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1、 I摘 要 经典逻辑的推理形式是演绎的、单调的，一般被称为单调推理。它在解决基础理论问题时发挥了精确性与严格性等特点。但是在处理日常复杂语境下的推理问题时，基于经典逻辑的单调推理具有一定的局限性。与之相反，非单调推理具有一定的灵活性。其特点是推理结论具有暂时性。随着新情况的出现，结论可能会被更正，以便符合实际情况。 单调推理与非单调推理之间的区别类似于弗雷格所提出的显微镜与眼睛在功能上的比较。即显微镜发挥了精确性的特点，有助于研究微观世界，但不具有眼睛在生活中的灵活性。然而，眼睛也不可能直接观察到只有通过显微镜才能看到的微观世界。 非单调这一概念于上世纪 70 年代被提出来。经过学者们数十年对
2、非单调推理的研究，逐渐形成了与单调的经典逻辑不同的非单调逻辑。两者之间最明显的差别是，单调逻辑的定理集随前提集的增加而单调递增， 而非单调逻辑的定理集是随前提集的增加而非单调递增。具体来说，在日常语境下，以已有知识和新加入的知识为前提，可以得出新结论。新结论往往会面临两种情况：要么是与已有知识无矛盾，要么是与已有知识发生矛盾。第一种情况符合单调逻辑的特点。第二种情况符合非单调逻辑的特点。对于第二种情况，如果能确保新结论符合一般事实，那么就要对已有知识做修改。从而更新知识。对已有知识不断修改，发展新知识的过程，符合人类认识世界的一般规律。一方面，非单调推理对于理解人类如何认识世界有重要启发意义。
3、另一方面，非单调推理也可以作为一种实用的推理工具，应用于其他学科的研究中。因此，研究非单调推理具有重要意义。 研究非单调推理首先需要研究非单调逻辑系统。从逻辑学的角度，研究非单调逻辑系统的一致性与完全性等性质，可以阐明非单调推理是如何满足对推理合理性的要求。到目前为止，讨论最多的非单调逻辑系统是模态非单调逻辑和缺省逻辑等等。通过探讨这两类逻辑系统，可以深入了解模态非单调推理与缺省推理。在正文中，首先要全面了解非单调推理。通过讨论模态非单调逻辑和缺省逻辑这两种非单调逻辑系统，对非单调推理有一个整体性的认识。 其次对单调推理和非单调推理之间的联系与区别有一个清楚的认识。在此基础上，深入探讨非单调推
4、理在解决常识推理问题方面的效用和在其他学科上所具有的理论价值。 II关键词：非单调推理，模态非单调逻辑，缺省逻辑 III ABSTRACT The inferential form of classical logic is deductive and monotonic, and it is generally named monotonic reasoning. In solving the issues of basic theories it is accurate and strict, but there are some limitations when it is used t
5、o solve the problems of daily complex reasoning. In contrast, nonmonotonic reasoning has certain flexibility and its reasoning conclusion is temporary. When new conditions appear, the conclusions will be corrected in order to comply with the fact. The difference between monotonic reasoning and nonmo
6、notonic reasoning is similar to the comparison proposed by Frege-the comparison between microscope and eyes on the function. Namely, microscope is characteristic of its accuracy and it is helpful to study the micro world but doesnt have the flexibility of eyes in daily life. However, eyes couldnt di
7、rectly observe the microscopic world which could be observed only through a microscope. The concept non-monotonic reasoning was put forward in 1970s. After years of study, nonmonotonic logic has been gradually formed which is different from classical monotonic logic. The most obvious different is no
8、nmonotonic theorem increases, with the increasing of the prerequisite of the set. Specifically, in daily context, people could draw new conclusions on the premise of existing knowledge and newly-added knowledge. Usually, new conclusions will face two kinds of situations: they are either in contradic
9、tion with existing knowledge or not. The first situation accords with the characteristic of monontonic logic and its second accords with nonmonotonic logic. For the second situation, if we could ensure that new conclusion accords with general facts. Then, we have to make changes to the existing know
10、ledge, thus to develop new knowledge. This process of modifying existing knowledge and developing new knowledge accords with the general rule of knowing the world. On the one hand, nonmonotonic reasoning has important enlightening significance to understand the way to know the world; on the other ha
11、nd, as a useful reasoning method, it could be applied to the study of other scientific fields. So it is of a great importance to study nonmonotonic IVreasoning. To study nonmonotonic reasoning, we must firstly study nonmonotonic logical systems. From the point of logic, through the study of consiste
12、ncy and completeness of nonmonotonic logical systems, we could prove that nonmonotonic reasoning can satisfy the legitimacy in daily reasoning. So far, the most often discussed systems are modal nonmonotonic logic and default logic. Through discussing the two logical systems, we could deeply underst
13、and the modal nonmonotonic reasoning and default reasoning. In the context, first of all, we should have a whole view about the nonmonotonic reasoning through the discussion of two of its systemsmodal nonmonotonic logic and default logic. And then, we should have a clear understanding about the rela
14、tion and distinction between monotonic reasoning and nonmonotonic reasoning. On this basis, we explore its utility in common sense reasoning and its theoretical value in other subjects. KEY WORDS: Nonmonotonic Reasoning, Modal Nonmonotonic Logic, Default Logic I引 言 1 引 言 一 选题背景及意义 一般来说，经典逻辑主要是指形式逻辑或
15、演绎逻辑。经典逻辑的推理形式是演绎的和单调的。演绎性和单调性表现在，推理以已有知识为前提必然能得到新的知识。或者说在保证已有知识为真的前提下，由推理所得的新知识必定也是真的。比如，设 为一已知的知识集，为一新的知识集。如果两者之间的推理形式是演绎的，就可以得到 ，根据演绎定理也可以写为。或者只要保证给 的赋值 V()=1，那么就会得到 V()=1 而不会出现 V()=0。用式子表示就是 V。由此可知，经典逻辑的优点就在于语形上保证推理的严格性，语义上保证推理的有效性。只需要确保前提部分的真就可以获取真的新知识。 然而，在日常语境下，这种情况并不总是出现。经常出现的是新知识与已有知识之间发生冲突
16、。在必要的时候人们会修改已有知识，以适应对新情况的解释。这就体现出单调推理的局限性。为解决这一难题，满足常识推理的要求，非单调推理便应运而生。 非单调推理不同于单调推理不仅表现在形式上和功用上， 也表现在推理有效性的标准上。单调推理的有效性是指语义上的保真性，而非单调推理的有效性主要是指符合实际情况的合理性。换句话说，单调推理只要满足前提真，那么结论一定为真。与之不同，非单调推理需要满足对现实情况的合理解释。 对非单调推理的研究一般有两种途径：一种是，认为经典逻辑对于研究非单调推理有不足之处，最好建立新的语义机制与逻辑系统。在此基础上进行非单调推理研究，用以解决一些问题。例如，赖特（Reiter）缺省逻辑和摩尔（Moore）的自认识逻辑。另一种途径与此相反。他们认为，在经典逻辑框架下研究非单调推理是可行的，关键问题是如何运用经典逻辑。例如，赖特的封闭世界假设 CWA（Closed World Assumption）和麦卡锡（McCarthy）的限定推理等等。 在此主要对非单调推理研究的第一种途径进行阐释并深刻理解非单调
