Vestnik KRAUNC. Fiz.-Mat. Nauki. 2022. vol. 39. no. 2. pp. 119–135. ISSN 2079-6641

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MSC 68T27

Research Article

Optimization of the structure of variable-valued logical functions when adding new production rules

D. P. Dimitrichenko

Institute of Applied Mathematics and Automation KBSC RAS, 360000, Nalchik, Shortanova st., 89a, Russia


This paper proposes a theoretical justification and practical implementation in the form of an algorithm for modifying variable-valued unions of functions when adding new production rules to an already formed (within the original subject area) union classifier. The proposed algorithm is based on the application of the method of
constructive transformation of variable-valued relationships of classifiers built on the basis of a system of production rules encoded using variable-valued predicates. The properties of changing the structure of production clauses and knowledge development clauses in the process of adding new production rules are studied. Conditions are found under which these clauses are guaranteed to vanish in the connection, or are in a constant form. Taking into account the conditions in the proposed algorithm makes it possible to reduce the number of necessary operations and reduce the computational costs for the required transformations.

Key words: combination of operations, variable-valued predicate, variablevalued logical function, training sample, production rule, mixed classifier, logical neural network.

DOI: 10.26117/2079-6641-2022-39-2-119–135

Original article submitted: 04.07.2022

Revision submitted: 20.08.2022

For citation. Dimitrichenko D.P. Optimization of the structure of variable-valued logical functions when adding new production rules. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 39: 2, 119–135. DOI: 10.26117/2079-6641-2022-39-2-119–135

Competing interests. The authors declare that there are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

The content is published under the terms of the Creative Commons Attribution 4.0
International License (

© Dimitrichenko D.P., 2022


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Dimitrichenko Dmitry Petrovich – Ph.D. (Tech.), Researcher, Department of Neural Networks and Machine Learning, Institute of Applied Mathematics and Automation, Kabardino-Balkarian Republic, Nalchik, Russia, ORCID 0000-0003-2399-3538.