Beyond Q-Resolution and Prenex Form: a Proof System for Quantified Constraint Satisfaction

Abstract

We consider the quanti fied constraint satisfaction problem (QCSP) which is to decide, given a structure and a first-order sentence (not assumed here to be in prenex form) built from conjunction and quanti fication, whether or not the sentence is true on the structure. We present a proof system for certifying the falsity of QCSP instances and develop its basic theory; for instance, we provide an algorithmic interpretation of its behavior. Our proof system places the established Q-resolution proof system in a broader context, and also allows us to derive QCSP tractability results.The author thanks Moritz Muller and Friedrich Slivovsky for useful comments. This work was supported by the Spanish project TIN2013-46181-C2-2-R, by the Basque project GIU12/26, and by the Basque grant UFI11/45