The article describes an ontologies merging algorithm used to ensure the semantic interoperability of information systems (IS). The algorithm is based on a set-theoretic approach for calculating measures of semantic proximity of vertices of homogeneous ontologies at the level of subject areas and the level of tasks. The measure of semantic proximity is calculated taking into account the comparison of the attributes of the compared concepts of ontologies and the values of these attributes, the location of the selected nodes within the corresponding ontologies, and also taking into account the comparison of the presence and types of links of the evaluated concepts.
At the first two levels of the EIF stack, initial requirements for the design of information systems are set, organizational measures are taken to unify the relevant regulatory documents and business processes.
To ensure the fourth and fifth levels of EIF stack in the design and development of information systems, they must include certain software tools. The indicated levels of interoperability are well enough studied and their practical implementation does not cause serious difficulties at present.
Currently, the greatest scientific and practical significance is the solution of problems of ensuring the semantic interoperability of information systems (IS). This is also due to the fact that in recent years the intelligence of IS, including devices operating on IoT technology, has sharply increased. Information systems are being created that are capable of replacing a person in many respects, including in the field of making intelligent decisions. Understanding the meaning of the request (and not just the syntax of the request) that comes to the IS from another system will allow you to give a more correct answer, which, in turn, should be as correctly understood as possible by the system that generated the request. Ensuring semantic interoperability is associated with the need to apply ontologies of concepts used in processes and describing the processes of functioning of an information system.
Based on the studies carried out [
To ensure the semantic interoperability of information systems, it is necessary to
compare the ontologies that underlie them and find out their commonality and
differences. This problem is solved by using methods for assessing the semantic proximity
of ontology concepts. Many well-known methods for finding a measure of proximity
between ontology concepts are based on Tversky's set-theoretic approach, based on
comparing the properties of concepts [
The most promising for use in algorithms used to calculate measures of semantic proximity of ontology concepts are the so-called hybrid measures. The hybrid measure proposed in [15] consists of three parts - taxonomic, relational, and attributive. Difficulties in comparing different ontologies of subject areas lie in the difference in the names of concepts and relations, as well as in the approaches to the definition of concepts. When mapping two ontologies, a search is performed for each concept of one ontology of a similar concept of another ontology, taking into account the synonymy of concepts. In works [16, 17], a method for calculating a measure is proposed, taking into account the lexical proximity of concepts, properties, domains and ranges of relations (ranges of values of the arguments of relations), parent/child concepts. The main disadvantage of most methods for determining semantic proximity is the need to involve an expert to confirm the correctness of detecting similarities and differences in semantic concepts.
Below we will consider the problems of integrating ontologies that reflect either
different points of view on the same subject area, or different points of view on the same
problem (i.e., we will integrate homogeneous ontologies at the level of subject areas
and levels of tasks). The purpose of the integration is to preserve the existing and
define new semantic dependencies of the concepts contained in both ontologies.
In accordance with the results of works [
C2 – concept of the "Object" type;
C3 – concept of the "Entity" type. 2) The set of relationships between concepts is defined as follows:
= { 1, 2, 3}, (2) where: 1– relationship "Inheritance" (relationship "class-subclass"); 2 – relation "Association";
R3 – is the "Action" relation. 3) The ontology used to ensure the semantic interoperability of the IS can be formally presented in the following form:
= {Ci (Аij, Sik), Rij, Pm}, (3) where: Ci - ontology concepts; Аij – j-th attribute of the i-th concept; Sik – the k-th synonym for the i-th concept; Rij – is the relationship between concepts i and j;
Pm – inference rules.
It is proposed to build an algorithm for integrating ontologies to ensure the semantic interoperability of the IS based on the calculation of the semantic proximity of the vertices of two ontologies 1 and 2. For each concept С1i of the ontology О1, we calculate the measures of semantic proximity with the concepts С2j of the ontology 2.
