Work

Intuitionistic Gödel-Löb without Sharps

Year: 2025

Type: article

Abstract: Das, van der Giessen, and Marin recently introduced \(\mathsf{IGL}\) , an intuitionistic version of Gödel-Löb logic. Their proof systems involves ill-founded proofs with a progressiveness condition. Their completeness proof uses the principle of \(\Sigma^{1}_{1}\) -determinacy; which is not provable in \(\mathsf{ZFC}\) . We define a cyclic proof system for \(\mathsf{IGL}\) and give a proof of its completeness theorem avoiding \(\Sigma^{1}_{1}\) -determinacy.

Source: ACM Transactions on Computational Logic

DOI: 10.1145/3748649

Authors: Juan P. Aguilera, Leonardo Pacheco

Institutions: TU Wien, Institute of Science Tokyo

Language: English

Topic: Logic, Reasoning, and Knowledge

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: bronze

Funder: Austrian Science Fund

Award: Borel Determinacy from Proofs