Transforming Geospatial Ontologies by Homomorphisms

An ontology was considered as an explicit specification of a conceptualization that provides the ways of thinking about a domain [14]. Ontologies are the silver bullet for many applications, such as, database integration, peer to peer systems, e-commerce, etc. [13]. A geospatial ontology is an ontology that implements a set of geospatial entities in a hierarchical structure [7, 10, 27, 28]. In the age of artificial intelligence, geospatial data, from multiple platforms with many different types, not only is big, heterogeneous, connected, but also keeps changing continuously, which results in tremendous potential for dynamic relationships. Geospatial data, ontologies, and models must be robust enough to the dynamic changes. After mathematical operations, e.g., +,,, and, being introduced, natural numbers can be used not only to count but also to solve real life problems. The set of natural numbers, along with the operations, forms an algebraic system that can be studied by its properties without any internal details of the numbers and operation. These operations establish the relations among natural numbers, which make more sense than isolated natural numbers. Geospatial ontologies are not isolated but connected by their relations.