In the algorithm described below, the calculation of measures of semantic proximity
of ontology concepts used to ensure the semantic interoperability of IS will be based
on the set-theoretic approach [
Let us introduce the following characteristics of measures of semantic proximity: • Equivalence. We will assume that the vertex C1i of the O1 ontology is equivalent to the vertex C2j of the O2 ontology if: 1) the composition of attributes and their values coincide or differ by intervals not exceeding the minimum threshold values (attributive measure); 2) the selected concepts are located in ontologies in such a way that the lengths of the minimum chains (bridges) between these concepts and two other equivalent concepts in each ontology does not exceed the minimum allowable threshold value (that is, in ontologies the selected concepts are "surrounded" by concepts the evaluations carried out are equivalent (geometric measure); 3) the evaluated concepts are associated with concepts with the same types of links, or the number of different types of links does not exceed a certain minimum threshold value (relational measure). • Conformity. Determined according to the rules described above. In the case when the minimum allowable threshold value of the corresponding measure of proximity is exceeded, a comparison is made with the maximum allowable threshold value of the corresponding measure of proximity of concepts. In this case, the maximum threshold value must not be exceeded. Vertices possessing the above characteristic of the proximity measure will be called corresponding. • Difference. Determined according to the rules described above. In the case when the maximum permissible threshold value of the corresponding proximity measure is exceeded. Vertices possessing the above-described characteristic of the measure of proximity will be called different.
To construct an ontology merging algorithm, it is also proposed to use the concept of a bridge - a chain of ontology vertices that correspond to equivalent concepts used to establish a mapping of two ontologies in [18].
To integrate ontologies used to ensure semantic interoperability, the following sequence of actions is proposed.
Step 1. In the ontologies O1 and O2, bridges are computed, consisting of vertices that in pairs have equivalent or corresponding proximity measures. The lengths of the bridges (the number of vertices) must coincide.
Step 2. Calculate the weight of each bridge. Assigning to the vertices with an equivalent measure of proximity, the maximum coefficient is equal to 1, and to the vertices with the corresponding measure of proximity - a coefficient in the range from 1 to 0.5, depending on the approach to the threshold values of the estimated parameters of the attributive, geometric, and relational measures of proximity.
Step 3. As the base for merging, we choose the ontology in which there is the largest number of vertices. Let in our case it be O1 ontology. We select in it all the bridges defined in the previous steps.
Step 4. For differing vertices in the O2 ontology, we find the bridges with the largest weight and the smallest length to the vertices included in the bridges defined in Step 2.
Step 5. Add the bridges found in Step 4 to O1 ontology.
Steps 4 and 5 are repeated iteratively. We start looking for bridges with a length equal to 1, sequentially increasing the length of the bridge by one vertex at each iteration. Moreover, if the new vertex C2i is already included in the O1 ontology as a result of performing Steps 3 and 4 (it became a new vertex C1j), then the vertices C2i and C1j are considered equivalent.
In this case, the algorithm, due to the formalization of the ontology structure (see
formulas 1-3 above), makes it possible to avoid the semantic conflicts described in
[19], which arise during the merging of ontologies at the time of transferring vertices
connected by the types of links of the type ". In ontologies used to ensure semantic
interoperability and constructed in accordance with the rules described in [
Currently, there are algorithms and their software implementations for the automatic merging of ontologies. Information about such algorithms is given, for example, in [20]. Each of the currently existing algorithms for automatic merging of ontologies has, along with advantages, a number of significant disadvantages. The disadvantages are primarily associated with attempts to create a universal algorithm for combining ontologies that describe concepts of one subject area, but have different structures and algorithms for their initial construction. The article presents an original algorithm for the integration of ontologies representing structured knowledge about each of the interacting ISs, taking into account the fact that their structures and construction algorithms are clearly defined and unified. 4
The authors of the article are grateful to the Russian Foundation for Basic Research for their support in writing the article (grants No. 18-07-01053 and No. 20-07-00926).
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