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