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BV and Pomset Logic Are Not the Same

Authors Lê Thành Dũng (Tito) Nguyễn , Lutz Straßburger



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Lê Thành Dũng (Tito) Nguyễn
  • CNRS & IRISA, Rennes, France
Lutz Straßburger
  • Inria Saclay & École Polytechnique, Palaiseau, France

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Lê Thành Dũng (Tito) Nguyễn and Lutz Straßburger. BV and Pomset Logic Are Not the Same. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 32:1-32:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.CSL.2022.32

Abstract

BV and pomset logic are two logics that both conservatively extend unit-free multiplicative linear logic by a third binary connective, which (i) is non-commutative, (ii) is self-dual, and (iii) lies between the "par" and the "tensor". It was conjectured early on (more than 20 years ago), that these two logics, that share the same language, that both admit cut elimination, and whose connectives have essentially the same properties, are in fact the same. In this paper we show that this is not the case. We present a formula that is provable in pomset logic but not in BV.

Subject Classification

ACM Subject Classification
  • Theory of computation → Linear logic
  • Theory of computation → Proof theory
Keywords
  • proof nets
  • deep inference
  • pomset logic
  • system BV
  • cographs
  • dicographs
  • series-parallel orders

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