On Conflict-Driven Reasoning

Automated formal methods and automated reasoning are interconnected, as formal methods generate reasoning problems and incorporate reasoning techniques. For example, formal methods tools employ reasoning engines to nd solutions of sets of constraints, or proofs of conjectures. From a reasoning perspective, the expressivity of the logical language is often directly proportional to the di culty of the problem. In propositional logic, Con ict-Driven Clause Learning (CDCL) is one of the key features of state-of-theart satis ability solvers. The idea is to restrict inferences to those needed to explain con icts, and use con icts to prune a backtracking search. A current research direction in automated reasoning is to generalize this notion of con ict-driven satis ability to a paradigm of con ict-driven reasoning in rst-order theories for satisability modulo theories and assignments, and even in full rstorder logic for generic automated theorem proving. While this is a promising and exciting lead, it also poses formidable challenges.