Quantifiers metamorphoses. Generalizations, variations, algorithmic semantics

TL;DR

This paper explores the nature and semantics of quantifiers in formal languages, introducing new quantifiers and analyzing their properties and algorithmic semantics within the context of knowledge representation.

Contribution

It introduces a lambda calculus representation of quantifiers, new quantifiers like # and sum, and provides algorithmic semantics for for_all and exists.

Findings

Quantifiers can be expressed as lambda calculus definitions.

New quantifiers # and sum are practical and do not cause logical issues.

Algorithmic semantics for for_all and exists are developed.

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.