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We present the computational counterpart of the KGP (Knowledge, Goals, Plan) declarative model of agency for Global Computing. In this context, a computational entity is seen as an agent developed using Computational Logic tools and techniques. We model a KGP agent by relying upon a collection of capabilities, which are then used to define a collection of transitions, to be used within logically specified, context sensitive control theories, which we call cycle theories. In close relationship to the declarative model, the computational model mirrors the logical architecture by specifying appropriate computational counterparts for the capabilities and using these to give the computational models of the transitions. These computational models and the one specified for the cycle theories are all based on, and are significant extensions of, existing proof procedures for abductive logic programming and logic programming with priorities. We also discuss a prototype implementation of the overall computational model for KGP.