Lemma Learning in the Model Evolution Calculus

Abstract

The Model Evolution (ME) Calculus is a proper lifting to first-order logic of the DPLL procedure, a backtracking-based search procedure for propositional satisfiability. Analogously to DPLL, the ME calculus is based on the idea of incrementally building a model of the input formula by alternating constraint propagation steps with non-deterministic decision steps. One of the major conceptual improvements over basic DPLL is lemma learning, a mechanism for generating new formulae that prevent later in the search combinations of decision steps guaranteed to lead to failure.
We introduce three lemma generation methods for ME proof procedures, with various degrees of power, effectiveness in reducing search, and computational overhead. Even if formally correct, each of these methods presents complications that do not exist at the propositional level but need to be addressed for learning to be effective in practice for ME. We discuss some of these issues and then present initial experimental results on the performance of an implementation within Darwin of the three learning procedures.