The NP Search Problems of Frege and Extended Frege Proofs-Reference-Cited by-同舟云学术

The NP Search Problems of Frege and Extended Frege Proofs

Published:2017-04-30 Issue:2 Volume:18 Page:1-19
ISSN:1529-3785
Container-title:ACM Transactions on Computational Logic
language:en
Short-container-title:ACM Trans. Comput. Logic

Author:

Beckmann Arnold¹,Buss Sam²^ORCID

Affiliation:

1. Swansea University, Swansea, UK

2. University of California, San Diego, La Jolla, CA, USA

Abstract

We study consistency search problems for Frege and extended Frege proofs—namely the NP search problems of finding syntactic errors in Frege and extended Frege proofs of contradictions. The input is a polynomial time function, or an oracle, describing a proof of a contradiction; the output is the location of a syntactic error in the proof. The consistency search problems for Frege and extended Frege systems are shown to be many-one complete for the provably total NP search problems of the second-order bounded arithmetic theories U 1 2 and V 1 2 , respectively.

Funder

NSF

Simons Foundation Fellowship

Publisher

Association for Computing Machinery (ACM)

Subject

Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science

Link

https://dl.acm.org/doi/pdf/10.1145/3060145

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