Object-Oriented Data as Prefix Rewriting Systems

Gutman, A. E.
Vladikavkaz Mathematical Journal 2015. Vol. 17. Issue 3.

Abstract:
A deterministic longest-prefix rewriting system is a rewriting system such that there are no rewriting rules \(X{\to}Y\), \(X{\to}Z\) with \(Y{\ne}Z\), and only longest prefixes of words are subject to rewriting. 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. A special attention is paid to the effective verification of various properties of the rewriting systems under consideration. In particular, algorithms are presented for answering the following questions: Are all words finitely rewritable? Do there exist recurrent words? Is the system conceptually consistent? Given two words \(X\) and \(Y\), does \(X\) conceptually depend on \(Y\)? Does the type of \(X\) coincide with that of \(Y\)? Is the type of \(X\) a subtype of that of \(Y\)?

Keywords: prefix rewriting, term rewriting, object-oriented data system, information system, consistency verification, ontology of a data model

Language: English Download the full text  

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