Date: 18 Sep 2002

Reasoning with Infinite Stable Models II: Disjunctive Programs

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The class of finitary normal logic programs—identified recently, in [1]—makes it possible to reason effectively with function symbols, recursion, and infinite stable models. These features may lead to a full integration of the standard logic programming paradigm with the answer set programming paradigm. For all finitary programs, ground goals are decidable, while nonground goals are semidecidable. Moreover, the existing engines (that currently accept only much more restricted programs [11,7]) can be extended to handle finitary programs by replacing their front-ends and keeping their core inference mechanism unchanged. In this paper, the theory of finitary normal programs is extended to disjunctive programs. More precisely, we introduce a suitable generalization of the notion of finitary program and extend all the results of [1] to this class. For this purpose, a consistency result by Fages is extended from normal programs to disjunctive programs. We also correct an error occurring in [1].