Continuity in Information Algebras

TL;DR

This paper explores the concepts of continuity in information algebras, introduces a general class of continuous functions, and demonstrates their algebraic structure and relationships between different types of information algebras.

Contribution

It introduces a new general concept of continuous functions between domain-free information algebras and shows their algebraic structure, linking domain-free and labeled information algebras.

Findings

Set of continuous functions forms an s-continuous algebra

Continuous functions preserve algebraic operations

Domain-free and labeled algebras correspond on s-compactness

Abstract

In this paper, the continuity and strong continuity in domain-free information algebras and labeled information algebras are introduced respectively. A more general concept of continuous function which is defined between two domain-free continuous information algebras is presented. It is shown that, with the operations combination and focusing, the set of all continuous functions between two domain-free s-continuous information algebras forms a new s-continuous information algebra. By studying the relationship between domain-free information algebras and labeled information algebras, it is demonstrated that they do correspond to each other on s-compactness.