Constraint Learning for Non-confluent Proof Search

Abstract

Proof search in non-confluent tableau calculi, such as the connection tableau calculus, suffers from excess backtracking, but simple restrictions on backtracking are incomplete. We adopt constraint learning to reduce backtracking in the classical first-order connection calculus, while retaining completeness. An initial constraint learning language for connection-driven search is iteratively refined to greatly reduce backtracking in practice. The approach may be useful for proof search in other non-confluent tableau calculi.