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The Consistency of OWL Full (with proofs)
Carroll, Jeremy; Turner, Dave
Keyword(s): OWL, semantics, Herbrand, OWL Full
Abstract: We show that OWL1 Full without the comprehension principles is consistent, and does not break most RDF graphs that do not use the OWL vocabulary. We discuss the role of the comprehension principles in OWL semantics, and how to maintain the relationship between OWL Full and OWL DL by reinterpreting the comprehension principles as permitted steps when checking an entailment, rather than as model theoretic principles constraining the universe of interpretation. Starting with such a graph we build a Herbrand model, using, amongst other things, an RDFS ruleset, and syntactic analogs of the semantic "if and only if" conditions on the RDFS and OWL vocabulary. The ordering of these steps is carefully chosen, along with some initialization data, to break the cyclic dependencies between the various conditions. The normal Herbrand interpretation of this graph as its own model then suffices. The main result follows by using an empty graph in this construction. We discuss the relevance of our results, both to OWL2, and more generally to a future revision of the Semantic Web recommendations. This longer version contains the proofs.
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