Positive Fragments of Coalgebraic Logics

  • Adriana Balan
  • Alexander Kurz
  • Jiří Velebil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8089)

Abstract

Positive modal logic was introduced in an influential 1995 paper of Dunn as the positive fragment of standard modal logic. His completeness result consists of an axiomatization that derives all modal formulas that are valid on all Kripke frames and are built only from atomic propositions, conjunction, disjunction, box and diamond.

In this paper, we provide a coalgebraic analysis of this theorem, which not only gives a conceptual proof based on duality theory, but also generalizes Dunn’s result from Kripke frames to coalgebras of weak-pullback preserving functors.

For possible application to fixed-point logics, it is note-worthy that the positive coalgebraic logic of a functor is given not by all predicate-liftings but by all monotone predicate liftings.

Keywords

coalgebraic logic duality positive modal logic 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Adriana Balan
    • 1
  • Alexander Kurz
    • 2
  • Jiří Velebil
    • 3
  1. 1.University Politehnica of BucharestRomania
  2. 2.University of LeicesterUK
  3. 3.Faculty of Electrical EngineeringCzech Technical University in PragueCzech Republic

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