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Studia Logica

, Volume 105, Issue 6, pp 1193–1219 | Cite as

Kripke Completeness of Bi-intuitionistic Multilattice Logic and its Connexive Variant

  • Norihiro KamideEmail author
  • Yaroslav Shramko
  • Heinrich Wansing
Article

Abstract

In this paper, bi-intuitionistic multilattice logic, which is a combination of multilattice logic and the bi-intuitionistic logic also known as Heyting–Brouwer logic, is introduced as a Gentzen-type sequent calculus. A Kripke semantics is developed for this logic, and the completeness theorem with respect to this semantics is proved via theorems for embedding this logic into bi-intuitionistic logic. The logic proposed is an extension of first-degree entailment logic and can be regarded as a bi-intuitionistic variant of the original classical multilattice logic determined by the algebraic structure of multilattices. Similar completeness and embedding results are also shown for another logic called bi-intuitionistic connexive multilattice logic, obtained by replacing the connectives of intuitionistic implication and co-implication with their connexive variants.

Keywords

First-degree entailment logic Multilattices Bi-intuitionistic logic Connexive logic 

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of Information and Electronic Engineering Faculty of Science and EngineeringTeikyo UniversityUtsunomiyaJapan
  2. 2.Department of PhilosophyKryvyi Rih State Pedagogical UniversityKryvyi RihUkraine
  3. 3.Department of Philosophy IIRuhr-University BochumBochumGermany

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