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The theory achieves an exhaustive and discrete enumeration of the data points. There is a pigeonhole for each observation. Descriptive adequacy. The theory formally specifies rules accounting for all observed arrangements of the data. The rules produce all and only the well-formed constructs (relations) of the protocol space.
Gradient well-formedness is a problem that arises in the analysis of data in generative linguistics, in which a linguistic entity is neither completely grammatical nor completely ungrammatical. A native speaker may judge a word, phrase or pronunciation as "not quite right" or "almost there," rather than dismissing it as completely unacceptable ...
W-grammars are two-level grammars: they are defined by a pair of grammars, that operate on different levels: the hypergrammar is an attribute grammar, i.e. a set of context-free grammar rules in which the nonterminals may have attributes; and; the metagrammar is a context-free grammar defining possible values for these attributes.
The deductive apparatus may consist of a set of transformation rules, which may be interpreted as valid rules of inference, or a set of axioms, or have both. A formal system is used to derive one expression from one or more other expressions. Although a formal language can be identified with its formulas, a formal system cannot be likewise ...
The phrase grammar of most programming languages can be specified using a Type-2 grammar, i.e., they are context-free grammars, [8] though the overall syntax is context-sensitive (due to variable declarations and nested scopes), hence Type-1. However, there are exceptions, and for some languages the phrase grammar is Type-0 (Turing-complete).
Set inclusions described by the Chomsky hierarchy. 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.
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According to Chomsky, a speaker's grammaticality judgement is based on two factors: . A native speaker's linguistic competence, which is the knowledge that they have of their language, allows them to easily judge whether a sentence is grammatical or ungrammatical based on intuitive introspection.