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Concept
Formal grammar
Summary
In formal language theory, a grammar (when the context is not given, often called a formal grammar for clarity) describes how to form strings from a language's alphabet that 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.
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).
A grammar mainly consists of a set of production rules, rewriting rules for transforming strings. Each rule specifies a replacement of a particular string (its left-hand side) with another (its right-hand side).
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Regular tree grammar
In theoretical computer science and formal language theory, a regular tree grammar is a formal grammar that describes a set of directed trees, or terms. A regular word grammar can be seen as a special kind of regular tree grammar, describing a set of single-path trees. A regular tree grammar G is defined by the tuple G = (N, Σ, Z, P), where N is a finite set of nonterminals, Σ is a ranked alphabet (i.e.
Formal grammar
In formal language theory, a grammar (when the context is not given, often called a formal grammar for clarity) describes how to form strings from a language's alphabet that 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.
Linguistics
Linguistics is the scientific study of language. The modern-day scientific study of linguistics takes all aspects of language into account — i.e., the cognitive, the social, the cultural, the psychological, the environmental, the biological, the literary, the grammatical, the paleographical, and the structural. Linguistics is based on a theoretical as well as descriptive study of language, and is also interlinked with the applied fields of language studies and language learning, which entails the study of specific languages.
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