@MISC{Ghani96adjointrewriting, author = {Neil Ghani}, title = {Adjoint Rewriting and the !-type constructor}, year = {1996} }

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Abstract

This paper provides a sound, complete and decidable equational theory for the terms of the (I;\Omega ; \Gammaffi; !)-fragment of intuitionistic linear logic with respect to the class of models known as linear categories. This work uses the natural deduction style presentation of the !- type constructor in DILL so as to be able to apply the ideas of adjoint rewriting. We obtain an expansionary j-rewrite rule and contractive fi-rewrite rule for each type constructor and then use a variety of term rewriting techniques to obtain a decision procedure for the associated equational theory. 1 Introduction This paper concerns the proof theory of an intuitionistic fragment of Girard's Linear Logic [9]. The major innovation of linear logic is the omission of the structural rules weakening and contraction with the consequence that in any proof of the logic, all the assumptions must be used exactly once. The expressiveness of intuitionistic linear logic is regained via the addition of a new type...