Transforming Geospatial Ontologies by Homomorphisms

In this paper, we study the geospatial ontologies that we are interested in together as a geospatial ontology system, consisting of a set of the geospatial ontologies and a set of geospatial ontology operations, without any internal details of the geospatial ontologies and their operations being needed, algebraically. A homomorphism between two geospatial ontology systems is a function between two sets of geospatial ontologies in the systems, which preserves the geospatial ontology operations. We view clustering a set of the ontologies as partitioning the set or defining an equivalence relation on the set or forming a quotient set of the set or obtaining the surjective image of the set. Each geospatial ontology system homomorphism can be factored as a surjective clustering to a quotient space, followed by an embedding. Geospatial ontology merging systems, natural partial orders on the systems, and geospatial ontology merging closures in the systems are then transformed under geospatial ontology system homomorphisms that are given by quotients and embeddings.