English

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

Logic in Computer Science 2017-03-08 v1 Logic

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.

Keywords

Cite

@article{arxiv.1703.02198,
  title  = {Strong Completeness and the Finite Model Property for Bi-Intuitionistic Stable Tense Logics},
  author = {Katsuhiko Sano and John G. Stell},
  journal= {arXiv preprint arXiv:1703.02198},
  year   = {2017}
}

Comments

In Proceedings M4M9 2017, arXiv:1703.01736