Beyond Q-Resolution and Prenex Form: A Proof System for Quantified Constraint Satisfaction
This work addresses a foundational challenge in computational logic and constraint satisfaction, offering a theoretical framework for verifying QCSP falsity, but it appears incremental as it builds on existing Q-resolution methods.
The authors tackled the problem of certifying falsity in quantified constraint satisfaction problems (QCSP) by presenting a new proof system that generalizes Q-resolution and handles sentences not in prenex form, enabling tractability results for QCSP instances.
We consider the quantified 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 quantification, 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.