We extend Answer Set Programming with, possibly infinite, open domains. Since this leads, in general, to undecidable reasoning, we restrict the syntax of programs, while carefully guarding useful knowledge representation mechanisms such as negation as failure and inequalities. Reasoning with the resulting Conceptual Logic Programs can be reduced to finite, normal Answer Set Programming, for which reasoners are available. We argue that Conceptual Logic Programming is a useful tool for uniformly representing and reasoning with both ontologies and rules on the Semantic Web, as they can capture a large fragment of the OWL DL ontology language, while extending it in various aspects.
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