A Non-commutative Extension of Multiplicative Exponential Linear Logic

Reference:

Guglielmi, A. and Straßburger, L., 2004. A Non-commutative Extension of Multiplicative Exponential Linear Logic. Discussion Paper.

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Official URL:

http://www.ps.uni-sb.de/~lutz/papers/NELbig.pdf

Abstract

We extend multiplicative exponential linear logic (MELL) by a noncommutative, 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 are then able to extend the expressiveness of MELL by modelling a broad notion of sequentiality. 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

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