认知模型的自动提取及其在解析几何问题求解中的应用

发布时间：2019-04-26 19:34

【摘要】：随着科学技术的发展,近年来,人们对人工智能的研究热情可谓如火如荼。在许多领域取得了重大突破,例如:google的AlphaGo就是著名一例,机器战胜了人类,是人工智能领域的一个新标杆,具有划时代的意义。人工智能在语音识别、人脸识别、自动驾驶、智能搜索、博弈、定理证明等领域得到了广泛应用。在教育教学方面,也陆续出现各种教学教辅平台,迄今为止,市场上还没有真正意义上的智能产品,能够像人一样的解答问题,并给出解题步骤。本文正是在这个背景下,研究和构建了基于规则流的认知模型,并将其应用于平面解析几何问题求解,设计和实现了一个类人智能答题系统,更好地为智能教育教学提供服务。本文主要研究内容包括以下几个部分:(1)初等数学概念与关系的知识表示。计算机进行初等数学解题的前提是必须能够理解其中的概念。本文将这些概念抽象为“实体”和“关系”,然后为这些实体和关系表示成一阶谓词逻辑的形式。这样,就可以把一个题目的已知条件和结论进行自动转换,然后系统就可基于这些已知条件及结论进行解题。(2)公理和定理等规则的知识表示。要想计算机能够进行类人答题,其每一步计算或推理都必须遵循相应的数学逻辑,而这些数学逻辑就是初等数学中的公理、定义、定理和推论等。本文将每一个公理、定理等表示成相应的产生式规则。(3)基于规则流的认知模型的自动构建。规则库中的规则在匹配执行的时候,是乱序的,不确定的,如果我们把执行频率比较高的规则提取出来,经过一定的拼接整理,形成认知模型链,存储在认知模型库中,供下次解题使用,那么系统的推理就具有了方向性和目的性。(4)基于认知模型的解析几何问题求解系统的设计与实现。由于认知模型使推理具有了目的性,减少了无效规则的匹配,所以基于认知模型的解析几何求解系统会在效率上有所提高。基于构建的认知推理模型,设计和实现了一个解析几何问题求解系统,可进行自动类人答题。通过大量的实验验证,系统的问题求解效率得到了较大提高,问题求解准确率可达60%。
[Abstract]:With the development of science and technology, in recent years, people's enthusiasm for artificial intelligence research can be said to be in full swing. Great breakthroughs have been made in many fields, for example: google's AlphaGo is a famous example, the machine defeated the human being, is a new benchmark in the field of artificial intelligence, has the epoch-making significance. Artificial intelligence is widely used in speech recognition, face recognition, autopilot, intelligent search, game, theorem proving and so on. In the aspect of education and teaching, a variety of teaching-assisted platforms have appeared one after another. Up to now, there are no real intelligent products in the market, which can solve problems like people and give the steps to solve the problems. Under this background, this paper studies and constructs a cognitive model based on rule flow, and applies it to solving plane analytic geometry problems, designs and implements a human-like intelligent problem answering system, and provides better services for intelligent education and teaching. The main contents of this paper are as follows: (1) knowledge representation of elementary mathematical concepts and relationships. The premise of computer solving elementary mathematics problem is that it must be able to understand its concept. In this paper, these concepts are abstracted as "entity" and "relation", and then expressed in the form of first-order predicate logic for these entities and relationships. In this way, the known conditions and conclusions of a problem can be automatically transformed, and then the system can solve the problem based on these known conditions and conclusions. (2) the knowledge representation of axioms and theorems and other rules. In order for a computer to be able to answer a class of questions, each step of its calculation or reasoning must follow the corresponding mathematical logic, which is axioms, definitions, theorems and corollaries in elementary mathematics. In this paper, each axiom, theorem and so on are expressed as corresponding production rules. (3) automatic construction of cognitive model based on rule flow. The rules in the rule base are random and uncertain when they are matched and executed. If we extract the rules with high frequency of execution and sort them together to form a cognitive model chain, we can store them in the cognitive model library. For the next time, the reasoning of the system has the directivity and purpose. (4) the design and implementation of the analytic geometry problem solving system based on cognitive model. Because the cognitive model makes reasoning purposeful and reduces the matching of invalid rules, the analytic geometric solution system based on cognitive model can improve the efficiency of the system. Based on the cognitive reasoning model, an analytic geometry problem solving system is designed and implemented. Through a large number of experiments, the problem-solving efficiency of the system is greatly improved, and the accuracy of the problem-solving is up to 60%.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O182

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