Construction of Frame-Struture Logic Capable of Structural Knowledge Representation and the Semantic Analysis for Natural Language

在本研究中，我们提出了一种新型的逻辑系统，称为框架-结构逻辑。提出的逻辑系统具有数学语义。这种逻辑能够将自然语言中与名词短语对应的复合对象、对象之间的类层次和对象之间的属性继承描述为符号之间的直接关系。因此，框架结构逻辑是一种形式化系统，它具有类似于自然语言或语义网络的“结构化知识表示”能力。框架结构Login的构造过程如下：1.提出了框架结构逻辑的基本公理系统及其语义，并证明了该逻辑的完备性定理和可判定性；2.在框架结构逻辑中引入了对象的否定和析取算子。扩展后的系统可以处理由“动植物”和“汤姆、玛丽和约翰”等对象算子产生的复合名词概念。3.为了丰富属性关系的表达能力，在框架结构逻辑中引入了属性函数和量词。最后，我们对框架结构逻辑进行了扩展，使其能够处理与动词谓语句相对应的事件对象。在谓词逻辑中，动词被视为关系符号，这样的句子被描述为命题。另一方面，在这个扩展逻辑中，不仅名词短语被视为宾语，动词也被视为宾语。因此，没有使用高阶谓词逻辑就不能表示的句子的含义可以用这个逻辑来描述。我们定义了该逻辑的语法和数学语义。

In this research, we proposed a new type logic system called "Frame-Structure Logic". The proposed logic system has a mathematical semantics. This logic is capable of describing a compound object corresponding to a noun phrase in natural language, class hierarchy between objects and attribute inheritance between objects, as direct relations between symbols. Consequently, Frame-Structure Logic is a formal system which is capable of "structural knowledge representation", similar to natural language or semantic networks. The construction of Frame-Structure Login was done as follows :1.Firstly, we proposed the basic axiom system and its semantics, and proved the completeness theorem and the decidability of this logic.2.Secondly, we introduced object operators of negation and disjunction into Frame-Structure Logic. The extended system can treat compound noun concepts produced by using these object operators, such as "animal and plant" and "Tom, Mary and John".3.In order to enrich the expressive power of the attribute relation, attribute functions and quantifiers were introduced into Frame-Structure Logic. In result, the objects such as students who has all kinds of fruits as the value of the attribute "favorite", and the value of the attribute "pet" for John, can be represented in this logic.4.Finaly, we extended Frame-Structure Logic so that it can treat event objects corresponding to sentences having verb predicates. In predicate logic, verbs are treated as relation symbols, and such sentences are described as propositions. On the other hand, in this extended logic, not only noun phrases but also verbs are treated as objects. Consequently, the meanings of sentences that can't be represented whithout using higher order predicate logic can be described in this logic. We defined the syntax and the mathematical semantics for this logic.