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A Decidable Class of Groundable Formulas in the General Theory of Stable Models

Last modified: 2010-04-27

#### Abstract

We present a decidable class of first-order formulas in the general theory of stable models that can be instantiated even in the presence of function constants. The notion of an argument-restricted formula presented here is a natural generalization of both the notion of an argument-restricted program and the notion of a semi-safe sentence that have been studied in different contexts. Based on this new notion, we extend the notion of safety defined by Cabalar, Pearce and Valverde to arbitrary formulas that allow function constants, and apply the result to $\raspl$ programs and programs with arbitrary aggregates, ensuring finite groundability of those programs in the presence of function constants. We also show that under a certain syntactic condition, argument-restricted formulas can be turned into argument-restricted programs.

#### Keywords

stable model semantics; answer set programming; grounding

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