Concurrent Realizability on Conjunctive Structures

Authors Emmanuel Beffara , Félix Castro , Mauricio Guillermo , Étienne Miquey

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Author Details

Emmanuel Beffara
  • Univ. Grenoble Alpes, CNRS, Grenoble INP, LIG, 38000 Grenoble, France
Félix Castro
  • IRIF, Université Paris Cité, France
  • IMERL, Facultad de Ingeniería, Universidad de la República, Montevideo, Uruguay
Mauricio Guillermo
  • IMERL, Facultad de Ingeniería, Universidad de la República, Montevideo, Uruguay
Étienne Miquey
  • Aix-Marseille Université, CNRS, I2M, Marseille, France

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Emmanuel Beffara, Félix Castro, Mauricio Guillermo, and Étienne Miquey. Concurrent Realizability on Conjunctive Structures. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 28:1-28:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


This work aims at exploring the algebraic structure of concurrent processes and their behavior independently of a particular formalism used to define them. We propose a new algebraic structure called conjunctive involutive monoidal algebra (CIMA) as a basis for an algebraic presentation of concurrent realizability, following ideas of the algebrization program already developed in the realm of classical and intuitionistic realizability. In particular, we show how any CIMA provides a sound interpretation of multiplicative linear logic. This new structure involves, in addition to the tensor and the orthogonal map, a parallel composition. We define a reference model of this structure as induced by a standard process calculus and we use this model to prove that parallel composition cannot be defined from the conjunctive structure alone.

Subject Classification

ACM Subject Classification
  • Theory of computation → Process calculi
  • Theory of computation → Proof theory
  • Theory of computation → Linear logic
  • Realizability
  • Process Algebras
  • Concurrent Processes
  • Linear Logic


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