A Sequent Calculus Prover for First-Order Logic with Functions

Asta Halkjær From 🌐 and Frederik Krogsdal Jacobsen 🌐

January 31, 2022

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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

Session FOL_Seq_Calc2

Depends on

Cite

× 
@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},
}
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