This paper discusses a mathematical concept of language that models both artiÿcial and natural languages and thus provides a framework for a uniÿed language processing methodology. This concept of a language is regarded as a communication tool that allows language users to develop knowledges, while interacting with their universe of discourse, and to communicate with each other, while exchanging knowledges. Criteria for consistent usage of a language are established using a Galois connection between language syntax and language semantics. Solutions to ambiguity, paraphrase, attitude, and other problems concerning the relationship between syntax and semantics are addressed. A general schema for language speciÿcation is introduced and algorithms that perform language generation and language analysis are discussed as universal tools deÿned by the speciÿcation schema. Language transformations performed by various kinds of translators are examined and correctness criteria of these translators are deÿned using the language Galois connection.
The paper is structured as follows: Section 1 introduces the framework and justiÿes the necessity of a uniÿed methodology for language processing. Section 2 presents the mathematical concept of a language. Section 3 illustrates the mathematical concept of a language with three kinds of language structures: natural language, logical language, and programming language. Section 4 discusses the algebraic mechanism of language speciÿcation that uniÿes the methodology for language processing tool development. Section 5 formalizes the criterion for the consistency of the language usage, deÿnes the architecture of a uniÿed language processing system, and shows how the consistency criteria for language usage can be employed as correctness criteria for the algorithms performing various language transformations.