The Unified Modeling Language (UML) is the de facto standard for object-oriented software model development. The UML class diagram plays an essential role in design and specification of software systems. The purpose of a class diagram is to display classes with their attributes and methods, hierarchy (generalization) class relationships, and associations (general, aggregation, and composition) between classes in one model. A model designing process can include a large number of designers. An issue with this is that the models created may be incorrectly designed. Moreover, there are many concepts in the UML that give rise to potential conflicts, uncertainty, and ambiguity. This paper evaluates the concept of software system model correctness. In this paper,a systematic literature review is conducted to examine how researchers identify problems related to software system model correctness. There are seven papers included in the literature review which cover different approaches for handling model correctness in software systems. The results of this review indicate that UML model correctness is a highly active area of research. There are already some valuable contributions in this direction. However, there are many concepts in the UML with imprecise semantics, which limit the use of the UML and reduce the quality of the UML models. This paper is concluded by providing some directions to identify and prove the mathematical equivalence of the UML class diagram models using standard graph theorems.