Given such a system, analogs are defined and examined of some concepts related to object-oriented data systems: inheritance of classes and objects, instances of classes, class and instance attributes, conceptual dependence and consistency, conceptual scheme, types and subtypes, etc. <...> In particular, algorithms are presented for answering the following questions: Are all words finitely rewritable? <...> Key words: prefix rewriting, term rewriting, object-oriented data system, information system, consistency verification, ontology of a data model. 1. <...> By saying “X has a Y” we mean that the object (or class) X possesses an attribute named Y, and we thus can speak of “the Y of X” or “X’s Y” as a property of X conventionally denoted by X.Y. For instance, if a web page has a submit button whose style assumes a border of a particular width, we can speak of “the width of the border of the style of the submit button of the page” and thus arrive at the object page.submitButton.style.border.width. <...> By claiming that “John.age is 40” we assign the value 40 to the age attribute of John. <...> By interpreting “is” as “inherits,” we assume that if “X is Y” then all the attributes of Y are inherited by X. In particular, if “X is Y” and “Y has a Z” then “X has a Z .” Moreover, if “X is Y” is the only explicit information on X, we can conclude that “X.Z is Y.Z.” (By the explicit information we mean the is rules which form the data system under consideration.) In doing so, we derive an implicit information on X and say that “X.Z is Y.Z implicitly.” Therefore, when evaluating the object X.Z , we rewrite its prefix X with Y according to the explicit rule “X is Y .” The same is applicable to objects of any length. <...> For instance, if we know explicitly that “A.B is P.Q.R” then A.B.C.D rewrites implicitly to P.Q.R.C.D. It is clear that the explicit rules supersede any implicit derivatives; therefore, if “X is Y,” “Y has a Z ,” and the data system contains the explicit rule “X. <...>
Владикавказский_математический_журнал_№3_2015.pdf
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