A Petri net-based design inference network (PNDN) architecture is presented in this paper. The network models the logical behaviour of any design artefact developed by designers at the conceptual design level by representing the subfunctions and their inter-relationships to perform a required overall function. The theoretical framework in developing the PNDN is based on the improved theory of Petri nets and hybrid automata. The theoretical PNDN architecture was implemented in a C++ based software called the design network simulator (DNS). The logical behaviour of a design artefact is modelled through the token flow within the PNDN. The token flow model is developed both for deterministic and nondeterministic PNDN, which involves uncertainties. In this paper we present the mathematical formalism of the deterministic token flow through the PNDN. We also provide a conceptual design example in order to explain the application of our theoretical architecture for structuring the PNDN.