A formal grammar describes which strings from an alphabet of a formal language are valid according to the language's syntax. A grammar does not describe the meaning of the strings or what can be done with them in whatever context—only their form. A formal grammar is defined as a set of production rules for such strings in a formal language.
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" from which rewriting starts. Therefore, a grammar is usually thought of as a language generator. However, it can also sometimes be used as the basis for a "recognizer"—a function in computing that determines whether a given string belongs to the language or is grammatically incorrect. To describe such recognizers, formal language theory uses separate formalisms, known as automata theory. One of the interesting results of automata theory is that it is not possible to design a recognizer for certain formal languages.[1] Parsing is the process of recognizing an utterance (a string in natural languages) by breaking it down to a set of symbols and analyzing each one against the grammar of the language. Most languages have the meanings of their utterances structured according to their syntax—a practice known as compositional semantics. As a result, the first step to describing the meaning of an utterance in language is to break it down part by part and look at its analyzed form (known as its parse tree in computer science, and as its deep structure in generative grammar).
^Meduna, Alexander (2014), Formal Languages and Computation: Models and Their Applications, CRC Press, p. 233, ISBN 9781466513457. For more on this subject, see undecidable problem.
A formalgrammar describes which strings from an alphabet of a formal language are valid according to the language's syntax. A grammar does not describe...
well-formed according to a specific set of rules called a formal grammar. The alphabet of a formal language consists of symbols, letters, or tokens that concatenate...
formulas, which are strings of symbols from an alphabet, formed by a formalgrammar (consisting of production rules or formation rules). Deductive system...
Montague grammar assumed a similar view of syntax. It continues to be a major paradigm, particularly within formal semantics. A categorial grammar consists...
fields of formal language theory, computer science, and linguistics, is a containment hierarchy of classes of formalgrammars. A formalgrammar describes...
In formal languages, terminal and nonterminal symbols are the lexical elements used in specifying the production rules constituting a formalgrammar. Terminal...
computer science Formalism (philosophy of mathematics) FormalgrammarFormal language Formal method Formal system Form and content Mathematical model Mathematical...
computer science, a parsing expression grammar (PEG) is a type of analytic formalgrammar, i.e. it describes a formal language in terms of a set of rules...
it – that is, before it has any meaning. Formal proofs are expressed in some formal languages. A formalgrammar (also called formation rules) is a precise...
comprising the symbolic "words" or "sentences" of a formal system Formalgrammar, a grammar describing a formal language Colloquialism, the linguistic style...
computer languages or data structures, conforming to the rules of a formalgrammar. The term parsing comes from Latin pars (orationis), meaning part (of...
In formal language theory, an LL grammar is a context-free grammar that can be parsed by an LL parser, which parses the input from Left to right, and...
In theoretical computer science and formal language theory, a regular grammar is a grammar that is right-regular or left-regular. While their exact definition...
somewhat complete formalgrammar for a natural language, but there are usually so many exceptions in real usage that a formalgrammar is of minimal help...
In linguistics, the grammar of a natural language is its set of structural rules on speakers' or writers' usage and creation of clauses, phrases, and...
out a series of types of formalgrammars with increasing expressive power. Among the simplest types are the regular grammars (type 3); Chomsky argues...
A grammar school is one of several different types of school in the history of education in the United Kingdom and other English-speaking countries, originally...
An attribute grammar is a formal way to supplement a formalgrammar with semantic information processing. Semantic information is stored in attributes...
In computer science, a lexical grammar or lexical structure is a formalgrammar defining the syntax of tokens. The program is written using characters...
and formal language theory, a regular tree grammar is a formalgrammar that describes a set of directed trees, or terms. A regular word grammar can be...
the language in question. Construction grammarFormalgrammar Ronald W. Langacker, Foundations of Cognitive Grammar Volume I, Stanford University Press,...
1970: "English as a Formal Language" (= EFL) 1973: "The Proper Treatment of Quantification in Ordinary English" (= PTQ) Montague grammar can represent the...
partially represented by categorial grammar, formal semantics, and transcendental phenomenology, Logical grammar consists of the analysis of the sentence...