Logics without the contraction rule and residuated lattices

  • Hiroakira Ono Japan Advanced Institute of Science and Technology

Abstract

In this paper, we will develop an algebraic study of substructural propositional logics over FLew, i.e. the logic which is obtained from intuitionistic logics by eliminating the contraction rule. Our main technical tool is to use residuated lattices as the algebraic semantics for them. This enables us to study different kinds of nonclassical logics, including intermediate logics, BCK-logics, Lukasiewicz’s many-valued logics and fuzzy logics, within a uniform framework.

Author Biography

Hiroakira Ono, Japan Advanced Institute of Science and Technology
Published
2010-09-22
How to Cite
ONO, Hiroakira. Logics without the contraction rule and residuated lattices. The Australasian Journal of Logic, [S.l.], v. 8, sep. 2010. ISSN 1448-5052. Available at: <https://ojs.victoria.ac.nz/ajl/article/view/1813>. Date accessed: 15 nov. 2019. doi: https://doi.org/10.26686/ajl.v8i0.1813.