The rise of standards for semi-structured machine processable information and the increasing awareness of the potentials of a semantic Web are leading the way towards a more meaningful Web of data. Questions regarding location and retrieval of relevant data remain fundamental in achieving a good integration of disparate resources and the effective delivery of data items to the needs of particular applications and users. We consider the basis of such a framework as an Information Retrieval system that can cope with semi-structured data. This thesis examines the development of an Information Retrieval model to support text-based search over formal Semantic Web knowledge bases. Our semantic search model adapts Bayesian Networks as a unifying modelling framework to represent, and make explicit in the retrieval process, the presence of multiple relations that potentially link semantic resources together or with primitive data values, as it is customary with Semantic Web data. We achieve this by developing a generative model that is capable to express Semantic Web data and expose their structure to statistical scrutiny and generation of inference procedures. We employ a variety of techniques to bring together a unified ranking strategy with a sound mathematical foundation and potential for further extensions and modifications. Part of our goal in designing this model has been to enable reasoning with more complex or expressive information requests, with semantics specified explicitly by users or incorporated via more implicit bindings. The ground foundations of the model offer a rich and extensible setting to satisfy an interesting set of queries and incorporate a variety of techniques for fusing probabilistic evidence, both new and familiar. Empirical evaluation of the model is carried out using conventional Recall/Precision effectiveness metrics to demonstrate its performance over a collection of RDF transposed government catalogue records. Statistical significance tests are employed to compare different implementations of the model over different query sets of relative complexity.