### Abstract

We formalize an automated theorem prover for first-order logic with functions. The proof search procedure is based on sequent calculus and we verify its soundness and completeness using the Abstract Soundness and Abstract Completeness theories. Our analytic completeness proof covers both open and closed formulas. Since our deterministic prover considers only the subset of terms relevant to proving a given sequent, we do so as well when building a countermodel from a failed proof. We formally connect our prover with the proof system and semantics of the existing SeCaV system. In particular, the prover's output can be post-processed in Haskell to generate human-readable SeCaV proofs which are also machine-verifiable proof certificates. Paper: doi.org/10.4230/LIPIcs.ITP.2022.13.

### License

BSD License

### Topics

- Logic/General logic/Classical first-order logic
- Logic/Proof theory
- Logic/General logic/Mechanization of proofs

### Session FOL_Seq_Calc2

- SeCaV
- Sequent1
- Sequent_Calculus_Verifier
- Prover
- Export
- ProverLemmas
- Hintikka
- EPathHintikka
- Usemantics
- Countermodel
- Soundness
- Completeness
- Results

### Depends on

- Abstract Completeness
- Abstract Soundness
- Collections Framework
- A Sequent Calculus for First-Order Logic

### Auto-related entries

- Pratt’s Primality Certificates
- Separata: Isabelle tactics for Separation Algebra

## Cite

×

FOL_Seq_Calc2-AFP

    @article{FOL_Seq_Calc2-AFP,
      author  = {Asta Halkjær From and Frederik Krogsdal Jacobsen},
      title   = {A Sequent Calculus Prover for First-Order Logic with Functions},
      journal = {Archive of Formal Proofs},
      month   = {January},
      year    = {2022},
      note    = {\url{https://isa-afp.org/entries/FOL_Seq_Calc2.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

Download

## Download

× Download latest

Older releases:

- Sep 13, 2023 : Isabelle2023
- Oct 27, 2022 : Isabelle2022
- Feb 2, 2022 : Isabelle2021-1