«IS-THE»-relations in semantic data models: basic notions and variants

«IS-A»-relations are important intellectual tools allowing to pass from the individual phenomena to their abstractions of the different levels and on the contrary. Importance of these relations in data modeling is underestimated. In fact, these relations in addition recover the unity of an object scattered in a database as unconnected abstract entities. In semantic model ERM (Entity-Relationship-Mapping) attempt of consistent «IS-A»-relation inclusion to rules of construction of structures and integrity constraints is undertaken. Main principle is maintenance of faultless logic canons with preservation of that functionality of these structures which has developed in data modeling. ^ere this natural for people form of the information representation has been offered not at once. In semantic models it has appeared together with the Enhanced Entity-Relationship Model in 80th years of the last century. In this model such structural concepts as specialization and categorization are entered for representation of «IS-A»-relations. But even in data modeling there is no common opinion about «IS-A»-structures so it is no wonder that these representations are different from logic bases. Ibe logician approach to the «IS-A»-relation problem looks more thorough, and it cannot be bypassed at the definition of the concepts describing these relations, but focused on data modeling. Т!ю second corner stone of this system of concepts are mappings and the semantically significant mapping theory. The analysis of the mappings accompanying «IS-A»-relations allows to consider this subject of inquiry more deeply. Two elements of scopes of the different concepts are connected by «IS-THE»-relation if and only if they represent the same application domain (AD) object. «IS-THE»-relation is the binary 1:1-relation determining pair of inverse functional «IS-THE»-mappings. AD objects or their abstractions (data) participate in these relation and mappings. If the known treatments of «IS-A»-relations connect a class with an object or a class with a class, «IS-THE»-relations connect objects. «IS-THE»-relation in maximum generalized understanding allows specifying «nearness» of concepts in such sense: concepts are near if there is at least one object falling under both these concepts. «IS-THE»-relation in such variant determines two partial functional mappings. If two concepts, one of which is generalization of another, are considered, then «IS-THE»-relation becomes a subsumption relation. «IS-THE»-mapping from scope of generic concept (superclass) to scope of specific concept (subclass) is still partial functional. And here, «IS-THE»-mapping from a subclass to a superclass becomes full functional. «IS-THE»-cluster (or, simply, cluster) is a system of classes constructed for restrictions of the same superclass concept; such, that all subclass concepts use the same mapping in the bases of them subtyping. Such mapping can be named discriminating; in fact it is this characteristic of superclass objects that determines their hits in subclasses. When an entity set is a subclass only in one «IS-THE»-cluster, it is said that full single inheritance takes place. When an entity set enters as a subclass in more than one «IS-THE»-cluster, it is said that full multiple inheritance is carried out. In both cases entities of subclass inherit characteristics of all their parent classes. In data modeling the special subspecies of two-level «IS-A»-hierarchies are entered. This is a categorization determining special «IS-THE»-relations between the union of superclass entity sets and subclass entity set (in this case named a category). To understand core of categorization it is necessary to present the content of the concept which scope is represented by subclass entity set. The first part of its logic expression is a disjunction of content conditions of superclass entity sets, and the second part is a condition to which should satisfy entities of these sets to be presented in a category. Such two-level «IS-A»-hierarchy we name «IS-THE»- categorization (or, simply, categorization). In categorization definition it is emphasized that superclasses do not contain entities been abstractions of the same objects and are so various that they are not connected with the common ancestor. In other words, concepts of superclasses are incompatible in pairs. In that case the element of a category always inherits characteristics only one superclass, where the parental element connected to it contains. Therefore it is said that such two-level «IS-A»-hierarchies assume selective inheritance. The definitions submitted in this article are based ERMM rules of data structurization and integrity constraint definition concerning representation of «IS-THE»- relations.

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