A Non-commutative Extension of MELL

Reference:

Guglielmi, A. and Strassburger, L., 2002. A Non-commutative Extension of MELL. In: Logic for Programming, Artificial Intelligence, and Reasoning - 9th International Conference, LPAR, 2002-10-01.

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Abstract

We extend multiplicative exponential linear logic (MELL) by a non-commutative, self-dual logical operator. The extended system, called NEL, is defined in the formalism of the calculus of structures, which is a generalisation of the sequent calculus and provides a more refined analysis of proofs. We should then be able to extend the range of applications of MELL, by modelling a broad notion of sequentiality and providing new properties of proofs. We show some proof theoretical results: decomposition and cut elimination. The new operator represents a significant challenge: to get our results we use here for the first time some novel techniques, which constitute a uniform and modular approach to cut elimination, contrary to what is possible in the sequent calculus.

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