Theoretical Computer Science
Phase semantics and sequent calculus for pure noncommutative classical linear propositional logic
Journal of Symbolic Logic
Games and full completeness for multiplicative linear logic
Journal of Symbolic Logic
A Purely Logical Account of Sequentiality in Proof Search
ICLP '02 Proceedings of the 18th International Conference on Logic Programming
A Local System for Classical Logic
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
A Non-commutative Extension of Classical Linear Logic
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
Non-commutative logic II: sequent calculus and phase semantics
Mathematical Structures in Computer Science
A system of interaction and structure IV: The exponentials and decomposition
ACM Transactions on Computational Logic (TOCL)
Reducing nondeterminism in the calculus of structures
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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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 EL,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.