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Communication Dans Un Congrès Année : 2022

A Graphical Proof Theory of Logical Time

Résumé

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, seriesparallel 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.
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Dates et versions

hal-03909486 , version 1 (21-12-2022)

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Matteo Acclavio, Ross Horne, Sjouke Mauw, Lutz Straßburger. A Graphical Proof Theory of Logical Time. FSCD 2022 - 7th International Conference on Formal Structures for Computation and Deduction, Aug 2022, Haifa, Israel. ⟨10.4230/LIPIcs.FSCD.2022.22⟩. ⟨hal-03909486⟩
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