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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.
A theorem of alternatives provides a reduction of validity in a substructural logic to validity in its multiplicative fragment. Notable examples include a theorem of Arnon Avron that reduces the validity of a disjunction of multiplicative formulas in
We interpret Linear Logic Proof Nets in a term language based on Solos calculus. The system includes a synchronisation mechanism, obtained by a conservative extension of the logic, that enables to define non-deterministic behaviours and multiparty sessions.
Separation logics are a family of extensions of Hoare logic for reasoning about programs that mutate memory. These logics are abstract because they are independent of any particular concrete memory model. Their assertion languages, called proposition
In this paper, we show how to interpret a language featuring concurrency, references and replication into proof nets, which correspond to a fragment of differential linear logic. We prove a simulation and adequacy theorem. A key element in our transl
In this paper we present a cut-free sequent calculus, called SeqS, for some standard conditional logics, namely CK, CK+ID, CK+MP and CK+MP+ID. The calculus uses labels and transition formulas and can be used to prove decidability and space complexity