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.FSTTCS.2022.35
URN: urn:nbn:de:0030-drops-174272
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17427/
Go to the corresponding LIPIcs Volume Portal

De, Abhishek ; Jafarrahmani, Farzad ; Saurin, Alexis

Phase Semantics for Linear Logic with Least and Greatest Fixed Points

pdf-format:
LIPIcs-FSTTCS-2022-35.pdf (0.9 MB)

Abstract

The truth semantics of linear logic (i.e. phase semantics) is often overlooked despite having a wide range of applications and deep connections with several denotational semantics. In phase semantics, one is concerned about the provability of formulas rather than the contents of their proofs (or refutations). Linear logic equipped with the least and greatest fixpoint operators (μMALL) has been an active field of research for the past one and a half decades. Various proof systems are known viz. finitary and non-wellfounded, based on explicit and implicit (co)induction respectively.
In this paper, we extend the phase semantics of multiplicative additive linear logic (a.k.a. MALL) to μMALL with explicit (co)induction (i.e. μMALL^{ind}). We introduce a Tait-style system for μMALL called μMALL_ω where proofs are wellfounded but potentially infinitely branching. We study its phase semantics and prove that it does not have the finite model property.

BibTeX - Entry

@InProceedings{de_et_al:LIPIcs.FSTTCS.2022.35,
  author =	{De, Abhishek and Jafarrahmani, Farzad and Saurin, Alexis},
  title =	{{Phase Semantics for Linear Logic with Least and Greatest Fixed Points}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{35:1--35:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17427},
  URN =		{urn:nbn:de:0030-drops-174272},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.35},
  annote =	{Keywords: Linear logic, fixed points, phase semantics, closure ordinals, cut elimination}
}

Keywords: Linear logic, fixed points, phase semantics, closure ordinals, cut elimination
Collection: 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)
Issue Date: 2022
Date of publication: 14.12.2022

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI