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

Katsuhiko Sano
John G. Stell

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.

In Sujata Ghosh and R. Ramanujam: Proceedings of the Ninth Workshop on Methods for Modalities (M4M9 2017), Indian Institute of Technology, Kanpur, India, 8th to 10th January 2017, Electronic Proceedings in Theoretical Computer Science 243, pp. 105–121.
Published: 6th March 2017.

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