Entailment vs. Verification for Partial-assignment Satisfiability and Enumeration
This addresses a foundational ambiguity in SAT solving for researchers and practitioners, though it is incremental as it clarifies existing concepts rather than introducing a new method.
The paper tackles the lack of a universally-agreed definition of formula satisfaction by partial assignments in SAT-related problems, showing that the entailment notion, though harder to check, has better theoretical properties and can improve the efficiency and effectiveness of enumeration procedures compared to the verification notion commonly used.
Many procedures for SAT-related problems, in particular for those requiring the complete enumeration of satisfying truth assignments, rely their efficiency and effectiveness on the detection of (possibly small) partial assignments satisfying an input formula. Surprisingly, there seems to be no unique universally-agreed definition of formula satisfaction by a partial assignment in the literature. In this paper we analyze in deep the issue of satisfaction by partial assignments, raising a flag about some ambiguities and subtleties of this concept, and investigating their practical consequences. We identify two alternative notions that are implicitly used in the literature, namely verification and entailment, which coincide if applied to CNF formulas but differ and present complementary properties if applied to non-CNF or to existentially-quantified formulas. We show that, although the former is easier to check and as such is implicitly used by most current search procedures, the latter has better theoretical properties, and can improve the efficiency and effectiveness of enumeration procedures.