Electronic Proceedings in Theoretical Computer Science (Mar 2017)

Strong Completeness and the Finite Model Property for Bi-Intuitionistic Stable Tense Logics

  • Katsuhiko Sano,
  • John G. Stell

DOI
https://doi.org/10.4204/EPTCS.243.8
Journal volume & issue
Vol. 243, no. Proc. M4M9 2017
pp. 105 – 121

Abstract

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Bi-Intuitionistic Stable Tense Logics (BIST Logics) are tense logics with a Kripke semantics where worlds in a frame are equipped with a pre-order as well as with an accessibility relation which is 'stable' with respect to this pre-order. BIST logics are extensions of a logic, BiSKt, which arose in the semantic context of hypergraphs, since a special case of the pre-order can represent the incidence structure of a hypergraph. In this paper we provide, for the first time, a Hilbert-style axiomatisation of BISKt and prove the strong completeness of BiSKt. We go on to prove strong completeness of a class of BIST logics obtained by extending BiSKt by formulas of a certain form. Moreover we show that the finite model property and the decidability hold for a class of BIST logics.