CHAPTER 5 - Formal and Natural Languages

Abstract

This chapter discusses formal and natural languages. An algebra or algebraic system is a set S together with a set F of finitary operators defined on S. Because of the simplicity of definition, semigroups form a large and complex class of objects with little structure. The simplest of algebraic systems are those having only a single binary operator. A formal language can be specified in terms of an alphabet and a grammar. An alphabet is a finite set of symbols. A natural language develops and grows through daily use by many people. A grammar for a natural language is subsequently developed to codify rules for the language. Thus, the language comes first and the grammar follows it. However, for a formal language, the grammar is developed first and firmly fixed. Thus, the formal language grows out of its grammar rather than the grammar arising from the already developed language. The formal languages are called phrase structure languages. A grammar for a language can be either generative, starting with the concept sentence and generating particular sentences, or descriptive, starting with a particular string of words and describing exactly how it can be deemed a sentence.