A survey of proof nets and matrices for substructural logics

This paper is a survey of two kinds of "compressed" proof schemes, the \emph{matrix method} and \emph{proof nets}, as applied to a variety of logics ranging along the substructural hierarchy from classical all the way down to the nonassociative Lambek system. A novel treatment of proof nets for the latter is provided. Descriptions of proof nets and matrices are given in a uniform notation based on sequents, so that the properties of the schemes for the various logics can be easily compared.