TAP is a general process modeling framework with which we can describe process specifications in terms of tasks, agents and products that are relevant to the concept of processes. However, its formal semantics and pragmatics have not been rigorously studied, i.e. the usage of vocabulary words provided by TAP framework and the pieces of reality which TAP framework captures has not been formally considered. In this paper, we clarify the pragmatics of TAP and the world structures of TAP process models by formal approach. We present the semantic structure for TAP process models and introduce a logical language to restrict world structures of TAP. A formal ontology for business process model TAP is the characterization described as a set of axioms in our logical language.