## Notre Dame Journal of Formal Logic

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

#### 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.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 39, Number 1 (1998), 94-113.

Dates
First available in Project Euclid: 7 December 2002

https://projecteuclid.org/euclid.ndjfl/1039293022

Digital Object Identifier
doi:10.1305/ndjfl/1039293022

Mathematical Reviews number (MathSciNet)
MR1671734

Zentralblatt MATH identifier
0967.03017

Subjects
Primary: 03B20: Subsystems of classical logic (including intuitionistic logic)
Secondary: 03F03: Proof theory, general

#### Citation

Naruse, H.; Surarso, Bayu; Ono, H. A Syntactic Approach to Maksimova's Principle of Variable Separation for Some Substructural Logics. Notre Dame J. Formal Logic 39 (1998), no. 1, 94--113. doi:10.1305/ndjfl/1039293022. https://projecteuclid.org/euclid.ndjfl/1039293022

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