Coalgebraic Predicate Logic

  • Tadeusz Litak
  • Dirk Pattinson
  • Katsuhiko Sano
  • Lutz Schröder
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7392)

Abstract

We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and completeness results for two natural classes of such logics. Moreover, we show that an entirely general completeness result is not possible. We study the expressive power of our language, contrasting it with both coalgebraic modal logic and existing first-order proposals for special classes of Set-coalgebras (apart for relational structures, also neighbourhood frames and topological spaces). The semantic characterization of expressivity is based on the fact that our language inherits a coalgebraic variant of the Van Benthem-Rosen Theorem. Basic model-theoretic constructions and results, in particular ultraproducts, obtain for the two classes which allow for completeness—and in some cases beyond that.

Keywords

Modal Logic Kripke Model Kripke Frame Conditional Logic Neighbourhood Frame 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Tadeusz Litak
    • 1
  • Dirk Pattinson
    • 2
  • Katsuhiko Sano
    • 3
  • Lutz Schröder
    • 4
  1. 1.Department of Computer ScienceUniversity of LeicesterUK
  2. 2.Department of ComputingImperial College LondonUK
  3. 3.School of Information ScienceJapan Advanced Institute of Science and TechnologyJapan
  4. 4.Department of Computer ScienceFriedrich-Alexander-Universität Erlangen-NürnbergGermany

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