As the Semantic Web is an open, complex and constantly evolving medium, it is the norm, but not exception that information at different sites is incomplete/inconsistent. This poses challenges for the engineering and development of agent systems on the Semantic Web since autonomous software agents need to understand, process and aggregate this information. Ontology language OWL provides core language constructs to semantically markup resources on the Semantic Web. However, as OWL was designed on top of (a subset of) classic predicate logic, it lacks the ability to reason about inconsistent/incomplete information. Belief Augmented Frames (BAF) is a frame-based logic system that associates with each frame/slot a supporting and a refuting belief value. In this paper, we propose a new ontology language BOWL (Belief-augmented OWL) by integrating OWL DL and BAF to incorporate the notion of confidence. The BOWL is paraconsistent, hence it can perform useful reasoning services in the presence of inconsistencies/incompleteness. We define the abstract syntax and semantics of BOWL by extending those of OWL. One example in the sensor fusion domain is presented to demonstrate the application of BOWL.