In this paper, we propose fuzzy pD* semantics which generalizes pD* semantics to reason over fuzzy RDF data using OWL vocabulary. We first define the notions of fuzzy RDF graph and fuzzy pD* interpretation. We then present a set of fuzzy pD*entailment rules and define the Best Degree Bound (BDB) of a triple derived from a fuzzy RDF graph. We show the existence of the BDB of an arbitrary triple. After that, we generalize the partial and full pD* closures to obtain the BDBs of derived triples. We show that the partial fuzzy closure exists and can be computed within polynomial time. Finally, we prove soundness and completeness results for the entailment relation. We also prove that the consistency checking is in P, the entailment is NP-complete, and in P if the target fuzzy RDF graph is ground. Therefore, extending the pD* semantics with fuzzy semantics does not increase the computational complexity.
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