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Structures for Epistemic Logic

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Book cover Johan van Benthem on Logic and Information Dynamics

Part of the book series: Outstanding Contributions to Logic ((OCTR,volume 5))

Abstract

In this chapter we overview the main structures of epistemic and doxastic logic. We start by discussing the most celebrated models for epistemic logic, i.e., epistemic Kripke structures. These structures provide a very intuitive interpretation of the accessibility relation, based on the notion of information. This also naturally extends to the multi-agent case. Based on Kripke models, we then look at systems that add a temporal or a computational component, and those that provide a ‘grounded’ semantics for knowledge. We also pay special attention to ‘non-standard semantics’ for knowledge and belief, i.e., semantics that are not based on an underlying relation on the sets of states. In particular, we discuss here neighbourhood semantics and topological semantics. In all of these approaches, we can clearly point at streams of results that are inspired by work by Johan van Benthem. We are extremely pleased and honoured to be part of this book dedicated to his work and influences.

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Notes

  1. 1.

    For easy of readability, we give the group notions with \(A = \mathsf {Ag}\): cases for \(A \subseteq \mathsf {Ag}\) are similar.

  2. 2.

    DSO stands for Derived Sets are Open.

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Acknowledgments

The authors would like to thank Guram Bezhanishvili, David Gabelaia, Ian Hodkinson, Clemens Kupke and Levan Uridia for many interesting discussions and useful suggestions. Thanks also go to Aybüke Özgün for pointing out a few small errors. The first author would also like to acknowledge the support of the Netherlands Organization for Scientific Research grant 639.032.918 and the Rustaveli Science Foundation of Georgia grant FR/489/5-105/11.

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Authors and Affiliations

  1. Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, The Netherlands

    Nick Bezhanishvili

  2. Department of Computer Science, University of Liverpool, Liverpool, UK

    Wiebe van der Hoek

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Correspondence to Nick Bezhanishvili .

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Editors and Affiliations

  1. University of Amsterdam Inst Logic,Language & Computation, Amsterdam, The Netherlands

    Alexandru Baltag

  2. Amsterdam, The Netherlands

    Sonja Smets

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Bezhanishvili, N., van der Hoek, W. (2014). Structures for Epistemic Logic. In: Baltag, A., Smets, S. (eds) Johan van Benthem on Logic and Information Dynamics. Outstanding Contributions to Logic, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-06025-5_12

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