Affiliation:
1. Saarland University , Saarland Informatics Campus, Saarbrücken, Germany and Munich Center for Mathematical Philosophy, LMU Munich, Munich, Germany
2. Saarland University , Saarland Informatics Campus, Saarbrücken, Germany
Abstract
Abstract
Artemov and Protopopescu proposed intuitionistic epistemic logic (IEL) to capture an intuitionistic conception of knowledge. By establishing completeness, they provided the base for a meta-theoretic investigation of IEL, which was continued by Krupski with a proof of cut-elimination, and Su and Sano establishing semantic cut-elimination and the finite model property. However, no analysis of these results in a constructive meta-logic has been conducted, arguably impeding the intuitionistic justification of IEL. We aim to close this gap and investigate IEL in the constructive-type theory of the Coq proof assistant. Concretely, we present a constructive and mechanised completeness proof for IEL, employing a syntactic decidability proof based on cut-elimination to constructivise the ideas from the literature. Following Su and Sano, we then also give constructive versions of semantic cut-elimination and the finite model property. Given our constructive and mechanised setting, all these results now bear executable algorithms. Our particular strategy to establish constructive completeness exploiting syntactic decidability can be used for similar modal logics, which we illustrate with the examples of the classical modal logics K, D and T. For modal logics including the four axioms, however, the method seems not to apply immediately.
Publisher
Oxford University Press (OUP)
Subject
Logic,Hardware and Architecture,Arts and Humanities (miscellaneous),Software,Theoretical Computer Science
Cited by
1 articles.
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1. A Mechanised and Constructive Reverse Analysis of Soundness and Completeness of Bi-intuitionistic Logic;Proceedings of the 13th ACM SIGPLAN International Conference on Certified Programs and Proofs;2024-01-09