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

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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.