Universal and Determined Constructors of Multisets of Objects

TL;DR

This paper introduces universal and determined constructors for multisets of objects within a constructive object-oriented set theory, enabling precise modeling of human thought processes and aiding intelligent information system development.

Contribution

It proposes a universal constructor and several determined constructors for multisets of objects, facilitating creation and analysis of multisets with large cardinalities.

Findings

Universal constructor allows arbitrary multisets creation.

Determined constructors enable precise multiset schema-based creation.

Constructors support modeling human thought processes.

Abstract

This paper contains analysis of creation of sets and multisets as an approach for modeling of some aspects of human thinking. The creation of sets is considered within constructive object-oriented version of set theory (COOST), from different sides, in particular classical set theory, object-oriented programming (OOP) and development of intelligent information systems (IIS). The main feature of COOST in contrast to other versions of set theory is an opportunity to describe essences of objects more precisely, using their properties and methods, which can be applied to them. That is why this version of set theory is object-oriented and close to OOP. Within COOST, the author proposes universal constructor of multisets of objects that gives us a possibility to create arbitrary multisets of objects. In addition, a few determined constructors of multisets of objects, which allow creating multisets, using strictly defined schemas, also are proposed in the paper. Such constructors are very useful in cases of very big cardinalities of multisets, because they give us an opportunity to calculate a multiplicity of each object and cardinality of multiset before its creation. The proposed constructors of multisets of objects allow us to model in a sense corresponding processes of human thought, that in turn give us an opportunity to develop IIS, using these tools.