Determination and Processing of Properties Existence Constraints in Ontological Data Analysis

Abstract

The research area is an extended methodology for the derivation of formal concepts from, as a rule, incomplete and inconsistent empirical data, which are the results of observations and multidimensional measurements in an unexplored, unstructured subject domain. This methodology, called "ontological data analysis", synthesizes two successful approaches to the acquisition of conceptual knowledge: analysis of formal concepts and analysis of the properties existence constraints of subject domain. Herewith, the subject of ontological analysis is given the opportunity to perform a new cognitive act of processing empirical data normalization of the formal context at the task of deriving formal concepts, which means matching a posteriori information about the studied subject domain with a priori representations about it, expressed by the so-called "existence constraints" of the measured properties. The article substantiates the possibility and advisability of transforming the "natural" specification of the existence constraints in the form of a set of measured properties with specified existential relations on it into a set of intersecting subsets of measured properties, which are homogeneous in the form of existential conjugation of member-properties. Algorithms for identifying such subsets in the system of measured properties are presented. A basic algorithm for processing a new representation of properties existence constraints is proposed; it is designed to simplify and accelerate the normalization of the formal context. The significance of the obtained results lies in the algorithmic support of a number of stages of ontological data analysis.