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arXiv · 1703.02198

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

Katsuhiko Sano·John G. Stell
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Abstract

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.

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Katsuhiko Sano, John G. Stell. 2017-03-07. Strong Completeness and the Finite Model Property for Bi-Intuitionistic Stable Tense Logics. https://doi.org/10.4204/eptcs.243.8

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