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Theoretical research is predominately an inductive process; while applied research is mainly a deductive process. Both inference processes are based on the cognitive process and means of abstraction. This paper describes the cognitive processes of abstraction and formal inferences such as deduction, induction, abduction, and analogy. The hierarchy of abstraction and the descriptivity of abstract means at different levels are analyzed. A set of mathematical models of formal inference methodologies are developed. Formal descriptions of the five cognitive processes of abstraction and inferences are presented using real-time process algebra (RTPA). Applications of abstraction and formal inferences in dealing with complicated problems in large-scale software system development in software engineering are discussed.