BayesOWL: Uncertainty Modeling in Semantic Web Ontologies. It is always essential but difficult to capture incomplete, partial or uncertain knowledge when using ontologies to conceptualize an application domain or to achieve semantic interoperability among heterogeneous systems. This chapter presents an on-going research on developing a framework which augments and supplements the semantic web ontology language OWL5 for representing and reasoning with uncertainty based on Bayesian networks (BN) [26], and its application in ontology mapping. This framework, named BayesOWL, has gone through several iterations since its conception in 2003 [8, 9]. BayesOWL provides a set of rules and procedures for direct translation of an OWL ontology into a BN directed acyclic graph (DAG), it also provides a method based on iterative proportional fitting procedure (IPFP) [19, 7, 6, 34, 2, 4] that incorporates available probability constraints when constructing the conditional probability tables (CPTs) of the BN. The translated BN, which preserves the semantics of the original ontology and is consistent with all the given probability constraints, can support ontology reasoning, both within and across ontologies as Bayesian inferences. At the present time, BayesOWL is restricted to translating only OWL-DL concept taxonomies into BNs, we are actively working on extending the framework to OWL ontologies with property restrictions.