# A Method of Ontology Integration for Designing Intelligent Problem Solvers
## 1 Introduction  
Nowadays, the knowledge from several sources needs to be integrated in order for machines to accomplish different tasks in a more intelligent way than conventional systems [1]. Knowledge integration is important in intelligent software development [2]. In order to achieve this, knowledgehas to be processed and synthesized into knowledge bases. Many intelligent systems have introduced knowledge integration to increase their power. Wolfram | Alpha is an engine for computing answers and providing knowledge [3]. The knowledge of this system is integrated from multiple knowledge domains, such as mathematics, science and technology, and society. The IMS Learning Information Services is a tool to share data about learning [4]. This service supports the exchange of information about courses and learning outcomes between users. It is a combined knowledge-integrated system of learning management platforms, student record systems, and personnel systems. Thus, knowledge integration is an imperative need for designing knowledge-based systems. Knowledge integration is the combination of multiple models for representing knowledge domains into a common model [1; 5]. This integration has to meet some requirements, as follows:  
* Practicality: The method for knowledge integration must be able to represent the real-world knowledge domain in a knowledge base, produce an inference engine that reasons upon the knowledge base, and solve practical problems via a similar reasoning process to that of humans;
* Accuracy: The components of the knowledge domain must be represented precisely and fully using the knowledge integration method, in a way that simulates human acquisition. Ontology design and ontology integration are a potential approach to solve the problems of the integration of heterogeneous knowledge [6]. They provide sophisticated knowledge about the environment for task execution [7]. They allow the users to organize information on the taxonomies of concepts, with their own attributes, to describe relationships between the concepts. When data are represented by means of ontologies, software agents can better understand the content of the data and messages [8]. Domain-based knowledge can be modeled in ontology using ontology markup languages and various ontology tools, like Protege, OILed [9], PDDL (_Planning Domain Definition Language_) [10], and NDDL (New Domain Definition Language) [11]. The structure of an ontology consists of these basic components: concepts, relationships, and rules [12]. Concepts are the foundation for building the knowledge base, they make the representation clearer and more exact. Relationships on ontology perform connections between concepts. Inference rules are mechanisms for the reasoning to solve problems of the knowledge domain. The model for the integration of knowledge bases needs a knowledge kernel as ontology. Besides, solving a problem with the integrated model may require the knowledge of another pre-solved problem in the knowledge kernel. For example, in the knowledge domain of linear algebra, the knowledge of matrixes is the knowledge kernel. When solving a linear equations system, problems on the matrix, such as row transformation and column tranformation, have to be solved first [13]. Similarly, before solving a problem about vector spaces, it has to be converted to a matrix problem. Hence, the ontology-based model for integrating knowledge-based systems is a combination of the kernel ontology and other knowledge. In this paper, an ontology model used as the knowledge kernel is presented. It includes concepts, relationships between concepts, and inference rules. Some problems for this kernel have been proposed and solved. This kernel is integrated with other knowledge, such as the knowledge of operators and functions, to form an integrated knowledge-based system. The integrating method works by integrating the knowledge components in the ontology structure. The problems in the integrated knowledge domain and the reasoning method to solve them are also studied.