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: https://drops.dagstuhl.de/opus/volltexte/2022/16777/
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From, Asta Halkjær

A Succinct Formalization of the Completeness of First-Order Logic

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LIPIcs-TYPES-2021-8.pdf (0.8 MB)


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}
}

Keywords: First-Order Logic, Completeness, Isabelle/HOL
Collection: 27th International Conference on Types for Proofs and Programs (TYPES 2021)
Issue Date: 2022
Date of publication: 04.08.2022
Supplementary Material: Software (Formalization (stable)): https://isa-afp.org/entries/FOL_Axiomatic.html
Software (Formalization (latest)): https://devel.isa-afp.org/entries/FOL_Axiomatic.html


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