A Formalization of the SCL(FOL) Calculus: Simple Clause Learning for First-Order Logic

Martin Desharnais 📧

April 20, 2023

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.


This Isabelle/HOL formalization covers the unexecutable specification of Simple Clause Learning for first-order logic without equality: SCL(FOL). The main results are formal proofs of soundness, non-redundancy of learned clauses, termination, and refutational completeness. Compared to the unformalized version, the formalized calculus is simpler, a number of results were generalized, and the non-redundancy statement was strengthened. We found and corrected one bug in a previously published version of the SCL Backtrack rule. Compared to related formalizations, we introduce a new technique for showing termination based on non-redundant clause learning.


BSD License


Session Simple_Clause_Learning