Abstract: Abstract interpretation was presented by CousotP and CousotR in 1977. Subsequently many scholars have done a lot of studies on it. Generally speaking, the classic abstract interpretation theory is developing within two equivalent formal frameworks of Galois connections and closure operators. This paper constructs a model based on partial equivalence relations and logical partial equivalence relations from a different perspective. It considers the abstract domain as a collection of “partial equivalence relations” and the semantic operator as a collection of “logical partial equivalence relations”. So this model is totally different from the traditional abstract interpretation models. Except that it requires that the concrete or abstract semantic operators have certain logical relations, the model never requires some special properties such as the monotonicity, so in this point it is different from the classic model. Besides, it is not an abstraction of a concrete system in an “approximate” sense, but rather an abstraction of all relations (including logical relations) on the original system. Thus this model is not a “simplification” of the original system but rather a “complication” of the original system.In some sense, it disjoins the “quality” unit from the original system, and it may be more complex than the original system. The advantage of this model is that it embodies some logical relations concerned with the system functions, because itdoes not require that concrete or abstract semantic operations have any special properties (e.g. monotonicity). Therefore here the abstraction is not as the classic understanding. The classic way is to treat some approximation of states as an abstraction, and require that both concrete semantic domains and abstract semantic domains have certain special mathematical structure, for example, lattice or cpo, that is the result of treating “approximation” as the basic essence of abstraction. Whereas our model help structure a concrete system from the semantic domain and the semantic operation the two parts by using partial equivalence relations and logical partial equivalence relations, i.e., it extracts their components separately and finally forms the collection of equivalence classes to discuss the semantic domain and semantic operators. Also, based on such a model, we can discuss the issues that are different from the traditional models, such as the complexity problem and the polymorphism problems, so that it may deepen our understanding for the abstract interpretation theory