### Abstract

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. Paper: doi.org/10.4230/LIPIcs.TYPES.2021.8.

### License

BSD License

### Topics

- Logic/General logic/Classical first-order logic
- Logic/Proof theory

### Session FOL_Axiomatic

- FOL_Axiomatic
- FOL_Axiomatic_Variant

## Cite

×

FOL_Axiomatic-AFP

    @article{FOL_Axiomatic-AFP,
      author  = {Asta Halkjær From},
      title   = {Soundness and Completeness of an Axiomatic System for First-Order Logic},
      journal = {Archive of Formal Proofs},
      month   = {September},
      year    = {2021},
      note    = {\url{https://isa-afp.org/entries/FOL_Axiomatic.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

Download

## Download

× Download latest

Older releases:

- Sep 13, 2023 : Isabelle2023
- Oct 27, 2022 : Isabelle2022
- Dec 14, 2021 : Isabelle2021-1
- Oct 5, 2021 : Isabelle2021