**:** ..
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**:**
**:**
**:** 2018
**:** ..

** :**
**:** 72
**:** .. // . 72. .: , 2018. .33-51. URL: https://doi.org/10.25728/ubs.2018.72.3

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** :** , , ,

** (.):** pattern matching, production system, category theory, universal algebra

**:** , . - , . . , . , - . , - . , .

** (.):** In previous works, the author proposed a mathematical language for describing the rules in artificial intelligence. A single production acts over a set of situation, taking one situation as a source and generating the another situation as the result of its application. The concept of pattern for a generalized description of similar situations is important in this theory. Both the situation and the pattern are coded in the proposed language by morphisms of the appropriately chosen category. Samples can be ordered by a degree of generality. Two methods of such ordering could be considered. We can assume that the first pattern is more general than the second one if the second can be obtained by specifying the first. We also can assume that the first pattern is more general than the second if each situation, suitable for the first pattern, is suitable for the second one. These two ways of ordering are close but not identical. The reformulation of these two definitions in the language of a category theory leads to the mathematical problem of comparing of two ways of ordering a certain set of morphisms. An article is devoted to an investigation of this problem.

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