Safe Formulas in the General Theory of Stable Models (Preliminary Report)

Authors:
Joohyung Lee;Vladimir Lifschitz;Ravi Palla
Affiliations:
School of Computing and Informatics, Arizona State University, USA;Department of Computer Sciences, University of Texas at Austin, USA;School of Computing and Informatics, Arizona State University, USA
Venue:
ICLP '08 Proceedings of the 24th International Conference on Logic Programming
Year:
2008

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Abstract

Safe first-order formulas generalize the concept of a safe rule, which plays an important role in the design of answer set solvers. We show that any safe sentence is equivalent, in a certain sense, to the result of its grounding--to the variable-free sentence obtained from it by replacing all quantifiers with multiple conjunctions and disjunctions. It follows that a safe sentence and the result of its grounding have the same stable models, and that stable models of a safe sentence can be characterized by a formula of a simple syntactic form.