Dependency Schemes in QBF Calculi: Semantics and Soundness

We study the parametrization of QBF resolution calculi by dependency schemes. One of the main problems in this area is to understand for which dependency schemes the resulting calculi are sound. Towards this end we propose a semantic framework for variable independence based on ‘exhibition’ by QBF models, and use it to define a property of dependency schemes called full exhibition. We prove that all CDCL-based resolution calculi, including Q-resolution, universal and long-distance Q-resolution, are sound when parametrized by a fully exhibited dependency scheme. To illustrate proof of concept, we show that the standard dependency scheme is fully exhibited.