Some Mathematical Aspects on Syntactic Discription

1965 International Conference on Computational Linguistics SOME MATHEMATICAL ASPECTS ON SYNTACTIC DISCRIPTION Itiroo Sakai Project on Linguistic Analysis Ohio State University 216 North Oval Drive Columbus, Ohio 43210 U. S. A. Sakai 1 Abstract. The purpose of this paper is to help linguists contruct a consistent, sufficient and less redundant syntax of language. An acceptable string corresponds to an expression or an utterance: it may be a natural text, a string of morphemes, a tree structure or any kind of representation. A sharp distinction is made between the syntactic function which is an attrib trin s and the distribution class which is a set of strings. Syntactic function of a continuous or discontinuous string is defined as the set of all the acceptable contexts of the string, and is called a com- plete neighborhood. Two contexts are equivalent if they accept or reject any given string at the same time. An elementary neighborhood is the set of all contexts equivalent to one context. Four simple distribution classes are proposed and their properties are discussed. Concatenation rules of a language can be described in terms of concatenated complete neighborhoods or concatenated distribution classes. Some possible representations and their consequences are discussed. Transformational rules are also described in a similar way. However, there is another problem of correspondence of original strings to their trans- forms. It is useful to establish subsets of elementary neighborhoods and this subclassification may contribute to a simplification of the clumsy represent- ation of derivational history. Finally, some trivial but practically useful conventions are described. 1. Introduction. ~he grammar of a language should be consistent throughout its whole system. No features should be left unformulated in order that the grammar be a complete one. At the same time, it is desirable to prepare the grammar as compact as possible. These are important requirements especially when the grammar is a machine-oriented one. The knowledge on the formal properties of syntax will help us construct an objective system of grammar. Every term used in a description should be rigorously defined and no ambiguous expressions are allowed. If the consequence of grammar rules deviates from the proper usage of the language~ we will be able to trace back the definitions and locate the source of trouble. When the grammar rules are given in terms of concatenated symbols, we must know the formal definition of the symbols before writing a program by which the rules are applied to the text. If a grammar rule describes the nature of a P-marker, the label given to each node in the P-marker must have an unambiguous definition which relates the meaning of the symbol to the strings supplied as texts. Sahai 2 We need, at least, an objective criterion by which we can specify a language. This criterion will be a dichotomous decision whether or not a given symbol string belongs to the language in question. We leave the decision to native speakers and consider the acceptable strings undefined. A substring of an acceptable string …

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