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Optimality Theory
Optimality theory (frequently abbreviated OT) is a linguistic model proposing that the observed forms of language arise from the optimal satisfaction of conflicting constraints. OT differs from other approaches to phonological analysis, which typically use rules rather than constraints. However, phonological models of representation, such as autosegmental phonology, prosodic phonology, and linear phonology (SPE), are equally compatible with rule-based and constraint-based models. OT views grammars as systems that provide mappings from inputs to outputs; typically, the inputs are conceived of as underlying representations, and the outputs as their surface realizations. It is an approach within the larger framework of generative grammar. Optimality theory has its origin in a talk given by Alan Prince and Paul Smolensky in 1991 which was later developed in a book manuscript by the same authors in 1993. Overview There are three basic components of the theory: * Generator () t ...
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Language
Language is a structured system of communication that consists of grammar and vocabulary. It is the primary means by which humans convey meaning, both in spoken and signed language, signed forms, and may also be conveyed through writing system, writing. Human language is characterized by its cultural and historical diversity, with significant variations observed between cultures and across time. Human languages possess the properties of Productivity (linguistics), productivity and Displacement (linguistics), displacement, which enable the creation of an infinite number of sentences, and the ability to refer to objects, events, and ideas that are not immediately present in the discourse. The use of human language relies on social convention and is acquired through learning. Estimates of the number of human languages in the world vary between and . Precise estimates depend on an arbitrary distinction (dichotomy) established between languages and dialects. Natural languages are ...
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Connectionist
Connectionism is an approach to the study of human mental processes and cognition that utilizes mathematical models known as connectionist networks or artificial neural networks. Connectionism has had many "waves" since its beginnings. The first wave appeared 1943 with Warren Sturgis McCulloch and Walter Pitts both focusing on comprehending neural circuitry through a formal and mathematical approach, and Frank Rosenblatt who published the 1958 paper "The Perceptron: A Probabilistic Model For Information Storage and Organization in the Brain" in ''Psychological Review'', while working at the Cornell Aeronautical Laboratory. The first wave ended with the 1969 book about the limitations of the original perceptron idea, written by Marvin Minsky and Seymour Papert, which contributed to discouraging major funding agencies in the US from investing in connectionist research. With a few noteworthy deviations, most connectionist research entered a period of inactivity until the mid-1980s. T ...
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Distinctive Feature
In linguistics, a distinctive feature is the most basic unit of phonology, phonological structure that distinguishes one Phone (phonetics), sound from another within a language. For example, the feature [+Voice (phonetics), voice] ''distinguishes'' the two bilabial plosives: [p] and [b] (i.e., it makes the two plosives ''distinct'' from one another). There are many different ways of defining and arranging features into ''feature systems'': some deal with only one language while others are developed to apply to all languages. Distinctive features are grouped into categories according to the natural classes of segment (linguistics), segments they describe: major class features, laryngeal features, manner features, and place features. These feature categories in turn are further specified on the basis of the phonetics, phonetic properties of the segments in question. Since the inception of the phonological analysis of distinctive features in the 1950s, features traditionally have be ...
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Reduplication
In linguistics, reduplication is a Morphology (linguistics), morphological process in which the Root (linguistics), root or Stem (linguistics), stem of a word, part of that, or the whole word is repeated exactly or with a slight change. The classic observation on the semantics of reduplication is Edward Sapir, Edward Sapir's: "Generally employed, with self-evident symbolism, to indicate such concepts as distribution, plurality, repetition, customary activity, increase of size, added intensity, continuance." It is used in inflections to convey a grammatical function, such as plurality or intensification, and in Lexicon, lexical Derivation (linguistics), derivation to create new words. It is often used when a speaker adopts a tone more expressive or figurative than ordinary speech and is also often, but not exclusively, Iconicity, iconic in meaning. It is found in a wide range of languages and language groups, though its level of Productivity (linguistics), linguistic productivit ...
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Elision
In linguistics, an elision or deletion is the omission of one or more sounds (such as a vowel, a consonant, or a whole syllable) in a word or phrase. However, these terms are also used to refer more narrowly to cases where two words are run together by the omission of a final sound. An example is the elision of word-final /t/ in English if it is preceded and followed by a consonant: "first light" is often pronounced "firs' light" (). Many other terms are used to refer to specific cases where sounds are omitted. Citation forms and contextual forms A word may be spoken individually in what is called the citation form. This corresponds to the pronunciation given in a dictionary. However, when words are spoken in context, it often happens that some sounds that belong to the citation form are omitted. Elision is not an all-or-nothing process: elision is more likely to occur in some styles of speaking and less likely in others. Many writers have described the styles of speech in wh ...
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Ordered Bell Number
In number theory and enumerative combinatorics, the ordered Bell numbers or Fubini numbers count the weak orderings on a set of n elements. Weak orderings arrange their elements into a sequence allowing ties, such as might arise as the outcome of a horse race. The ordered Bell numbers were studied in the 19th century by Arthur Cayley and William Allen Whitworth. They are named after Eric Temple Bell, who wrote about the Bell numbers, which count the partitions of a set; the ordered Bell numbers count partitions that have been equipped with a total order. Their alternative name, the Fubini numbers, comes from a connection to Guido Fubini and Fubini's theorem on equivalent forms of multiple integrals. Because weak orderings have many names, ordered Bell numbers may also be called by those names, for instance as the numbers of preferential arrangements or the numbers of asymmetric generalized weak orders. These numbers may be computed via a summation formula involving binomial coe ...
