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F. Slivovsky, S. Szeider:
"Soundness of Q-resolution with dependency schemes";
Theoretical Computer Science, 612 (2016), 83 - 101.

Q-resolution and Q-term resolution are proof systems for quantified Boolean formulas (QBFs). We introduce generalizations of these proof systems named Q(D)-resolution and Q(D)-term resolution. Q(D)-resolution and Q(D)-term resolution are parameterized by a dependency scheme Dand use more powerful ∀-reduction and ∃-reduction rules, respectively. We show soundness of these systems for particular dependency schemes: we prove (1)soundness of Q(D)-resolution parameterized by the reflexive resolution-path dependency scheme, and (2)soundness of Q(D)-term resolution parameterized by the resolution-path dependency scheme. These results entail soundness of the proof systems used for certificate generation in the state-of-the-art solver DepQBF.

http://dx.doi.org/10.1016/j.tcs.2015.10.020

http://publik.tuwien.ac.at/files/publik_253433.pdf