Resolution and Clause Learning for Multi-Valued CNF Formulas

Conflict-directed clause learning (CDCL) is the basis of SAT solvers with impressive performance on many problems. CDCL with restarts (CDCL-R) has been shown to have essentially the same reasoning power as unrestricted resolution (formally, they p-Simulate each other). We show that this property generalizes to multi-valued CNF formulas. In particular, for Signed (or Multi-Valued) CNF formulas, and Regular Formulas, we show that a natural generalization of CDCL-R to these logics has essentially the same reasoning power as natural generalizations of resolution from the literature. These formulas are possible reduction targets for a number of multi-valued logics, and thus a possible basis for efficient reasoning systems for these logics.