On Propositional QBF Expansions and Q-Resolution

摘要

Over the years, proof systems for propositional satisfiability (SAT) have been extensively studied. Recently, proof systems for quantified Boolean formulas (QBFs) have also been gaining attention. Q-resolution is a calculus enabling producing proofs from DPLL-based QBF solvers. While DPLL has become a dominating technique for SAT, QBF has been tackled by other complementary and competitive approaches. One of these approaches is based on expanding variables until the formula contains only one type of quantifier; upon which a SAT solver is invoked. This approach motivates the theoretical analysis carried out in this paper. We focus on a two phase proof system, which expands the formula in the first phase and applies propositional resolution in the second. Fragments of this proof system are defined and compared to Q-resolution.