Theoretical Computer Science
A Local System for Classical Logic
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
Non-commutativity and MELL in the Calculus of Structures
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Full Completeness of the Multiplicative Linear Logic of Chu Spaces
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
A system of interaction and structure
ACM Transactions on Computational Logic (TOCL)
Linear lambda calculus and deep inference
TLCA'11 Proceedings of the 10th international conference on Typed lambda calculi and applications
Proof Nets for Herbrand’s Theorem
ACM Transactions on Computational Logic (TOCL)
Subformula linking as an interaction method
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
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We investigate the question of what constitutes a proof when quantifiers and multiplicative units are both present. On the technical level this paper provides two new aspects of the proof theory of MLL2 with units. First, we give a novel proof system in the framework of the calculus of structures. The main feature of the new system is the consequent use of deep inference, which allows us to observe a decomposition which is a version of Herbrand's theorem that is not visible in the sequent calculus. Second, we show a new notion of proof nets which is independent from any deductive system. We have "sequentialisation" into the calculus of structures as well as into the sequent calculus. Since cut elimination is terminating and confluent, we have a category of MLL2 proof nets. The treatment of the units is such that this category is star-autonomous.