On parametric closure operator extensions by means of logical connectives

Background. Closure operators are one of functional classification tools of multivalued logic. Besides a well-recognized superposition operator, there is a number of so-called strong closure operators - operators that generate finite or calculating classifications of a set of functions of k-valued logic at any $k \geq 2$. The first of such operators was a parametric closure operator introduced by A.V. Kuznetsov in the middle of 1970s. On the basis of his idea there were introduced and examined two more strong closure operators: a positive closure operator and an operator with a full system of logic connectives. This idea may be implemented in any system of logic connectives, first of all, for the most commonly used coonectives: implication, exclusive disjunction etc. The aim of the work is to research closure operators that occur on the way. Materials and methods. In constructions and proving the author used logical and functional methods. Results and conclusions. The article considers closure operators that appear from a parametric closure operator by adding one of the following logic connectives: denial, disjunction, implication, equivalence, exclusive disjunction and ternary connective $\varphi$ that corresponds to Boolean function $x \oplus y\oplus z$. The first two operators (an operator with a full system of logic connectives and a posivite closure operator) are well-studied. The work shows that that closure operator that meets exclusive disjunction coincides with the operator with a full system of logic connectives. The other three operators are extensions of the positive closure operators, but differ from the operator with a full system of logic connectives. Besides, the operators, based on connectives of implication and equivalence, coincide. However, on a set of Boolean functions they generate the same classification as the positive closure operator. The results obtained may be used in further research of strong closure operators that appear to be extensions of the parametric closure operator.