Substructural Logics and Residuated Lattices — an Introduction

This is an introductory survey of substructural logics and of residuated lattices which are algebraic structures for substructural logics. Our survey starts from sequent systems for basic substructural logics and develops the proof theory of them. Then, residuated lattices are introduced as algebraic structures for substructural logics, and some recent developments of their algebraic study are presented. Based on these facts, we conclude at the end that substructural logics are logics of residuated structures, and in this way explain why sequent systems are suitable for formalizing substructural logics.