Studia Logica

, Volume 83, Issue 1, pp 279–308

Algebraization, Parametrized Local Deduction Theorem and Interpolation for Substructural Logics over FL

Article

DOI: 10.1007/s11225-006-8305-5

Cite this article as:
Galatos, N. & Ono, H. Stud Logica (2006) 83: 279. doi:10.1007/s11225-006-8305-5

Abstract

Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices.

Keywords

Substructural logicpointed residuated latticealgebraic semanticsparametrized local deduction theoreminterpolation

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Japan Advanced Institute of Science and TechnologyIshikawaJapan