## Abstract

The paper discusses various aspects of application of the notion of isomorphism of elementary conjunc- tions of predicate formulas in Artificial Intelligence (AI) problems that can be formalized by means of predicate calculus. The notion of isomorphism of various objects is widespread in mathematics. Moreover, isomorphic objects have a large number of identical properties. The definition of isomorphic elementary conjunctions of predicate formulas is given in the paper. The main property of such formulas is that they define the same relation between their arguments. The main difference between the notion of isomorphism and the notion of equivalence is that the equivalent formulas must have the same arguments, and the arguments of isomorphic formulas may be significantly different. In the framework of the logic-objective approach to solving AI problems, the following problems, for solving which the notion of isomorphism is used, are considered: the problem of object classification; creating a level description of classes to decrease the computational complexity of the analysis problem of a complex object; creating a level description

of the database to decrease computational complexity while multiple solution of the problem Conjunctive Boolean Query; definition of a metric in the space of elementary conjunctions of predicate formulas.

of the database to decrease computational complexity while multiple solution of the problem Conjunctive Boolean Query; definition of a metric in the space of elementary conjunctions of predicate formulas.

Translated title of the contribution | Изоморфизм предикатных формул в задачах Искусственного Интеллекта |
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Original language | English |

Pages (from-to) | 221–230 |

Journal | International Journal on Information Theory and Applications |

Volume | 26 |

Issue number | 3 |

Publication status | Published - Jun 2019 |

Event | "ITHEA ISS Joint International Events of Informatics" - Varna Duration: 1 Jul 2019 → 12 Jul 2019 Conference number: 22 |

## Scopus subject areas

- Computer Science(all)