Abstract
We define and investigate a structure incorporating what is true, what is known and what is believed by a rational agent in models of the S4.2 logic of knowledge. The notion of KB R -structures introduced, provides a fine-grained modal analysis of an agent’s epistemic state, actually one that differentiates knowledge from belief and accounts for an agent without full introspective power (concerning her knowledge sets). Many epistemic properties of this structure are proved and it is shown that belief collapses in the form of a Stalnaker stable set (while knowledge does not). Finally, a representation theorem is proved, which exactly matches KB R -structures to S4.2 models of the world.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
van Benthem, J.: Modal Logic for Open Minds. CSLI Publications, Stanford (2010)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge Tracts in Theoretical Computer Science, vol. 53. Cambridge University Press, Cambridge (2001)
Chellas, B.F.: Modal Logic, an Introduction. Cambridge University Press, Cambridge (1980)
van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Springer, Heidelberg (2007)
Fagin, R., Halpern, J., Moses, Y., Vardi, M.: Reasoning about Knowledge. MIT Press, Cambridge (2003)
Gabbay, D.M., Woods, J. (eds.): Logic and the Modalities in the Twentieth Century. Handbook of the History of Logic, vol. 7. North-Holland, Amsterdam (2006)
Gochet, P., Gribomont, P.: Epistemic logic. In: Gabbay, Woods (eds.) [6], vol. 7, pp. 99–195 (2006)
Goldblatt, R.: Logics of Time and Computation, 2nd edn. CSLI Lecture Notes, vol. 7. Center for the Study of Language and Information, Stanford University (1992)
Halpern, J.: A theory of knowledge and ignorance for many agents. Journal of Logic and Computation 7(1), 79–108 (1997)
Hintikka, J.: Knowledge and Belief: an Introduction to the Logic of the two notions. Cornell University Press, Ithaca (1962)
Hughes, G.E., Cresswell, M.J.: A New Introduction to Modal Logic. Routledge, New York (1996)
Janhunen, T., Niemelä, I. (eds.): JELIA 2010. LNCS, vol. 6341. Springer, Heidelberg (2010)
Koutras, C., Zikos, Y.: Relating Truth, Knowledge and Belief in epistemic states. Technical Report, draft version, available through the authors’ web pages, in particular (January 2011), http://users.att.sch.gr/zikos/index/logic/KZ-KBr-full.pdf
Koutras, C.D., Zikos, Y.: Stable belief sets revisited. In: Janhunen, Niemelä (eds.) [12], pp. 221–233
Lenzen, W.: Epistemologische Betrachtungen zu [S4,S5]. Erkenntnis 14, 33–56 (1979)
Marek, V.W., Truszczyński, M.: Non-Monotonic Logic: Context-dependent Reasoning. Springer, Heidelberg (1993)
Segerberg, K.: An essay in Clasical Modal Logic. Filosofiska Studies, Uppsala (1971)
Stalnaker, R.: A note on non-monotonic modal logic. Artificial Intelligence 64, 183–196 (1993); Revised version of the unpublished note originally circulated in 1980
Wooldridge, M.: An Introduction to Multi Agent Systems. John Wiley & Sons, Chichester (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Koutras, C.D., Zikos, Y. (2011). Relating Truth, Knowledge and Belief in Epistemic States. In: Liu, W. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2011. Lecture Notes in Computer Science(), vol 6717. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22152-1_32
Download citation
DOI: https://doi.org/10.1007/978-3-642-22152-1_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22151-4
Online ISBN: 978-3-642-22152-1
eBook Packages: Computer ScienceComputer Science (R0)