ASP-QRAT: A Conditionally Optimal Dual Proof System for ASP

Answer Set Programming (ASP) is a declarative programming approach that captures many problems in knowledge representation and reasoning. To certify an ASP solver's decision, whether the program is consistent or inconsistent, we need a certificate or proof that can be independently verified. This paper proposes the dual proof system ASP-QRAT that certifies both consistent and inconsistent ASPs. ASP-QRAT is based on a translation of ASP to QBF (Quantified Boolean Formus) and the QBF proof system QRAT as a checking format. We show that ASP-QRAT p-simulates ASP-DRUPE, an existing refutation system for inconsistent disjunctive ASPs. We show that ASP-QRAT is conditionally optimal for consistent and inconsistent ASPs, i.e., any super-polynomial lower bound on the shortest proof size of ASP-QRAT implies a major breakthrough in theoretical computer science. The case for consistent ASPs is remarkable because no analog exists in the QBF case.