Properties of a relational framework synthesized over a set of semantically atomic predicates
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PROPERTIES OF A RELATIONAL FRAMEWORK SYNTHESIZED OVER A SET OF SEMANTICALLY ATOMIC PREDICATES B. E. Panchenkoa and I. M. Pysankob
UDC 004.652
Properties of a relational framework synthesized over a set of semantically atomic predicates are analyzed. A relational framework is shown to be stable with respect to a modification in the basic predicate set. The stability, uniqueness, and completeness allow one to consider a relational framework as a universal “carrier” for object domains with arbitrary semantics. Keywords: relational framework, semantically atomic predicate, scheme of a relational database, cortege, domain.
A scheme of a relational database (DB) is traditionally understood to be some fixed collection of relational schemes R j , i.e., named sets of attributes and keys [1]. As a rule, for the construction of such a scheme, a collection of attributes x i and sets of values, i.e., domains D ( x i ), that are uniquely associated with these attributes are introduced [2]. In this case, collections of the attributes themselves are associated with objects or entities, and collections of values of attributes are associated with instances of objects or entities. It is the first step to the mapping of the semantics of an object domain into the scheme of a DB. Note that the set of x i and the collection of sets D ( x i ) are common for schemes R j in the sense that a separate attribute can belong to several schemes. Finally, an instance of each relational scheme R j is represented in the form of a collection of corteges K p , i.e., ordered sequences of values of attributes x i of the jth scheme R j , and we have K p Ì D ( x1 ) ´ K´ D ( x i ) ´ K´ D ( x K ) , x i Î R j . Heterogeneous interrelations revealed between sets of attributes by the analysis of semantics of object domains, play the decisive role during the normalization of the scheme of a DB. It may be said that, in the approach “attributes-domains,” an amorphous “field” is first specified over which the revealed semantic relationships make it possible to form (after a number of transformations that is, as a rule, rather large for nontrivial examples) a normalized structure of a DB. This “formation of a normalized structure” is one of the most labor-consuming stages of developing the logic scheme of any DB. Despite the existence of advanced techniques of decomposition of DB schemes, this approach to design has a cardinal drawback [2] , namely, the absence of flexibility. It is a change in the collection of attributes and/or interrelations between them (for example, after an extension of the object domain of a DB, which mostly happens in practice) that causes the necessity of repeated formation of the normalized scheme of a DB. In such cases, the logical scheme of a DB is difficultly modified or cannot be modified at all (since there is no strict continuity between old and new schemes of the DB). To represent new (additional) objects, entities, and relationships in a DB, it is required to form an extended collection of objects and relationships and then aga
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