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Notre Dame Journal of Formal Logic

A Syntactic Approach to Maksimova's Principle of Variable Separation for Some Substructural Logics

Bayu Surarso, H. Naruse, and H. Ono
Source: Notre Dame J. Formal Logic Volume 39, Number 1 (1998), 94-113.

Abstract

Maksimova's principle of variable separation says that if propositional formulas $A_1 \supset A_2$ and $B_1 \supset B_2$ have no propositional variables in common and if a formula $A_1\wedge B_1 \supset A_2\vee B_2$ is provable, then either $A_1 \supset A_2$ or $B_1 \supset B_2$ is provable. Results on Maksimova's principle until now are obtained mostly by using semantical arguments. In the present paper, a proof-theoretic approach to this principle in some substructural logics is given, which analyzes a given cut-free proof of the formula $A_1\wedge B_1 \supset A_2\vee B_2$ and examines how the formula is derived. This analysis will make clear why Maksimova's principle holds for these logics.

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Primary Subjects: 03B20
Secondary Subjects: 03F03
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1039293022
Mathematical Reviews number (MathSciNet): MR1671734
Digital Object Identifier: doi:10.1305/ndjfl/1039293022
Zentralblatt MATH identifier: 0967.03017

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