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Summary: Compact Propositional Encoding of First-Order Theories
Deepak Ramachandran and Eyal Amir
Computer Science Department
University of Illinois at Urbana-Champaign
Urbana, IL 61801, USA
{dramacha,eyal}@cs.uiuc.edu
Abstract
In this paper we present polynomial-time algorithms that
translate First-Order Logic (FOL) theories to smaller propo-
sitional encodings than achievable before in polynomial time.
For example, we can sometimes reduce the number of propo-
sitions to O(|P| + |C|), or O(|P|k
· log |P|), for |P| predi-
cates of arity k and |C| constant symbols. The guarantee de-
pends on availability of some graphical structure in the FOL
representation. Our algorithms accept all FOL theories, and
preserve soundness and completeness (sometimes requiring
the Domain Closure Assumption). Our experiments show
significant speedup in inference with a SAT solver on real-
world problems. Our results address a common approach
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