresswell, M. J, Logics and Languages, Methuen and Co., 1973.

Ditmarsch, van H., W. van der Hoek, and B. Kooi, Dynamic Epistemic Logic, Springer, 2008.

Drapkin, J., and D. Perlis, “A preliminary excursion into step-logics”, pages 262–269 in Proceedings of the SIGART International Symposium on Methodologies for Intelligent Systems, C. Ghidini, P. Giodini, and W. van der Hoek (eds.), 1986. DOI: 10.1145/12808.12837

Drapkin, J., and D. Perlis, ‘Reasoning situated in time I: Basic concepts”. Journal of Experimental and Theoretical Artificial Intelligence, 2 (1990): 75–98.

Duc, H. N., “Logical omniscience vs. logical ignorance on a dilemma of epistemic logic”, Chapter 20 in Progress in Artificial Intelligence. 7th Portuguese Conference on Artificial Intelligence, EPIA’95, Funchal, Madeira Island, Portugal, C. A. Pinto-Ferreira and N. J. Mamede (eds.), 1995. DOI: 10.1007/3-540-60428-6_20

Duc, H. N., “Reasoning about rational, but not logically omniscient, agents”, Journal of Logic and Computation, 7, 5 (1997): 633–648. DOI: 10.1093/logcom/7.5.633

Duc, H. N., “Resource-bounded reasoning about knowledge”, 2001.

Elgot-Drapkin, J., “Active logics: A unified formal approach to episodic reasoning”, Technical report, University of Maryland, 1999.

Fagin, R., and J. Halpern, “Belief, awareness and limited reasoning”, Artificial Intelligence, 34 (1988): 39–76. DOI: 10.1016/0004-3702(87)90003-8

Fagin, R., J. Halpern, and M. Vardi, “A nonstandard approach to the logical omniscience problem”, Artificial Intelligence, 79 (1995): 203–240. DOI: 10.1016/0004-3702(94)00060-3

Fagin, R., J. Halpern, M. Vardi, and Y. Moses, Reasoning About Knowledge, MIT Press, 1995.

Heyting, A., Intuitionism: An Introduction, North Holland: Amsterdam, 1956.

Hintikka, J., Knowledge and Belief: An Introduction to the Two Notions, Cornell University Press, 1962.

Hintikka, J., “Impossible possible worlds vindicated”, Journal of Philosophical Logic, 4, 4 (1975): 475–484. DOI: 10.1007/BF00558761

Jago, M., “Logics for resource-bounded agents”, 2006.

Jago, M., “The problem of rational knowledge”, Erkenntnis, 79, S6 (2014): 1151. DOI: 10.1007/s10670-013-9545-1

Jago, M., The Impossible: An Essay on Hyperintensionality, Oxford University Press, 2014.

Konolige, K., A Deduction Model of Belief, Morgan Kaufman, 1986.

Lakemeyer, G., “Tractable meta-reasoning in propositional logics of belief”, pages 198–202 in Tenth International Joint Conference on Artificial Intelligence, 1987.

Lemmon, E. J., Beginning Logic, Hacker Publishing Company, 1998.

Levesque, H. J., “A logic of implicit and explicit belief”, pages 198–202 in National Conference on Artificial Intelligence, 1984.

Priest, G., An Introduction to Non-Classical Logic, second edition, Cambridge University Press, 2008.

Rantala, V., “Impossible worlds semantics and logical omniscience”, Acta Philosophica Fennica, 35 (1982): 106–115.

Routley, R., and R. Meyer, “The semantics of entailment II”, Journal of Philosophical Logic, 1 (1972): 53–73. DOI: 10.1007/BF00649991

Routley, R., and R. Meyer, “The semantics of entailment III”, Journal of Philosophical Logic, 1 (1972): 192–208. DOI: 10.1007/BF00650498

Routley, R., and R. Meyer, The Semantics of Entailment I, pages 194–243 in Truth, Syntax and Modality, series “Studies in Logic and the Foundations of Mathematics”, 1973. DOI: 10.1016/S0049-237X(08)71541-6

Wansing, H., “A general possible worlds framework for reasoning about knowledge and belief”, Studia Logica, 49 (1990): 523–539. DOI: 10.1007/BF00370163








Print ISSN: 1425-3305
Online ISSN: 2300-9802

Partnerzy platformy czasopism