Coherence for Sharing Proof Nets
نویسندگان
چکیده
Sharing graphs are an implementation of linear logic proofnets in such a way that their reduction never duplicate a redex. In their usual formulations, proof-nets present a problem of coherence: if the proof-net N reduces by standard cutelimination to N’, then, by reducing the sharing graph of N we do not obtain the sharing graph of N’. We solve this problem by changing the way the information is coded into sharing graphs and introducing a new reduction rule (absorption). The rewriting system is confluent and terminating. The proof of this fact exploits an algebraic semantics for sharing graphs. Comments University of Pennsylvania Institute for Research in Cognitive Science Technical Report No. IRCS-97-03. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/ircs_reports/77
منابع مشابه
On the relation between coherence semantics and multiplicative proof nets
It is known that (mix) proof nets admit a coherence semantics, computed as a set of experiments. We prove here the converse: a proof structure is shown to be a proof net whenever its set of experiments is a semantical object — a clique of the corresponding coherence space. Moreover the interpretation of atomic formulae can be restricted to a given coherent space with four tokens in its web. Thi...
متن کاملProfunctor Semantics for Linear Logic
Linear logic is a sort of “resource-aware” logic underlying intuitionistic logic. Investigations into the proof theory of this logic typically revolve around proof nets, certain two-dimensional graphical representations of proofs. Where sequent calculus deductions enforce arbitrary distinctions between proofs and complicate these investigations, proof nets represent sequent calculus deductions ...
متن کاملCoherence for sharing proof - nets 1
aDipartimento di Scienze dell’Informazione Università Roma I, ‘La Sapienza’ Via Salaria, 113 I-00198, Roma, Italy Email: [email protected] bDipartimento di Matematica, Università di Trento Via Sommarive 14 I-38050, Povo-Trento, Italy email: [email protected] cDipartimento di Matematica e Informatica, Università di Udine Via delle Scienze, 206 I-33100, Udine, Italy email: martini@di...
متن کاملLinear Logic Without Boxes
Girard's original deenition of proof nets for linear logic involves boxes. The box is the unit for erasing and duplicating fragments of proof nets. It imposes synchronization, limits sharing, and impedes a completely local view of computation. Here we describe an implementation of proof nets without boxes. Proof nets are translated into graphs of the sort used in optimal calculus implementation...
متن کاملProofs, denotational semantics and observational equivalences in Multiplicative Linear Logic
We study full completeness and syntactical separability of MLL proof nets with the mix rule. The general method we use consists first in addressing the two questions in the less restrictive framework of proof structures, and then in adapting the results to proof nets. At the level of proof structures, we find a semantical characterization of their interpretations in relational semantics, and we...
متن کامل