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Some Properties of Several Proof Systems for Intuitionistic, Johanssons and Monotone Propositional Logics

Chubaryan Anahit, Karabakhtsyan Arman and Petrosyan Garik
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Chubaryan Anahit: Doctor of Physical and Mathematical Sciences, Full Professor of Yerevan State University and Russian-Armenian University, Armenia
Karabakhtsyan Arman: Master Student of Department of Applied Mathematics and Informatics of Russian-Armenian University, Armenia
Petrosyan Garik: Master Student of Department of Informatics and Applied Mathematics of Yerevan State University, Armenia

Journal of Asian Scientific Research, 2018, vol. 8, issue 2, 61-72

Abstract: In this paper we investigate two properties of some propositional systems of Intuitionistic, Johansson?s and Monotone logics: 1) the relations between the proofs complexities of strongly equal tautologies (valid sequents) and 2) the relations between the proofs complexities of minimal tautologies (valid sequents) and of results of substitutions in them. We show that 1) strongly equal tautologies (valid sequents) can have essential different proof complexities in the same system and 2) the result of substitution can be proved easier, than corresponding minimal tautology (valid sequents), therefore the systems, which are considered in this paper, are no monotonous neither by lines nor by size.

Keywords: Strongly equal tautology; Minimal tautology; Sequent proof systems; Frege systems; Proof complexity measures; Monotonous system. (search for similar items in EconPapers)
Date: 2018
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Handle: RePEc:asi:joasrj:2018:p:61-72