Algebraic and logical methods in computer science and artificial intelligence

Implicatively precomplete sets of multioperations defined on a set of three elements

V. I. Panteleev<sup>ab

a</sup> Banzarov Buryat State University, Ulan-Ude, Russian Federation
^b Irkutsk State University, Irkutsk, Russian Federation

Abstract: We study the completeness criterion on the set of rank-3 multioperations with respect to the implicative closure operator. The problem is a special case of the problem of finite classification of multioperations defined on an arbitrary set. A description of all precomplete sets is obtained. The expressive possibilities of the operator are described, including the conditions under which a set of operations implicatively generates all sets of multoperations. The obtained result can be used in the study of multioperations defined on an arbitrary set.

Keywords: closure, multioperation, closed set, composition, completeness, representability.

UDC: 519.716

MSC: 03B50, 08A99

Received: 14.10.2024
Revised: 29.11.2024
Accepted: 04.12.2024

DOI: 10.26516/1997-7670.2025.51.130