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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;
Another central idea of linguistic formalism is that human language can be defined as a formal language like the language of mathematics and programming languages. 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 ...
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 ...
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 ...
The formal description of language was further developed by linguists including J. R. Firth and Simon Dik, giving rise to modern grammatical frameworks such as systemic functional linguistics and functional discourse grammar. Computational methods have been developed by the framework functional generative description among others.
Any language that one uses to talk about a formal system is called a metalanguage. The metalanguage may be a natural language, or it may be partially formalized itself, but it is generally less completely formalized than the formal language component of the formal system under examination, which is then called the object language , that is, the ...
Conjunctive grammars are a class of formal grammars studied in formal language theory. They extend the basic type of grammars, the context-free grammars , with a conjunction operation. Besides explicit conjunction, conjunctive grammars allow implicit disjunction represented by multiple rules for a single nonterminal symbol, which is the only ...
For example, indexed languages & grammars have been around since Aho (1968) and have been well studied since then, in e.g. Hopcroft & Ullman (1979), not to mention mildly context-sensitive (Joshi et al, 1975), deterministic context-free, and other major formal languages and grammars.