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Antimatroid
In mathematics, an antimatroid is a formal system that describes processes in which a set is built up by including elements one at a time, and in which an element, once available for inclusion, remains available until it is included. Antimatroids are commonly axiomatized in two equivalent ways, either as a set system modeling the possible states of such a process, or as a formal language modeling the different sequences in which elements may be included. Dilworth (1940) was the first to study antimatroids, using yet another axiomatization based on lattice theory, and they have been frequently rediscovered in other contexts. The axioms defining antimatroids as set systems are very similar to those of matroids, but whereas matroids are defined by an '' exchange axiom'', antimatroids are defined instead by an ''anti-exchange axiom'', from which their name derives. Antimatroids can be viewed as a special case of greedoids and of semimodular lattices, and as a generalization of parti ...
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Factorial
In mathematics, the factorial of a non-negative denoted is the Product (mathematics), product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times (n-1) \times (n-2) \times (n-3) \times \cdots \times 3 \times 2 \times 1 \\ &= n\times(n-1)!\\ \end For example, 5! = 5\times 4! = 5 \times 4 \times 3 \times 2 \times 1 = 120. The value of 0! is 1, according to the convention for an empty product. Factorials have been discovered in several ancient cultures, notably in Indian mathematics in the canonical works of Jain literature, and by Jewish mystics in the Talmudic book ''Sefer Yetzirah''. The factorial operation is encountered in many areas of mathematics, notably in combinatorics, where its most basic use counts the possible distinct sequences – the permutations – of n distinct objects: there In mathematical analysis, factorials are used in power series for the ex ...
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Well-formedness
__NOTOC__ In linguistics, well-formedness is the quality of a clause, word, or other linguistic element that conforms to the grammar of the language of which it is a part. Well-formed words or phrases are grammatical, meaning they obey all relevant rules of grammar. In contrast, a form that violates some grammar rule is ill-formed and does not constitute part of the language. A word may be phonologically well-formed, meaning it conforms to the sound pattern of the language. For example, the nonce word ''wug'' coined by Jean Berko Gleason is phonologically well-formed, so informants are able to pluralize it regularly. A word, phrase, clause, or utterance may be grammatically well-formed, meaning it obeys the rules of morphology and syntax. A semantically well-formed utterance or sentence is one that is meaningful. Grammatical well-formedness and semantic well-formedness do not always coincide. For example, the following sentence is grammatically well-formed, but has no clear m ...
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Elision
In linguistics, an elision or deletion is the omission of one or more sounds (such as a vowel, a consonant, or a whole syllable) in a word or phrase. However, these terms are also used to refer more narrowly to cases where two words are run together by the omission of a final sound. An example is the elision of word-final /t/ in English if it is preceded and followed by a consonant: "first light" is often pronounced "firs' light" (). Many other terms are used to refer to specific cases where sounds are omitted. Citation forms and contextual forms A word may be spoken individually in what is called the citation form. This corresponds to the pronunciation given in a dictionary. However, when words are spoken in context, it often happens that some sounds that belong to the citation form are omitted. Elision is not an all-or-nothing process: elision is more likely to occur in some styles of speaking and less likely in others. Many writers have described the styles of speech in wh ...
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Epenthesis
In phonology, epenthesis (; Greek ) means the addition of one or more sounds to a word, especially in the first syllable ('' prothesis''), the last syllable ('' paragoge''), or between two syllabic sounds in a word. The opposite process in which one or more sounds are removed is referred to as syncope or elision. Etymology The word ''epenthesis'' comes from and ''en-'' and ''thesis'' . Epenthesis may be divided into two types: excrescence for the addition of a consonant, and for the addition of a vowel, svarabhakti (in Sanskrit) or alternatively anaptyxis (). Uses Epenthesis arises for a variety of reasons. The phonotactics of a given language may discourage vowels in hiatus or consonant clusters, and a consonant or vowel may be added to help pronunciation. Epenthesis may be represented in writing, or it may be a feature only of the spoken language. Separating vowels A consonant may be added to separate vowels in hiatus, as is the case with linking and intrusive R in ...
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Consonant Cluster
In linguistics, a consonant cluster, consonant sequence or consonant compound is a group of consonants which have no intervening vowel. In English, for example, the groups and are consonant clusters in the word ''splits''. In the education field it is variously called a consonant cluster or a consonant blend. Some linguists argue that the term can be properly applied only to those consonant clusters that occur within one syllable. Others claim that the concept is more useful when it includes consonant sequences across syllable boundaries. According to the former definition, the longest consonant clusters in the word ''extra'' would be and , whereas the latter allows , which is phonetically in some accents. Phonotactics Each language has an associated set of phonotactic constraints. Languages' phonotactics differ as to what consonant clusters they permit. Many languages are more restrictive than English in terms of consonant clusters, and some forbid consonant clusters ...
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