This paper introduces the orchestration calculus Knorc, which is a conservative extension of the Orc calculus designed by J. Misra et. al. Orc is a simple but powerful calculus for wide area computing, whose simplicity makes it a solid kernel for orchestration programming. But on the other hand Orc leaves everything else to the programmer, which often makes the programming task complicated. The design idea of Knorc was to provide Orc with a delicately selected set of facilities to greatly increase the expressive power of the calculus and at the same time keep the calculus concise. The distinguished features of Knorc include, but not limited to: combination of process algebra and logic programming, site considered as remote Boolean procedure, Horn-like logic programming and inference, diversity of different parallelism mechanisms, network of abstract knowledge sources, open world assumption as opposed to closed world assumption where OWA means existing sites need not be known to the programmer, symmetric process-to-process communication, batch processing facilities of knowledge and data, as well as broad band message transmission. Besides introducing the general structures of the language Knorc, we present also a formal structural operational semantics. This is one of the major foci of this paper.