An algebraic view of sequent formulation of substructural logics
by
Hiroakira Ono
Japan Advanced Institute of Science and Technology (JAIST)

Substructural logics are usually defined as logics that lack some or all of structural rules when formulated as sequent systems. Recent studies have revealed that algebraic structures for these logics are exactly equal to residuated lattices, which are familiar to algebraists. In my talk, I will explain first why sequent formulation is essential in introducing substructural logics from algebraic viewpoint, and how it offers us suitable systems for logics with "the law of residuation", in general.

Then, I will examine algebraic aspects of some of syntactic properties of sequent systems. They include relation between proof-search procedures and finite model property, and also distinction between derivability and admissibility of rules of inference in terms of algebra.

Date received: December 28, 2002