Some Mathematical Aspects on Syntactic Discription
نویسنده
چکیده
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 complete 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 transforms. It is useful to establish subsets of elementary neighborhoods and this subclassification may contribute to a simplification of the clumsy representation of derivational history. Finally, some trivial but practically useful conventions are described.
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