Theoretical Computer Science
Games and full completeness for multiplicative linear logic
Journal of Symbolic Logic
A Local System for Classical Logic
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
A Local System for Linear Logic
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
A Non-commutative Extension of MELL
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
A Non-commutative Extension of Classical Linear Logic
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
Non-commutativity and MELL in the Calculus of Structures
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
MELL in the calculus of structures
Theoretical Computer Science
A system of interaction and structure
ACM Transactions on Computational Logic (TOCL)
On the proof complexity of deep inference
ACM Transactions on Computational Logic (TOCL)
Deep inference and its normal form of derivations
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
A system of interaction and structure v: The exponentials and splitting
Mathematical Structures in Computer Science
Linear lambda calculus and deep inference
TLCA'11 Proceedings of the 10th international conference on Typed lambda calculi and applications
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We study a system, called NEL, which is the mixed commutative/noncommutative linear logic BV augmented with linear logic's exponentials. Equivalently, NEL is MELL augmented with the noncommutative self-dual connective seq. In this article, we show a basic compositionality property of NEL, which we call decomposition. This result leads to a cut-elimination theorem, which is proved in the next article of this series. To control the induction measure for the theorem, we rely on a novel technique that extracts from NEL proofs the structure of exponentials, into what we call !-?-Flow-Graphs.