One of the fundamental human cognitive processes is problem solving. Most of the decisions we make relate to some kind of problems we try to solve no matter how trivial and critical the problem may be. The problem solving process entails performing in a new situation with information acquired and knowledge learned from past situations. As a higher level cognitive process, problem solving involves the correlation process effort to connect newly encounter problem object(s) with the objectattribute- relation (OAR) model representation of knowledge in the brain. The goal of problem solving is to search along various solution paths within the problem solver?s knowledge base in the memory. When a problem object is identified, problem solving can be perceived as a search process in the memory space for finding a relationship between a set of problem-solving goals and a set of alternative paths.

This paper presents a mathematical and cognitive model that describes problem solving as a cognitive process. The cognitive structures of the brain and the mechanisms of internal knowledge representation behind the cognitive process of problem solving are explained. The cognitive process will then be formally and rigorously described using Real-Time Process Algebra (RTPA) base on the aforementioned models. Extended discussions are presented on applications of the cognitive process model of problem solving in software engineering and psychology.