Popescu, A. orcid.org/0000-0001-8747-0619 (2025) Completing Gordon’s Higher-Order Logic. In: 2025 40th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). 2025 40th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 23-26 Jun 2025, Singapore, Singapore. Institute of Electrical and Electronics Engineers, pp. 1-15. ISSN: 1043-6871.
Abstract
Mike Gordon's Higher-Order Logic (HOL) is one of the most important logical foundations for interactive theorem proving. The standard semantics of HOL, due to Andrew Pitts, employs a downward closed universe of sets, and interprets HOL's Hilbert choice operator via a global choice function on the universe. In this paper we fill a gap in the meta-theory of HOL: We provide a natural Henkin-style notion of general model corresponding to the standard models, and discover an enrichment of HOL deduction that we prove to be sound and complete w.r.t. these general models.
Metadata
| Item Type: | Proceedings Paper |
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| Authors/Creators: |
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| Copyright, Publisher and Additional Information: | © 2025 The Authors. Except as otherwise noted, this author-accepted version of a journal article published in 2025 40th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) is made available via the University of Sheffield Research Publications and Copyright Policy under the terms of the Creative Commons Attribution 4.0 International License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ |
| Keywords: | Computer science; Computational modeling; Semantics; Logic; Standards |
| Dates: |
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| Institution: | The University of Sheffield |
| Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
| Funding Information: | Funder Grant number ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL EP/V039156/1 ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL EP/X015114/1 |
| Date Deposited: | 13 Jan 2026 10:32 |
| Last Modified: | 19 Jan 2026 09:54 |
| Status: | Published |
| Publisher: | Institute of Electrical and Electronics Engineers |
| Refereed: | Yes |
| Identification Number: | 10.1109/lics65433.2025.00008 |
| Related URLs: | |
| Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:236445 |
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Filename: completingGordonHOL.pdf
Licence: CC-BY 4.0

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