Relating truth, knowledge and belief in epistemic states

Authors:
Costas D. Koutras;Yorgos Zikos
Affiliations:
Department of Computer Science and Technology, University of Peloponnese, Tripolis, Greece;Graduate Programme in Logic, Algorithms and Computation, Department of Mathematics, University of Athens, Ilissia, Greece
Venue:
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
Year:
2011

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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 KBR-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 KBR-structures to S4.2 models of the world.