### 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.

Original language | English |
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Pages | 231-246 |

Number of pages | 16 |

Publication status | Published - Oct 2002 |

Event | Logic for Programming, Artificial Intelligence, and Reasoning - 9th International Conference, LPAR - Duration: 1 Oct 2002 → … |

### Conference

Conference | Logic for Programming, Artificial Intelligence, and Reasoning - 9th International Conference, LPAR |
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Period | 1/10/02 → … |

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## Cite this

Guglielmi, A., & Strassburger, L. (2002).

*A Non-commutative Extension of MELL*. 231-246. Paper presented at Logic for Programming, Artificial Intelligence, and Reasoning - 9th International Conference, LPAR, .