Theory Of N-ary Relations And Its Application In Modeling Knowledge System

Knowledge system is a highly complex and abstract system. Constructing models for this kind of system is a effective way to study it. Generally, modeling system needs study elements and relation of it. If this relation links two elements, it is called binary relation. If more than two are linked, it is called n-ary relation. The theories which can reflect the binary relations properties of systems are widely talked in recently years. The example is complex networks, OWL (Web Ontology Language), RDF (Resource Describe Framework) and so on.However, the n-ary relation is one of important properties of knowledge systems. The ex-ample is that in research corporation network model the number of authors in one works may be more than two. Another example is that "one thing happened in sometime" needs ternary relations for representing. The studies in n-ary field are not enough. The purpose of this article is to fill this gap.After reviewing of relate works, the issues about n-ary in knowledge system model will be analyzed. The network models and semantic models willed discussed in this article. From the point of the research process, this article obtains from the theoretical research, and the related theory and method is applied to the actual knowledge system modeling. In this article, two problems are discussed. One is that the reification in OWL based on relation polygon is studies at first. The related theory is applied in the semantic model of emergency plans of China. The other is that the n-ary relation representing of YAGO is discussed. The hyper network of wiki article is constructed with the YAGO.The main contents of the paper are shown as follows.1. Reification is a universal method for describing n-ary relations in OWL. But the struc-tures of reified the n-ary relations need extra classes, predicates, individuals and axioms, which will make it quite unreadable and inconsistency in ontologies. The aim of our paper is to simplify the reification. A concept model called relation triangle is proposed firstly to find Apical Con-cept (AC for short) in ternary relations. Then, this method is extended to n-ary relations (n>3). The n-ary relation with AC can be reified by the combination of the n-1binary relation with-out defining new concept. And the results will not lose any information. Moreover, the Apical Concept Set can simplify reifications also. Our methods can reduce codifications in ontologies, save concept for reification and keep more semantic information in original statement. More importantly, our theories can guide domain experts in the reification of n-ary relations.2. Wikipedia as a largest knowledge base is an important platform for sharing knowledge in the world. It can help understand the developing trend in the field of science, technology and society through the macro-level statistical properties of the knowledge and their evolution regularities. The semantic information of the article in Wiki can be gotten from the labels and the infobox in the pages, which can be formally represented by ontology. Two important characters of Wiki ontology are proposed. One is there are n-ary relations in it. The other is the size of this ontology is enlarging. Moreover, we propose the evolution mechanism of the ontology of Wiki.3. An important part of Chinese disaster plans is to provide useful information for different emergency responders, which tells them what should be done in a certain kind of scenario. A formal model can help responders get these kinds of information from internet. In this chapter, we proposed a formal model based on upper ontology. The jobs are listed as follows:1) A domain ontology of Chinese plans is constructed.2) N-ary relations can be represented in our model.3) The users can retrieval the useful information from our model.4) Temporal reasoning can help to link the rescue works which scatter in different chapters and sections.