Categorical proof theory of classical propositional calculus

Authors:
Gianluigi Bellin;Martin Hyland;Edmund Robinson;Christian Urban
Affiliations:
Queen Mary, University of London, UK;University of Cambridge, UK;Queen Mary, University of London, UK;Technical University of Munich (TUM), Germany
Venue:
Theoretical Computer Science - Logic, language, information and computation
Year:
2006

Citing 11
Cited 3

Linear logic

Theoretical Computer Science
A formulae-as-type notion of control

POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The duality of computation

ICFP '00 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming
Premonoidal categories as categories with algebraic structure

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
Call-by-value is dual to call-by-name

ICFP '03 Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
Two paradigms of logical computation in affine logic?

Logic for concurrency and synchronisation
Control categories and duality: on the categorical semantics of the lambda-mu calculus

Mathematical Structures 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
Naming proofs in classical propositional logic

TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
Strong Normalisation of Cut-Elimination in Classical Logic

Fundamenta Informaticae - Typed Lambda Calculi and Applications (TLCA'99)

Towards Hilbert's 24th Problem: Combinatorial Proof Invariants

Electronic Notes in Theoretical Computer Science (ENTCS)
Expansion nets: proof-nets for propositional classical logic

LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Proof Nets for Herbrand’s Theorem

ACM Transactions on Computational Logic (TOCL)

Quantified Score

Hi-index	0.00

Visualization

Abstract

We investigate semantics for classical proof based on the sequent calculus. We show that the propositional connectives are not quite well-behaved from a traditional categorical perspective, and give a more refined, but necessarily complex, analysis of how connectives may be characterised abstractly. Finally we explain the consequences of insisting on more familiar categorical behaviour.