License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TYPES.2021.8
URN: urn:nbn:de:0030-drops-167771
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16777/
From, Asta Halkjær
A Succinct Formalization of the Completeness of First-Order Logic
Abstract
I succinctly formalize the soundness and completeness of a small Hilbert system for first-order logic in the proof assistant Isabelle/HOL. The proof combines and details ideas from de Bruijn, Henkin, Herbrand, Hilbert, Hintikka, Lindenbaum, Smullyan and others in a novel way, and I use a declarative style, custom notation and proof automation to obtain a readable formalization. The formalized definitions of Hintikka sets and Herbrand structures allow open and closed formulas to be treated uniformly, making free variables a non-concern. This paper collects important techniques in mathematical logic in a way suited for both study and further work.
BibTeX - Entry
@InProceedings{from:LIPIcs.TYPES.2021.8,
author = {From, Asta Halkj{\ae}r},
title = {{A Succinct Formalization of the Completeness of First-Order Logic}},
booktitle = {27th International Conference on Types for Proofs and Programs (TYPES 2021)},
pages = {8:1--8:24},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-254-9},
ISSN = {1868-8969},
year = {2022},
volume = {239},
editor = {Basold, Henning and Cockx, Jesper and Ghilezan, Silvia},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16777},
URN = {urn:nbn:de:0030-drops-167771},
doi = {10.4230/LIPIcs.TYPES.2021.8},
annote = {Keywords: First-Order Logic, Completeness, Isabelle/HOL}
}
