License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2021.29
URN: urn:nbn:de:0030-drops-134632
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Kori, Mayuko ; Tsukada, Takeshi ; Kobayashi, Naoki

A Cyclic Proof System for HFL_ℕ

LIPIcs-CSL-2021-29.pdf (0.6 MB)


A cyclic proof system allows us to perform inductive reasoning without explicit inductions. We propose a cyclic proof system for HFL_ℕ, which is a higher-order predicate logic with natural numbers and alternating fixed-points. Ours is the first cyclic proof system for a higher-order logic, to our knowledge. Due to the presence of higher-order predicates and alternating fixed-points, our cyclic proof system requires a more delicate global condition on cyclic proofs than the original system of Brotherston and Simpson. We prove the decidability of checking the global condition and soundness of this system, and also prove a restricted form of standard completeness for an infinitary variant of our cyclic proof system. A potential application of our cyclic proof system is semi-automated verification of higher-order programs, based on Kobayashi et al.’s recent work on reductions from program verification to HFL_ℕ validity checking.

BibTeX - Entry

  author =	{Mayuko Kori and Takeshi Tsukada and Naoki Kobayashi},
  title =	{{A Cyclic Proof System for HFL_ℕ}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{29:1--29:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-175-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{183},
  editor =	{Christel Baier and Jean Goubault-Larrecq},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-134632},
  doi =		{10.4230/LIPIcs.CSL.2021.29},
  annote =	{Keywords: Cyclic proof, higher-order logic, fixed-point logic, sequent calculus}

Keywords: Cyclic proof, higher-order logic, fixed-point logic, sequent calculus
Collection: 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)
Issue Date: 2021
Date of publication: 13.01.2021

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