Continuity in Information Algebras
This work addresses foundational mathematical structures in information algebras, likely for researchers in theoretical computer science or AI, but appears incremental as it builds on existing algebra frameworks.
The paper introduces continuity and strong continuity concepts in domain-free and labeled information algebras, and presents a general continuous function between them, showing that the set of such functions forms a new s-continuous information algebra and demonstrating correspondence between the algebras on s-compactness.
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.