Proofs and types
A semantics of evidence for classical arithmetic
Journal of Symbolic Logic
Polarized proof-nets and λµ-calculus
Theoretical Computer Science
Lambda-My-Calculus: An Algorithmic Interpretation of Classical Natural Deduction
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
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-commutativity and MELL in the Calculus of Structures
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Proof Nets for Unit-free Multiplicative-Additive Linear Logic (Extended abstract)
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
On the Geometry of Interaction for Classical Logic
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
A system of interaction and structure
ACM Transactions on Computational Logic (TOCL)
IEEE Transactions on Computers
Proof nets for unit-free multiplicative-additive linear logic
ACM Transactions on Computational Logic (TOCL)
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
Proof Identity for Classical Logic: Generalizing to Normality
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
On Linear Logic Planning and Concurrency
Language and Automata Theory and Applications
On the proof complexity of deep inference
ACM Transactions on Computational Logic (TOCL)
Information and Computation
What is the problem with proof nets for classical logic?
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Expansion nets: proof-nets for propositional classical logic
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Deep inference and its normal form of derivations
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Research perspectives for logic and deduction
Reasoning, Action and Interaction in AI Theories and Systems
Proof Nets for Herbrand’s Theorem
ACM Transactions on Computational Logic (TOCL)
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We present a theory of proof denotations in classical propositional logic. The abstract definition is in terms of a semiring of weights, and two concrete instances are explored. With the Boolean semiring we get a theory of classical proof nets, with a geometric correctness criterion, a sequentialization theorem, and a strongly normalizing cut-elimination procedure. This gives us a “Boolean” category, which is not a poset. With the semiring of natural numbers, we obtain a sound semantics for classical logic, in which fewer proofs are identified. Though a “real” sequentialization theorem is missing, these proof nets have a grip on complexity issues. In both cases the cut elimination procedure is closely related to its equivalent in the calculus of structures.