Coalgebraic semantics for positive modal logic

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Abstract

Positive Modal Logic is the restriction of the modal local consequence relation defined by the class of all Kripke models to the propositional negation-free modal language. The class of positive modal algebras is the one canonically associated with PML according to the theory of the algebraization of logics. In [4], a Priestley-style duality is established between the category of positive modal algebras and the category of K+-spaces. In this paper, we establish a categorical equivalence between the category K+ of K+-spaces and the category Coalg(V) of coalgebras of a suitable endofunctor V on the category of Priestley spaces.

Original languageEnglish
Pages (from-to)221-236
Number of pages16
JournalElectronic Notes in Theoretical Computer Science
Volume82
Issue number1
DOIs
Publication statusPublished - 1 Jan 2003
Externally publishedYes
EventCMCS'03, Coalgebraic Methods in Computer Science Satellite Event for ETAPS 2003) - Warsaw, Poland
Duration: 5 Apr 20036 Apr 2003

Keywords

  • Positive modal algebra
  • Positive Modal Logic
  • Priestley space
  • Vietoris functor

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