Cross-serial Dependencies
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Cross-serial Dependencies
In linguistics, cross-serial dependencies (also called crossing dependencies by some authors.) occur when the lines representing the dependency relations between two series of words cross over each other.. They are of particular interest to linguists who wish to determine the syntactic structure of natural language; languages containing an arbitrary number of them are non- context-free. By this fact, Dutch. and Swiss-German. have been proved to be non-context-free. Example As Swiss-German allows verbs and their arguments to be ordered cross-serially, we have the following example, taken from Shieber: That is, "we help Hans paint the house." Notice that the sequential noun phrases ''em Hans'' (''Hans'') and ''es huus'' (''the house''), and the sequential verbs ''hälfed'' (''help'') and ''aastriiche'' (''paint'') both form two separate series of constituents. Notice also that the dative verb ''hälfed'' and the accusative verb ''aastriiche'' take the dative ''em Hans'' and ...
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Schematic Of Cross-serial Dependency
A schematic, or schematic diagram, is a designed representation of the elements of a system using abstract, graphic symbols rather than realistic pictures. A schematic usually omits all details that are not relevant to the key information the schematic is intended to convey, and may include oversimplified elements in order to make this essential meaning easier to grasp, as well as additional organization of the information. For example, a subway map intended for passengers may represent a subway station with a dot. The dot is not intended to resemble the actual station at all but aims to give the viewer information without unnecessary visual clutter. A schematic diagram of a chemical process uses symbols in place of detailed representations of the vessels, piping, valves, pumps, and other equipment that compose the system, thus emphasizing the functions of the individual elements and the interconnections among them and suppresses their physical details. In an electronic circuit d ...
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Regular Language
In theoretical computer science and formal language theory, a regular language (also called a rational language) is a formal language that can be defined by a regular expression, in the strict sense in theoretical computer science (as opposed to many modern regular expressions engines, which are augmented with features that allow recognition of non-regular languages). Alternatively, a regular language can be defined as a language recognized by a finite automaton. The equivalence of regular expressions and finite automata is known as Kleene's theorem (after American mathematician Stephen Cole Kleene). In the Chomsky hierarchy, regular languages are the languages generated by Type-3 grammars. Formal definition The collection of regular languages over an alphabet Σ is defined recursively as follows: * The empty language Ø is a regular language. * For each ''a'' ∈ Σ (''a'' belongs to Σ), the singleton language is a regular language. * If ''A'' is a regular language, ''A''* ( ...
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Linear Context-free Rewriting System
Generalized context-free grammar (GCFG) is a grammar formalism that expands on context-free grammars by adding potentially non-context-free composition functions to rewrite rules. Head grammar (and its weak equivalents) is an instance of such a GCFG which is known to be especially adept at handling a wide variety of non-CF properties of natural language. Description A GCFG consists of two components: a set of composition functions that combine string tuples, and a set of rewrite rules. The composition functions all have the form f(\langle x_1, ..., x_m \rangle, \langle y_1, ..., y_n \rangle, ...) = \gamma, where \gamma is either a single string tuple, or some use of a (potentially different) composition function which reduces to a string tuple. Rewrite rules look like X \to f(Y, Z, ...), where Y, Z, ... are string tuples or non-terminal symbols. The rewrite semantics of GCFGs is fairly straightforward. An occurrence of a non-terminal symbol is rewritten using rewrite rules as in ...
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Context-sensitive Language
In formal language theory, a context-sensitive language is a language that can be defined by a context-sensitive grammar (and equivalently by a noncontracting grammar). Context-sensitive is one of the four types of grammars in the Chomsky hierarchy. Computational properties Computationally, a context-sensitive language is equivalent to a linear bounded nondeterministic Turing machine, also called a linear bounded automaton. That is a non-deterministic Turing machine with a tape of only kn cells, where n is the size of the input and k is a constant associated with the machine. This means that every formal language that can be decided by such a machine is a context-sensitive language, and every context-sensitive language can be decided by such a machine. This set of languages is also known as NLINSPACE or NSPACE(''O''(''n'')), because they can be accepted using linear space on a non-deterministic Turing machine. The class LINSPACE (or DSPACE(''O''(''n''))) is defined the same, ...
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Mildly Context-sensitive Language
In computational linguistics, the term mildly context-sensitive grammar formalisms refers to several grammar formalisms that have been developed in an effort to provide adequate descriptions of the syntactic structure of natural language. Every mildly context-sensitive grammar formalism defines a class of mildly context-sensitive grammars (the grammars that can be specified in the formalism), and therefore also a class of mildly context-sensitive languages (the formal languages generated by the grammars). Background By 1985, several researchers in descriptive and mathematical linguistics had provided evidence against the hypothesis that the syntactic structure of natural language can be adequately described by context-free grammars.Riny Huybregts. "The Weak Inadequacy of Context-Free Phrase Structure Grammars". In Ger de Haan, Mieke Trommelen, and Wim Zonneveld, editors, ''Van periferie naar kern'', pages 81–99. Foris, Dordrecht, The Netherlands, 1984.Stuart M. Shieber.Eviden ...
