A new classification of Intelligent Manufacturing Systems (IMS) based on consistency analysis is proposed. Through this approach, IMS can be initially classified into Declarative Manufacturing Systems(DMS), which are absolutely consistent manufacturing systems, and Descriptive Manufacturing Systems (D'MS), which the consistency of manufacturing systems have to be checked or verified. Furthermore two main types of DMS, Functional Manufacturing Systems (F'MS) and Relational Manufacturing Systems(RMS), are analyzed in detail using lambda calculus and predicate calculus, respectively. On the other hand the Touretzky's inheritance theory is used as an analytical tool for checking the consistency of D'MS. In summary, because different manufacturing systems use different mathematical tools, a category-theoric foundation of intelligent manufacturing systems is conjectured for the future research.