Theoretical Computer Science
LO and behold! Concurrent structured processes
OOPSLA/ECOOP '90 Proceedings of the European conference on object-oriented programming on Object-oriented programming systems, languages, and applications
Logic programming in a fragment of intuitionistic linear logic
Papers presented at the IEEE symposium on Logic in computer science
Forum: a multiple-conclusion specification logic
ALP Proceedings of the fourth international conference on Algebraic and logic programming
A Non-commutative Extension of Classical Linear Logic
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
Non-commutative logic II: sequent calculus and phase semantics
Mathematical Structures in Computer Science
LINK: A Proof Environment Based on Proof Nets
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Jump from parallel to sequential proofs: multiplicatives
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Rewriting Computation and Proof
Hi-index | 0.00 |
Linesir Logic [4] has raised a lot of interest in computer research, especially because of its resource sensitive nature. One line of research studies proof construction procedures and their interpretation as computational models, in the "Logic Programming" tradition. An efficient proof search procedure, based on a proof normalization result called "Focusing", has been described in [2]. Focusing is described in terms of the sequent system of commutative Linear Logic, which it refines in two steps. It is shown here that Focusing can also be interpreted in the proof-net formalism, where it appecirs, at least in the multiplicative fragment, to be a simple refinement of the "Splitting lemma" for proof-nets. This change of perspective allows to generalize the Focusing result to (the multiplicative fragment of) any logic where the "Splitting lemma" holds. This is, in particular, the case of the Non-Commutative logic of [1], and all the computational exploitation of Focusing which has been performed in the commutative case can thus be revised and adapted to the non commutative case.