Email Gateway (Oct 04 2021 at 23:55): Email Gateway (Oct 04 2021 at 23:55):From: Gerwin Klein <kleing@unsw.edu.au>
A new entry is available in the AFP:
Soundness and Completeness of an Axiomatic System for First-Order Logic
by Asta Halkjær From
This work is a formalization of the soundness and completeness of an axiomatic system for first-order logic. The proof system is based on System Q1 by Smullyan and the completeness proof follows his textbook "First-Order Logic" (Springer-Verlag 1968). The completeness proof is in the Henkin style where a consistent set is extended to a maximal consistent set using Lindenbaum's construction and Henkin witnesses are added during the construction to ensure saturation as well. The resulting set is a Hintikka set which, by the model existence theorem, is satisfiable in the Herbrand universe.
https://www.isa-afp.org/entries/FOL_Axiomatic.html
Enjoy!
Gerwin
Last updated: Jan 04 2025 at 20:18 UTC