We formalize in Isabelle/HOL soundness and completeness of a one-sided sequent calculus for first-order logic. The completeness is shown via a translation from a semantic tableau calculus, whose completeness proof we base on the theory entry “First-Order Logic According to Fitting” by Berghofer in the Archive of Formal Proofs (AFP). The calculi and proof techniques are taken from Ben-Ari’s textbook Mathematical Logic for Computer Science (Springer 2012). We thereby demonstrate that Berghofer’s approach works not only for natural deduction but constitutes a framework for mechanically-checked completeness proofs for a range of proof systems.
|Title of host publication||Proceedings of the 36th Italian Conference on Computational Logic|
|Publication status||Published - 2021|
|Event||36th Italian Conference on Computational Logic - Centro Sant’Elisabetta, Parma, Italy|
Duration: 7 Sep 2021 → 9 Sep 2021
|Conference||36th Italian Conference on Computational Logic|
|Period||07/09/2021 → 09/09/2021|
|Series||CEUR Workshop Proceedings|