Work

Syntactic Cut-Elimination for Provability Logic GL via Nested Sequents

Year: 2024

Type: article

Abstract: The cut-elimination procedure for the provability logic is known to be problematic: a Löb-like rule keeps cut-formulae intact on reduction, even in the principal case, thereby complicating the proof of termination.In this paper, we present a syntactic cut-elimination proof based on nested sequents, a generalization of sequents that allows a sequent to contain other sequents as single elements.A similar calculus was developed by Poggiolesi (2009), but there are certain ambiguities in the proof.Adopting the idea of Kushida (2020) into nested sequents, our proof does not require an extra measure on cuts or error-prone, intricate rewriting on derivations, but only straightforward inductions, thus leading to less ambiguity and confusion.

Source: Electronic Proceedings in Theoretical Computer Science

DOI: 10.4204/eptcs.415.11

Authors: Akinori Maniwa, Ryo Kashima

Institution: Tokyo Institute of Technology

Language: English

Topic: Advanced Algebra and Logic

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: Japan Society for the Promotion of Science

Award: 中間２階命題論理の研究