### Abstract

This work formalizes soundness and completeness of a one-sided sequent calculus for first-order logic. The completeness is shown via a translation from a complete semantic tableau calculus, the proof of which is based on the First-Order Logic According to Fitting theory. The calculi and proof techniques are taken from Ben-Ari's Mathematical Logic for Computer Science. Papers: ceur-ws.org/Vol-3002/paper7.pdf and doi.org/10.1093/logcom/exad013.

### License

BSD License

### Topics

- Logic/Proof theory

### Session FOL_Seq_Calc1

- Common
- Tableau
- Sequent
- Sequent2

### Depends on

- First-Order Logic According to Fitting

### Used by

- A Sequent Calculus Prover for First-Order Logic with Functions

### Auto-related entries

- Metatheory of Q0
- A First Complete Algorithm for Real Quantifier Elimination in Isabelle/HOL
- Soundness and Completeness of an Axiomatic System for First-Order Logic
- Relational Characterisations of Paths
- Abstract Soundness

## Cite

×

FOL_Seq_Calc1-AFP

    @article{FOL_Seq_Calc1-AFP,
      author  = {Asta Halkjær From},
      title   = {A Sequent Calculus for First-Order Logic},
      journal = {Archive of Formal Proofs},
      month   = {July},
      year    = {2019},
      note    = {\url{https://isa-afp.org/entries/FOL_Seq_Calc1.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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