The failure of cut-elimination in cyclic proof for first-order logic with inductive definitions-Reference-Cited by-同舟云学术

The failure of cut-elimination in cyclic proof for first-order logic with inductive definitions

Published:2023-12-07 Issue: Volume: Page:
ISSN:0955-792X
Container-title:Journal of Logic and Computation
language:en
Short-container-title:

Author:

Oda Yukihiro¹,Brotherston James²,Tatsuta Makoto¹

Affiliation:

1. Department of Informatics , The Graduate University for Advanced Studies, Chiyoda-ku, 101-8430, Tokyo, Japan

2. Department of Computer Science , University College London, Gower Street, WC1E 6BT, London, United Kingdom

Abstract

Abstract A cyclic proof system is a proof system whose proof figure is a tree with cycles. The cut-elimination in a proof system is fundamental. It is conjectured that the cut-elimination in the cyclic proof system for first-order logic with inductive definitions does not hold. This paper shows that the conjecture is correct by giving a sequent not provable without the cut rule but provable in the cyclic proof system.

Publisher

Oxford University Press (OUP)

Subject

Logic,Hardware and Architecture,Arts and Humanities (miscellaneous),Software,Theoretical Computer Science

Link

https://academic.oup.com/logcom/advance-article-pdf/doi/10.1093/logcom/exad068/54092828/exad068.pdf

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