Topological Semantics of Justification Logic

  • Sergei Artemov
  • Elena Nogina
Conference paper

DOI: 10.1007/978-3-540-79709-8_7

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5010)
Cite this paper as:
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

Abstract

The Justification Logic is a family of logical systems obtained from epistemic logics by adding new type of formulas Open image in new window 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 Open image in new window. This topological semantics interprets modality as the interior, terms t represent tests, and a justification assertion Open image in new window 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.

Keywords

Justification Logic Logic of Proofs modal logic topological semantics Tarski 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Sergei Artemov
    • 1
  • Elena Nogina
    • 2
  1. 1.CUNY Graduate CenterNew York CityUSA
  2. 2.Dept. of MathBMCC CUNYNew YorkU.S.A.

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