Abstract
In this paper, we study the (geospatial) ontologies we are interested in together as an ontology (a geospatial ontology) system, consisting of a set of the (geospatial) ontologies and a set of ontology operations. A homomorphism between two ontology systems is a function between two sets of ontologies, which preserves these ontology operations. We view clustering a set of the ontologies we are interested in 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 ontology system homomorphism can be factored as a surjective clustering to a quotient space, followed by an embedding. Ontology (merging) systems, natural partial orders on the systems, and ontology merging closures in the systems are then transformed under ontology system homomorphisms, given by quotients and embeddings.
Abstract (translated)
在本文中，我们将研究我们感兴趣的(空间上的)本体论作为一個本体论(空间上的本体论)系统，由一组(空间上的)本体论和一组本体论操作组成。两个本体论系统的映射是这两个本体论集合之间的函数，保持了这些本体论操作。我们将将我们感兴趣的本体论集合进行分组视为将该集合划分成子集或将该集合中的等价关系定义或形成该集合的子集或得到该集合的满射图像。每个本体论系统映射都可以分解为满射分组到一个子集空间，然后嵌入。本体论合并系统、系统的自然 partial orders 以及系统中的本体合并结束 are then transformed under Ontology system homomorphisms, given by quotients and embeddings.
URL
https://arxiv.org/abs/2305.13135
