A semantics of evidence for classical arithmetic
Journal of Symbolic Logic
Proceedings of the workshop on Advances in linear logic
Basic proof theory
ICFP '00 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming
Constructing Free Boolean Categories
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Towards Hilbert's 24th Problem: Combinatorial Proof Invariants
Electronic Notes in Theoretical Computer Science (ENTCS)
Categorical proof theory of classical propositional calculus
Theoretical Computer Science - Logic, language, information and computation
On categorical models of classical logic and the Geometry of Interaction
Mathematical Structures in Computer Science
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Some Observations on the Proof Theory of Second Order Propositional Multiplicative Linear Logic
TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
Expansion nets: proof-nets for propositional classical logic
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Naming proofs in classical propositional logic
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
Correctness of multiplicative (and exponential) proof structures is NL-complete
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Hi-index | 0.00 |
This article explores Herbrand’s theorem as the source of a natural notion of abstract proof object for classical logic, embodying the “essence” of a sequent calculus proof. We see how to view a calculus of abstract Herbrand proofs (Herbrand nets) as an analytic proof system with syntactic cut-elimination. Herbrand nets can also be seen as a natural generalization of Miller’s expansion tree proofs to a setting including cut. We demonstrate sequentialization of Herbrand nets into a sequent calculus LKH; each net corresponds to an equivalence class of LKH proofs under natural proof transformations. A surprising property of our cut-reduction algorithm is that it is non-confluent despite not supporting the usual examples of non-confluent reduction in classical logic.