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Ogden's Lemma
In the theory of formal languages, Ogden's lemma (named after William F. Ogden) is a generalization of the pumping lemma for context-free languages Pumping may refer to: * The operation of a pump, for moving a liquid from one location to another **The use of a breast pump for extraction of milk * Pumping (audio), a creative misuse of dynamic range compression * Pumping (computer systems), the .... Statement Ogden's lemma states that if a language is context-free, then there exists some number p\geq 1 (where may or may not be a pumping length) such that for any string of length at least in and every way of "marking" or more of the positions in , can be written as :s = uvwxy with strings and , such that # has at least one marked position, # has at most marked positions, and #uv^n wx^n y \in L for all n \geq 0. In the special case where every position is marked, Ogden's lemma is equivalent to the pumping lemma for context-free languages. Ogden's lemma can be used to show ...
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Jeffrey D
Jeffrey may refer to: * Jeffrey (name), including a list of people with the name * ''Jeffrey'' (1995 film), a 1995 film by Paul Rudnick, based on Rudnick's play of the same name * ''Jeffrey'' (2016 film), a 2016 Dominican Republic documentary film *Jeffrey's, Newfoundland and Labrador, Canada *Jeffrey City, Wyoming, United States *Jeffrey Street, Sydney, Australia * Jeffrey's sketch, a sketch on American TV show ''Saturday Night Live'' *'' Nurse Jeffrey'', a spin-off miniseries from the American medical drama series ''House, MD'' *Jeffreys Bay, Western Cape, South Africa People with the surname * Alexander Jeffrey (1806–1874), Scottish solicitor and historian * Charles Jeffrey (footballer) (died 1915), Scottish footballer * E. C. Jeffrey (1866–1952), Canadian-American botanist *Grant Jeffrey (1948–2012), Canadian writer *Hester C. Jeffrey (1842–1934), American activist, suffragist and community organizer *Richard Jeffrey (1926–2002), American philosopher, logician, and pro ...
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John E
John is a common English name and surname: * John (given name) * John (surname) John may also refer to: New Testament Works * Gospel of John, a title often shortened to John * First Epistle of John, often shortened to 1 John * Second Epistle of John, often shortened to 2 John * Third Epistle of John, often shortened to 3 John People * John the Baptist (died c. AD 30), regarded as a prophet and the forerunner of Jesus Christ * John the Apostle (lived c. AD 30), one of the twelve apostles of Jesus * John the Evangelist, assigned author of the Fourth Gospel, once identified with the Apostle * John of Patmos, also known as John the Divine or John the Revelator, the author of the Book of Revelation, once identified with the Apostle * John the Presbyter, a figure either identified with or distinguished from the Apostle, the Evangelist and John of Patmos Other people with the given name Religious figures * John, father of Andrew the Apostle and Saint Peter * Pope J ...
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Formal Language
In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of symbols, letters, or tokens that concatenate into strings of the language. Each string concatenated from symbols of this alphabet is called a word, and the words that belong to a particular formal language are sometimes called ''well-formed words'' or ''well-formed formulas''. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar, which consists of its formation rules. In computer science, formal languages are used among others as the basis for defining the grammar of programming languages and formalized versions of subsets of natural languages in which the words of the language represent concepts that are associated with particular meanings or semantics. In computational complexity ...
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Linguistics
Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure. Linguistics is concerned with both the cognitive and social aspects of language. It is considered a scientific field as well as an academic discipline; it has been classified as a social science, natural science, cognitive science,Thagard, PaulCognitive Science, The Stanford Encyclopedia of Philosophy (Fall 2008 Edition), Edward N. Zalta (ed.). or part of the humanities. Traditional areas of linguistic analysis correspond to phenomena found in human linguistic systems, such as syntax (rules governing the structure of sentences); semantics (meaning); morphology (structure of words); phonetics (speech sounds and equivalent gestures in sign languages); phonology (the abstract sound system of a particular language); and pragmatics (how social con ...
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Grammatical Case
A grammatical case is a category of nouns and noun modifiers (determiners, adjectives, participles, and Numeral (linguistics), numerals), which corresponds to one or more potential grammatical functions for a nominal group in a wording. In various languages, nominal groups consisting of a noun and its modifiers belong to one of a few such categories. For instance, in English language, English, one says ''I see them'' and ''they see me'': the nominative case, nominative pronouns ''I/they'' represent the perceiver and the accusative case, accusative pronouns ''me/them'' represent the phenomenon perceived. Here, nominative case, nominative and accusative case, accusative are cases, that is, categories of pronouns corresponding to the functions they have in representation. English language, English has largely lost its inflected case system but personal pronouns still have three cases, which are simplified forms of the Nominative case, nominative, Accusative case, accusative and gen ...
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Accusative Case
The accusative case (abbreviated ) of a noun is the grammatical case used to mark the direct object of a transitive verb. In the English language, the only words that occur in the accusative case are pronouns: 'me,' 'him,' 'her,' 'us,' and ‘them’. The spelling of those words will change depending on how they are used in a sentence. For example, the pronoun ''they'', as the subject of a sentence, is in the nominative case ("They wrote a book"); but if the pronoun is instead the object, it is in the accusative case and ''they'' becomes ''them'' ("The book was written by them"). The accusative case is used in many languages for the objects of (some or all) prepositions. It is usually combined with the nominative case (for example in Latin). The English term, "accusative", derives from the Latin , which, in turn, is a translation of the Greek . The word may also mean "causative", and this may have been the Greeks' intention in this name, but the sense of the Roman translation has ...
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