Extending SMT Solving with Non-Ground Clause Learning

Abstract:Quantifier instantiation is currently the main approach to non-ground SMT solving: solvers generate ground instances and solve the resulting ground SMT problems with CDCL(T)-style reasoning. When a conflict is found, conflict analysis learns only a ground clause, even though the conflict comes from instances of non-ground clauses. Yet non-ground reasoning can give exponentially shorter proofs than purely ground reasoning. We propose a calculus that consists of ground instantiations, CDCL(T)-style rules, and non-ground conflict analysis. The solver reasons on ground instances, but the resolution steps of conflict analysis are performed on their original non-ground clauses. This produces learned clauses that are typically more general than the ground conflict. With a suitable strategy, the learned clauses are even non-redundant. We also show how chronological backtracking can be included in SMT solving. Our calculus gives a common setting for CDCL(T)-style SMT solving, a range of instantiation-based procedures, and non-ground clause learning, and we prove that it simulates CDCL, SCL(FOL), SCL(T), and even Resolution.

Artificial Intelligence (cs.AI); Logic in Computer Science (cs.LO)

arXiv:2609.11509 [cs.AI]

(or arXiv:2609.11509v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2609.11509 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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