TY - GEN
T1 - Constructive and Mechanised Meta-Theory of Intuitionistic Epistemic Logic
AU - Hagemeier, Christian
AU - Kirst, Dominik
N1 - Publisher Copyright:
© 2022, Springer Nature Switzerland AG.
PY - 2022/1/1
Y1 - 2022/1/1
N2 - 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, to the best of our knowledge, no analysis of these results in a constructive meta-logic has been conducted. 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. We expect that our methods used for mechanising cut-elimination and decidability also extend to other modal logics (and have verified this observation for the classical modal logic K).
AB - 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, to the best of our knowledge, no analysis of these results in a constructive meta-logic has been conducted. 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. We expect that our methods used for mechanising cut-elimination and decidability also extend to other modal logics (and have verified this observation for the classical modal logic K).
KW - Completeness
KW - Constructivisation
KW - Epistemic logic
UR - http://www.scopus.com/inward/record.url?scp=85122030142&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-93100-1_7
DO - 10.1007/978-3-030-93100-1_7
M3 - Conference contribution
AN - SCOPUS:85122030142
SN - 9783030930998
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 90
EP - 111
BT - Logical Foundations of Computer Science - International Symposium, LFCS 2022, Proceedings
A2 - Artemov, Sergei
A2 - Nerode, Anil
PB - Springer Science and Business Media Deutschland GmbH
T2 - International Symposium on Logical Foundations of Computer Science, LFCS 2022
Y2 - 10 January 2022 through 13 January 2022
ER -