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Studia Logica

, Volume 40, Issue 1, pp 39–54 | Cite as

On fragments of Medvedev's logic

  • Miros>law Szatkowski
Article

Abstract

Medvedev's intermediate logic (MV) can be defined by means of Kripke semantics as the family of Kripke frames given by finite Boolean algebras without units as partially ordered sets. The aim of this paper is to present a proof of the theorem: For every set of connectivesΦ such that\(\{ \to , \vee , \urcorner \} \not \subseteq \Phi \subseteq \{ \to , \wedge , \urcorner \} \) theΦ-fragment ofMV equals theΦ fragment of intuitionistic logic. The final part of the paper brings the negative solution to the problem set forth by T. Hosoi and H. Ono, namely: is an intermediate logic based on the axiom (⌝a→b∨c) →(⌉a→b)∨(⌝a → c) separable?

Keywords

Mathematical Logic Boolean Algebra Computational Linguistic Final Part Intuitionistic Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1981

Authors and Affiliations

  • Miros>law Szatkowski
    • 1
  1. 1.Jagiellohian UniversityCracow

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