Forum: a multiple-conclusion specification logic
ALP Proceedings of the fourth international conference on Algebraic and logic programming
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 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
A system of interaction and structure
ACM Transactions on Computational Logic (TOCL)
Electronic Notes in Theoretical Computer Science (ENTCS)
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
A pattern matching compiler for multiple target languages
CC'03 Proceedings of the 12th international conference on Compiler construction
A local system for intuitionistic logic
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Maude as a Platform for Designing and Implementing Deep Inference Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
On the proof complexity of deep inference
ACM Transactions on Computational Logic (TOCL)
On linear logic planning and concurrency
Information and Computation
Hi-index | 0.00 |
The calculus of structures is a proof theoretical formalism which generalizes the sequent calculus with the feature of deep inference: In contrast to the sequent calculus, inference rules can be applied at any depth inside a formula, bringing shorter proofs than any other formalisms supporting analytical proofs. However, deep applicability of the inference rules causes greater nondeterminism than in the sequent calculus regarding proof search. In this paper, we introduce a new technique which reduces nondeterminism without breaking proof theoretical properties and provides a more immediate access to shorter proofs. We present this technique on system BV, the smallest technically non-trivial system in the calculus of structures, extending multiplicative linear logic with the rules mix, nullary mix, and a self-dual non-commutative logical operator. Because our technique exploits a scheme common to all the systems in the calculus of structures, we argue that it generalizes to these systems for classical logic, linear logic, and modal logics.