Conflict nets Efficient locally canonical MALL proof nets

Proof nets for MLL (unit-free multiplicative linear logic) and ALL (unit-free additive linear logic) are graphical abstractions of proofs which are efficient (proofs translate in linear time) and canonical (invariant under rule commutation). This paper solves a three-decade open problem: are there e...

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Bibliographic Details
Published in:Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science pp. 437 - 446
Main Authors: Hughes, Dominic, Heijltjes, Willem
Format: Conference Proceeding
Language:English
Published: New York, NY, USA ACM 05.07.2016
Series:ACM Conferences
Subjects:
Computing methodologies > Symbolic and algebraic manipulation > Symbolic and algebraic algorithms > Theorem proving algorithms
Theory of computation > Logic > Proof theory
multiplicative-additive linear logic
linear logic
MALL
proof nets
ISBN:9781450343916, 1450343910
Online Access:Get full text
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Summary:Proof nets for MLL (unit-free multiplicative linear logic) and ALL (unit-free additive linear logic) are graphical abstractions of proofs which are efficient (proofs translate in linear time) and canonical (invariant under rule commutation). This paper solves a three-decade open problem: are there efficient canonical proof nets for MALL (unit-free multiplicative-additive linear logic)? Honouring MLL and ALL canonicity, in which all commutations are strictly local proof-tree rewrites, we define local canonicity for MALL: invariance under local rule commutation. We present new proof nets for MALL, called conflict nets, which are both efficient and locally canonical.
ISBN:9781450343916
1450343910
DOI:10.1145/2933575.2934559