License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2022.22
URN: urn:nbn:de:0030-drops-163037
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Acclavio, Matteo ; Horne, Ross ; Mauw, Sjouke ; Stra├čburger, Lutz

A Graphical Proof Theory of Logical Time

LIPIcs-FSCD-2022-22.pdf (1 MB)


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.

BibTeX - Entry

  author =	{Acclavio, Matteo and Horne, Ross and Mauw, Sjouke and Stra{\ss}burger, Lutz},
  title =	{{A Graphical Proof Theory of Logical Time}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{22:1--22:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-163037},
  doi =		{10.4230/LIPIcs.FSCD.2022.22},
  annote =	{Keywords: proof theory, causality, deep inference}

Keywords: proof theory, causality, deep inference
Collection: 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)
Issue Date: 2022
Date of publication: 28.06.2022

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