With the production system shifting to a multi-variety and small-batch production mode, the production process faces more user requirements, changes, and uncertainties. To solve the above problems, it is necessary to obtain the status and trend changes information and provide information support for the optimization of decision-making and dynamic adjustment of the production system. However, the production system cognition faces the problems of state coupling, state dynamic transfer and transition, and multi-system interweaving, which makes the production system cognition face huge challenges. Combining technologies such as the Internet of Things, industrial big data, and artificial intelligence, cognitive manufacturing can realize dynamic cognition of the production process, support dynamic adjustment, and become a promising way to solve the dynamic changes and uncertainties of production systems. In addition, as a formal expression of information processing and knowledge learning process in cognitive informatics, the Object-Attribute-Relation (OAR) model can effectively guide the construction of the production process cognitive mechanism. Therefore, this paper proposes a multi-dimensional cognitive framework based on OAR model of the human cognitive world for the dynamic cognitive needs of production system. The framework carries out dynamic cognition from the three dimensions of the manufacturing unit, production situation, and production system, and builds the continuous cognitive abilities from the three dimensions of analysis, decision-making, and learning. By integrating intelligent algorithms in the fields of artificial intelligence, a computable digital twin model is constructed as a carrier to provide the cognitive enabling technologies and capabilities for the production system. Finally, the feasibility of the proposed framework is illustrated by the developed computational digital twin platform. The computable digital twin platform provides the production system with important cognitive capabilities such as states perception, trend prediction, optimization decision-making, and knowledge learning, to support the dynamic cognition and optimization decision-making of the production system, and lay a technical foundation for adaptive production and cognitive manufacturing.