A logic of non-monotonic interactions

Giovanni Boniolo, Marcello D'Agostino, Mario Piazza, Gabriele Pulcini

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, which is part of the Zsyntax project outlined in Boniolo et al. (2010) [2], we provide a proof-theoretical setting for the study of context-sensitive interactions by means of a non-monotonic conjunction operator. The resulting system is a non-associative variant of MLLpol (the multiplicative polarised fragment of Linear Logic) in which the monotonicity of interactions, depending on the context, is governed by specific devices called control sets. Following the spirit of Linear Logic, the ordinary sequent calculus presentation is also framed into a theory of proof-nets and the set of sequential proofs is shown to be sound and complete with respect to the class of corresponding proof-nets. Some possible biochemical applications are also discussed.

Original languageEnglish
Pages (from-to)52-62
Number of pages11
JournalJournal of Applied Logic
Volume11
Issue number1
DOIs
Publication statusPublished - Mar 2013

Keywords

  • Molecular biology
  • Non-associative sequent calculi
  • Non-monotonicity
  • Proof-nets
  • Substructural logics
  • Zsyntax

ASJC Scopus subject areas

  • Logic
  • Applied Mathematics

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