Discovery of Web Services (WSs) has gained great research attention due to proliferation of available WSs and the failure of the syntactic approach of UDDI. Semantic discovery mechanisms have been invented in order to provide more precise results. However, many functionally-equivalent WSs are returned by semantic WS registries. Fortunately, the solution is to enforce the semantic QoS-based description and discovery of WSs. We have already presented a rich and extensible ontology language for QoS-based WS description and we have proposed a semantic QoS metric matching algorithm. Based on this algorithm, we have extended a CSP-based approach for QoS-based WS discovery. In this journal paper, we show an extension of OWL-Q with SWRL rules as OWL alone fails in some aspects of QoS description. We also propose a modification to the metric matching algorithm to make it more feasible. Then we propose two novel semantic QoS-based WS Discovery algorithms that return matches even for over-constra...