Theoretical Computer Science
Proofs and types
A decision procedure revisited: notes on direct logic, linear logic and its implementation
Theoretical Computer Science
On the &pgr;-calculus and linear logic
MFPS '92 Selected papers of the conference on Meeting on the mathematical foundations of programming semantics, part I : linear logic: linear logic
Constant-only multiplicative linear logic is NP-complete
MFPS '92 Selected papers of the conference on Meeting on the mathematical foundations of programming semantics, part I : linear logic: linear logic
Proceedings of the workshop on Advances in linear logic
Proceedings of the workshop on Advances in linear logic
Free Deduction: An Analysis of "Computations" in Classical Logic
Proceedings of the First Russian Conference on Logic Programming
Mechanizing proof theory: resource-aware logics and proof-transformations to extract implicit information
Categorical proof theory of classical propositional calculus
Theoretical Computer Science - Logic, language, information and computation
Expansion nets: proof-nets for propositional classical logic
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
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We propose a notion of symmetric reduction for a system of proof-nets for Multiplicative Affine Logic with Mix (MAL + Mix) (namely, multiplicative linear logic with the mix-rule the unrestricted weakening-rule). We prove that such a reduction has the strong normalization and Church-Rosser properties. A notion of irrelevance in a proof-net is defined and the possibility of cancelling the irrelevant parts of a proof-net without erasing the entire net is taken as one of the correctness conditions; therefore purely local cut-reductions are given, minimizing cancellation and suggesting a paradigm of "computation without garbage collection". Reconsidering Ketonen and Weyhranch's decision procedure for affine logic [15, 4], the use of the mix-rule is related to the non-determinism of classical proof-theory. The question arises, whether these features of classical cut-elimination are really irreducible to the familiar paradigm of cut-elimination for intuitionistic and linear logic.