Defining degree of semantic similarity using description logic tools

Establishing the semantic similarity of information is an integral part of the process of solving any information retrieval tasks, including tasks related to big data processing, discovery of semantic web services, categorization and classification of information, etc. The special functions to determine quantitative indicators of degree of semantic similarity of the information allow ranking the found information on its semantic proximity to the purpose or search request/template. Forming such measures should take into account many aspects from the meanings of the matched concepts to the specifics of the business-task in which it is done. Usually, to construct such similarity functions, semantic approaches are combined with structural ones, which provide syntactic comparison of concepts descriptions. This allows to do descriptions of the concepts more detail, and the impact of syntactic matching can be significantly reduced by using more expressive descriptive logics to represent information and by moving the focus to semantic properties. Today, DL-ontologies are the most developed tools for representing semantics, and the mechanisms of reasoning of descriptive logics (DL) provide the possibility of logical inference. Most of the estimates presented in this paper are based on basic DLs that support only the intersection constructor, but the described approaches can be applied to any DL that provides basic reasoning services. This article contains the analysis of existing approaches, models and measures based on descriptive logics. Classification of the estimation methods both on the levels of defining similarity and the matching types is proposed. The main attention is paid to establishing the similarity between concepts (conceptual level models). The task of establishing the value of similarity between instances and between concept and instance consists of finding the most specific concept for the instance / instances and evaluating the similarity between the concepts. The term of existential similarity is introduced. In this paper the examples of applying certain types of measures to evaluate the degree of semantic similarity of notions and/or knowledge based on the geometry ontology is demonstrated.