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Formal languages are used as tools in multiple disciplines. However, formal language theory rarely concerns itself with particular languages (except as examples), but is mainly concerned with the study of various types of formalisms to describe languages. For instance, a language can be given as those strings generated by some formal grammar;
Formal language theory, the discipline that studies formal grammars and languages, is a branch of applied mathematics. Its applications are found in theoretical computer science, theoretical linguistics, formal semantics, mathematical logic, and other areas. A formal grammar is a set of rules for rewriting strings, along with a "start symbol ...
Translation of an English sentence to first-order logic. Logic translation is the process of representing a text in the formal language of a logical system.If the original text is formulated in ordinary language then the term natural language formalization is often used.
The Chomsky hierarchy in the fields of formal language theory, computer science, and linguistics, is a containment hierarchy of classes of formal grammars. A formal grammar describes how to form strings from a language's vocabulary (or alphabet) that are valid according to the language's syntax.
Additionally, formal rules can be applied outside of logic or mathematics to human language, treating it as a mathematical formal system with a formal grammar. [ 27 ] A characteristic stance of formalist approaches is the primacy of form (like syntax ), and the conception of language as a system in isolation from the outer world.
C. Categorial grammar; Chomsky hierarchy; Chomsky normal form; Chomsky–Schützenberger enumeration theorem; Chomsky–Schützenberger representation theorem
Formal language, which is a set of well-formed formulas, which are strings of symbols from an alphabet, formed by a formal grammar (consisting of production rules or formation rules). Deductive system , deductive apparatus, or proof system , which has rules of inference that take axioms and infers theorems , both of which are part of the formal ...
An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation. The general study of interpretations of formal languages is ...