Quantifiers metamorphoses. Generalizations, variations, algorithmic semantics

Abstract: This article contains ideas and their elaboration for quantifiers, which appeared after checking in practice the experimental language of the formal knowledge representation YAFOLL [1]: - looking at for_all and exists quantifiers as operators clarifying two trivial properties of a function: the constancy of result value and presence of a value in the result; -It turned out that the quantifier term can be written in the lambda calculus technique, i.e. as definition; -quantifier of quantity # is introduced into the language, as needed in practice and does not cause logical and algorithmic problems on finite structures; - the quantifier of the sum is mentioned because it is a quantifier of the language; -algorithmic semantics is written for for_all and exists quantifiers as an introduction to the topic.