An Algebraic Approach to Substructural Logics - An Overview.

We will give a state-of-the-art survey of the study of substructural logics. Originally, substructural logics were introduced as logics which, when formulated as Gentzen-style systems, lack some of the three basic structural rules, i.e. contraction, weakening and exchange. For example, relevance logics and linear logic lack the weakening rule, many-valued logics, fuzzy logics and linear logic lack the contraction rule, and hence all of them can be regarded as substructural logics. These logics have been studied extensively and various theories have been developed for their investigation. However their study has been carried out independently, mainly due to the different motivations behind them, avoiding comparisons between different substructural logics. [ABSTRACT FROM AUTHOR]