Towards a Formal Description of Understandability (Causality, Pre-Requisites): From Prosorov's Phonocentric Topology to More General Interior (Closure) Structures

Authors

Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

8-2014

Comments

Technical Report: UTEP-CS-14-56

Published in Mathematical Structures and Modeling, 2014, Vol. 31, pp. 18-26.

Abstract

In many real life situations, a text consists of related parts; so, to understand a part, we need to first understand some (or all) preceding parts: e.g., to understand Chapter 3, we first need to understand Chapters 1 and 2. In many cases, this dependence is described by a partial order. For this case, O.~Prosorov proposed a natural description of the dependence structure as a topology (satisfying the separation axiom T₀).

In some practical situations, dependence is more general than partial order: e.g., to understand Chapter 3, we may need to understand either Chapter 1 or Chapter 2, but it is not necessary to understand both. We show that such a general dependence can be naturally described by a known generalization of topology: the notion of an interior (or, equivalently, closure) structure (provided, of course, that this structure satisfies a natural analog of T₀-separability).