Open Access
Translator Disclaimer
2007 An Algebraic Approach to the Disjunction Property of Substructural Logics
Daisuke Souma
Notre Dame J. Formal Logic 48(4): 489-495 (2007). DOI: 10.1305/ndjfl/1193667706


Some of the basic substructural logics are shown by Ono to have the disjunction property (DP) by using cut elimination of sequent calculi for these logics. On the other hand, this syntactic method works only for a limited number of substructural logics. Here we show that Maksimova's criterion on the DP of superintuitionistic logics can be naturally extended to one on the DP of substructural logics over FL. By using this, we show the DP for some of the substructural logics for which syntactic methods don't work well.


Download Citation

Daisuke Souma. "An Algebraic Approach to the Disjunction Property of Substructural Logics." Notre Dame J. Formal Logic 48 (4) 489 - 495, 2007.


Published: 2007
First available in Project Euclid: 29 October 2007

zbMATH: 1137.03012
MathSciNet: MR2357523
Digital Object Identifier: 10.1305/ndjfl/1193667706

Primary: 03B47 , 03G25

Keywords: disjunction property , residuated lattice , substructural logic , well-connectedness

Rights: Copyright © 2007 University of Notre Dame


Vol.48 • No. 4 • 2007
Back to Top