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A Graphical Proof Theory of Logical Time

Authors Matteo Acclavio , Ross Horne , Sjouke Mauw , Lutz Straßburger

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Matteo Acclavio
  • Department of Computer Science, University of Luxembourg, Luxembourg
Ross Horne
  • Department of Computer Science, University of Luxembourg, Luxembourg
Sjouke Mauw
  • Department of Computer Science, University of Luxembourg, Luxembourg
Lutz Straßburger
  • Inria-Saclay, Palaiseau, France

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Matteo Acclavio, Ross Horne, Sjouke Mauw, and Lutz Straßburger. A Graphical Proof Theory of Logical Time. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 22:1-22:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.FSCD.2022.22

Abstract

Logical time is a partial order over events in distributed systems, constraining which events precede others. Special interest has been given to series-parallel orders since they correspond to formulas constructed via the two operations for "series" and "parallel" composition. For this reason, series-parallel orders have received attention from proof theory, leading to pomset logic, the logic BV, and their extensions. However, logical time does not always form a series-parallel order; indeed, ubiquitous structures in distributed systems are beyond current proof theoretic methods. In this paper, we explore how this restriction can be lifted. We design new logics that work directly on graphs instead of formulas, we develop their proof theory, and we show that our logics are conservative extensions of the logic BV.

Subject Classification

ACM Subject Classification
  • Theory of computation → Proof theory
  • Theory of computation → Linear logic
  • Theory of computation → Process calculi
Keywords
  • proof theory
  • causality
  • deep inference

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