# A Non-commutative Extension of MELL

• Alessio Guglielmi
• Lutz Straßburger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2514)

## Abstract

We extend multiplicative exponential linear logic(M EL)L 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 M E L,L 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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