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Summary: Solving Satisfiability in Ground Logic with
Equality by Efficient Conversion to
Propositional Logic
Igor Gammer and Eyal Amir
Department of Computer Science
University of Illinois, Urbana-Champaign
{igammer2,eyal}@uiuc.edu
Abstract 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 expres-
siveness 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 Knowl-
edge 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
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