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.
Citation
H. Naruse. H. Ono. Bayu Surarso. "A Syntactic Approach to Maksimova's Principle of Variable Separation for Some Substructural Logics." Notre Dame J. Formal Logic 39 (1) 94 - 113, Winter 1998. https://doi.org/10.1305/ndjfl/1039293022
Information