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Knowledge, Time, and Logical Omniscience

  • Conference paper
Logic, Language, Information and Computation (WoLLIC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5514))

Abstract

Knowledge’s acquisition happens in time. However, this feature is not reflected in the standard epistemic logics, e.g. S4 with its possible world semantics suggested by Hintikka in [1], and hence their applications are limited. In this paper we adapt these normal modal logics to increase their expressive power such that not only is what is known modeled but also when it is known is recorded. We supplement each world with an awareness function which is an augmentation of Fagin-Halpern’s to keep track of the time when each formula is to be derived. This provides a new response to the logical omniscience problem. Our work originates from the tradition of study of Justification Logic, also known as Logic of Proofs, LP, introduced by Artemov ([2],[3],[4]). We will give the axiom systems of the models built here, accompanied with soundness and completeness results.

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Author information

Authors and Affiliations

  1. Computer Science, CUNY Graduate Center, 365 Fifth Avenue, New York, NY 10016, USA

    Ren-June Wang

Authors
  1. Ren-June Wang
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Editor information

Editors and Affiliations

  1. Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, 923-1292, Ishikawa, Japan

    Hiroakira Ono

  2. National Institute of Informatics, 2–1–2 Hitotsubashi, Chiyoda-ku, 101–8430, Tokyo, Japan

    Makoto Kanazawa

  3. Centro de Informática, Universidade Federal de Pernambuco, Recife, PE, Brazil

    Ruy de Queiroz

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Wang, RJ. (2009). Knowledge, Time, and Logical Omniscience. In: Ono, H., Kanazawa, M., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2009. Lecture Notes in Computer Science(), vol 5514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02261-6_31

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  • DOI: https://doi.org/10.1007/978-3-642-02261-6_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02260-9

  • Online ISBN: 978-3-642-02261-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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