The P-type Model: From Databases to Knowledge Bases

Ana Simonet and Michel Simonet Laboratoire TIMC-IMAG, 38706 La Tronche cedex FRANCE e-mail : (Ana,Michel)[email protected] 1 The P-type Model The p-type data model was conceived in the early eighties as an answer to database needs [12]. It was expressed within the Algebraic Data Types (ADT) paradigm [7] [8] and its main concern was the sharing of objects by several kinds of users seeing them through one or several views. A p-type is organized in a hierarchy of classes, where classes model database views. An object belongs to one and only one p-type, and to several views. Multiple specialisation is not necessary to express that an object belongs to several subclasses (views of a p-type). It is used only to specify a subset of the views intersection. To specify a p-type one rst gives its minimal view then its other views by simple or multiple strict specialisation, adding attributes and/or assertions. The root of the hierarchy of views is called the minimal view in that all the objects of the p-type must satisfy its properties. The ADT of a p-type is derived from its views declaration. This type contains all the attributes and methods which appear in the views of the p-type, including the minimal view. An object belongs to a view i it satis es its assertions. Objects which are instances of a p-type may belong to several views, among which only the minimal view is mandatory. A p-type is de ned as an algebraic data type < S;F;E > where S is a set of sorts fs1; :::; sng, the carrier of the type, F a set of functions si sj ::: sk ! sl and E a set of equations [12]. One sort, T , called the set of interest of the type, is central, in that the aim of the type de nition is to establish the elements of the type and de ne their behaviour. In general, the type is given the name of its set of interest : T . Among all possible functions, we call attributes those of the form T ! s; s 2 S. Other functions are called methods. The algebraic type of the p-type is derived from the views declarations (including the minimal view). The type PERSON contains all the attributes and methods which appear in its views. The domain of an attribute in type PERSON is the union of its domains in the views where it is declared. Let tmin : < S;Fmin;Emin >, t1 : < S;F1; E1 >, t2 : < S;F2; E2 >, : : :be the views of a p-type T . T is de ned as < S;F;E > where S is the support set of T , F = Si Fi and E = Emin. As a simple example, consider a p-type PERSON whose minimal view has the attributes Name, Age, and Sex, and its di erent views are ADULT : PERSON (Age 18), SENIOR : PERSON (Age>65), and STUDENT, characterized by speci c attributes. In the graph presented in gure 1, a student aged between 18 and 65 belongs to the views PERSON (the minimal view is mandatory), STUDENT, and ADULT, provided it satis es the properties of these views.