Software composition via workflow specifications has received a great deal of attention recently. One reason is the high degree of fit with the encapsulation of software modules in service-oriented fashion. In the Industry, existing workflow languages have been merged to form WS-BPEL, the Business Process Execution Language for Web Services. In the Research community OWL-S, a ontology for web services, has been submitted for standardisation alongside OWL, the Web Ontology Language in which it is expressed. The OWL-S Process Model is based on an abstraction of the common features of industrial workflow languages. On the one hand, WS-BPEL has only informal semantics; on the other, the type of semantics given to ontology-based work tends to be structural rather than computationally oriented. As a result the semantics developed for DAML-S, which led to OWL-S, are still deficient in some regards. In this paper we shall survey the existing semantics and introduce a novel semantics for the latest version of OWL-S that is focussed on the principle of compositionality, so far not tackled.