Email Gateway (Oct 30 2024 at 12:19): Email Gateway (Oct 30 2024 at 12:19):From: Dmitriy Traytel <traytel@di.ku.dk>
Dear all,
Building on the previously announced library, but also many other AFP entries, such as the saturation framework, first-order terms and KBO, Martin Desharnais and Balazs Toth, prove an impressive result: the completeness of the superposition calculus. This is the second formalization of this result in the AFP (after Peltier’s https://www.isa-afp.org/entries/SuperCalc.html). The authors’ ITP’24 paper (https://doi.org/10.4230/LIPICS.ITP.2024.12) details the differences.
A Modular Formalization of Superposition
by Martin Desharnais and Balazs Toth
Superposition is an efficient proof calculus for reasoning about first-order logic with equality that is implemented in many automatic theorem provers. It works by saturating the given set of clauses and is refutationally complete, meaning that if the set is inconsistent, the saturation will contain a contradiction. In this formalization, we restructured the completeness proof to cleanly separate the ground (i.e., variable-free) and nonground aspects. We relied on the IsaFoR library for first-order terms and on the Isabelle saturation framework. A paper describing this formalization was published at the 15th International Conference on Interactive Theorem Proving (ITP 2024).
https://www.isa-afp.org/entries/Superposition_Calculus.html
Enjoy!
Dmitriy
Last updated: Jan 04 2025 at 20:18 UTC