Solving Satisfiability in Ground Logic with Equality by Efficient Conversion to Propositional Logic

Ground Logic with Equality (GL) is a subset of First-Order Logic (FOL) in which functions or quantifiers are excluded, but equality is preserved. We argue about GL’s unique position (in terms of expressiveness and ease of decidability) between FOL and Propositional Logic (PL). We aim to solve satisfiability (SAT) problems formulated in GL by converting them into PL using a satisfiability-preserving conversion algorithms, and running a general SAT solver on the resulting PL Knowledge Base (KB). We introduce two conversion algorithms, with the latter utilizing the former as a subroutine, and prove their correctness that is, that the translation preserves satisfiability. The main contribution of this work is in utilizing input fragmentation to yield PL KBs that are smaller than possible prior to our work, thus resulting in the ability to solve GL SAT problems faster than was possible before.