A category theoretic approach in changing networks of semantics

Abstract

Mathematical models such as sets of equations are used in engineering to analyze the behaviour of physical systems. The conventional notations in formulating engineering models do not always provide the details required in fully comprehending those equations and, therefore, artefacts like ontologies, which are the building blocks of knowledge representation models, are used to fulfil this gap. Since ontologies are the outcome of an inter-subjective agreement among a group of individuals about the same fragment of the objective world, their development and use are questions in debate with regard to their competencies and limitations to univocally conceptualize a domain of interest. A network of semantics is defined as a directed graph, consisting of vertices representing heterogeneous ontologies and edges representing alignments among them. Both its components are carriers of meaning and they undergo changes in order to be adapted to different contexts of applications. This paper aims at, firstly, defining changes occurring in networks of aligned ontologies, a difficult task, since one has to take into account that making changes based on isolated components, while ignoring the semantic interrelations among them, may result in non logical continuity, or inconsistency of the underlying semantic model and, secondly, proposing a category theoretic framework in order to overcome the obstacles emerging from the changes occurring in networks of semantics, by introducing an enriched category that can capture the overall structure of a network of aligned ontologies.