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Topological Semantics of Justification Logic

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Computer Science – Theory and Applications (CSR 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5010))

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Abstract

The Justification Logic is a family of logical systems obtained from epistemic logics by adding new type of formulas which reads as t is a justification for F. The major epistemic modal logic S4 has a well-known Tarski topological interpretation which interprets \(\Box F\) as the interior of F (a topological equivalent of the ‘knowable part of F’). In this paper we extend the Tarski topological interpretation from epistemic modal logics to justification logics which have both: knowledge assertions \(\Box F\) and justification assertions . This topological semantics interprets modality as the interior, terms t represent tests, and a justification assertion represents a part of F which is accessible for test t. We establish a number of soundness and completeness results with respect to Kripke topology and the real line topology for S4-based systems of Justification Logic.

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Authors and Affiliations

  1. CUNY Graduate Center, 365 Fifth Ave., New York City, NY 10016, USA

    Sergei Artemov

  2. Dept. of Math, BMCC CUNY, 199 Chambers Street, New York, NY 10007, U.S.A.

    Elena Nogina

Authors
  1. Sergei Artemov
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  2. Elena Nogina
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Editor information

Edward A. Hirsch Alexander A. Razborov Alexei Semenov Anatol Slissenko

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Artemov, S., Nogina, E. (2008). Topological Semantics of Justification Logic. In: Hirsch, E.A., Razborov, A.A., Semenov, A., Slissenko, A. (eds) Computer Science – Theory and Applications. CSR 2008. Lecture Notes in Computer Science, vol 5010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79709-8_7

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  • DOI: https://doi.org/10.1007/978-3-540-79709-8_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79708-1

  • Online ISBN: 978-3-540-79709-8

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