Structural Rules and a Logical Hierarchy

Gentzen-type sequent calculi usually contain three structural rules, i.e., exchange, contraction and weakening rules. In recent years, however, there have been various studies on logics that have not included some or any of these structural rules. The motives or purposes of these studies have been so diverse that sometimes close connections between them have been overlooked. Here we will make a brief survey of recent results on these logics in an attempt to make these interrelationships clearer.

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