Algorithms for the formation and pragmatic transformation of existence constraints

The research area of this article is data mining, specifically the direction “ontological data analysis” developed by the authors, which should be understood as the analysis of empirical data on an unexplored, unstructured knowledge domain in order to build its formal ontology. The research subject of this article is the formation of a set of properties which are supposed to characterize objects of the studied knowledge domain (and, therefore, are subject to measurement in the broadest sense of the word), but with restrictions on the combination of such characteristics in objects - properties “existence constraints”. The objectives of the research are to develop algorithms for the step-by-step formation of a set of measured properties with existence constraints, algorithms for modifying such a set (replacing and deleting properties), an algorithm for transforming the “natural” description of this set as a set with relations specified on it into a form convenient for the subsequent constructive use of information about existence constraints in ontological data analysis. In the paper we use the methods of set theory, binary relations, models and methods of formal concept analysis and the methodology for applying the existence constraints to construct formal ontologies. The difference and novelty of the proposed algorithms for the formation of a set of properties with existence constraints lies, first of all, in the “natural” and efficient representation of such sets in the form of graphs and incidence matrices (from the point of view of machine implementation). The novelty of the algorithms for modifying a set of properties with existence constraints lies in performed for the first time algorithmization of unique methods for expanding the set of measured properties that address directly the fundamen tal laws of classical logic. The same is true for the algorithm for transforming a set of measured properties into a set of properties groups that are homogeneous in the form of existential conjugation of member properties. The significance of the results obtained lies in the algorithmic support of a number of stages of ontological data analysis.