Verified completeness in Henkin-style for intuitionistic propositional logic

In Bruno Bentzen, Beishui Liao, Davide Liga, Reka Markovich, Bin Wei, Minghui Xiong & Tianwen Xu (eds.), Logics for AI and Law: Joint Proceedings of the Third International Workshop on Logics for New-Generation Artificial Intelligence and the International Workshop on Logic, AI and Law, September 8-9 and 11-12, 2023, Hangzhou. College Publications. pp. 36-48 (2023)
  Copy   BIBTEX

Abstract

This paper presents a formalization of the classical proof of completeness in Henkin-style developed by Troelstra and van Dalen for intuitionistic logic with respect to Kripke models. The completeness proof incorporates their insights in a fresh and elegant manner that is better suited for mechanization. We discuss details of our implementation in the Lean theorem prover with emphasis on the prime extension lemma and construction of the canonical model. Our implementation is restricted to a system of intuitionistic propositional logic with implication, conjunction, disjunction, and falsity given in terms of a Hilbert-style axiomatization. As far as we know, our implementation is the first verified Henkin-style proof of completeness for intuitionistic logic following Troelstra and van Dalen's method in the literature.

Other Versions

No versions found

Links

PhilArchive

External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

A Henkin-style completeness proof for the pure implicational calculus.George F. Schumm - 1975 - Notre Dame Journal of Formal Logic 16 (3):402-404.
Completeness and incompleteness for intuitionistic logic.Charles Mccarty - 2008 - Journal of Symbolic Logic 73 (4):1315-1327.
Reverse Mathematics and Completeness Theorems for Intuitionistic Logic.Takeshi Yamazaki - 2001 - Notre Dame Journal of Formal Logic 42 (3):143-148.

Analytics

Added to PP
2023-10-19

Downloads
379 (#67,490)

6 months
167 (#21,968)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Huayu Guo
Zhejiang University
Bruno Bentzen
Zhejiang University

Citations of this work

No citations found.

Add more citations

References found in this work

Constructivism in Mathematics: An Introduction.A. S. Troelstra & Dirk Van Dalen - 1988 - Amsterdam: North Holland. Edited by D. van Dalen.

Add more references