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Let R be the set of all sets that are not members of themselves. (This set is sometimes called "the Russell set".) If R is not a member of itself, then its definition entails that it is a member of itself; yet, if it is a member of itself, then it is not a member of itself, since it is the set of all sets that are not members of themselves. The ...
Grammatical: it uses rules based on sampling of the lexical corpus; Register-specific: it uses the same word differently and/or less frequently in different contexts; A major area of study, psycholinguistics and neurolinguistics, involves the question of how words are retrieved from the mental lexical corpus in online language processing and ...
It disregards word order (and thus most of syntax or grammar) but captures multiplicity. The bag-of-words model is commonly used in methods of document classification where, for example, the (frequency of) occurrence of each word is used as a feature for training a classifier. [1] It has also been used for computer vision. [2]
A lexical set is a group of words that share a particular vowel or consonant sound. A phoneme is a basic unit of sound in a language that can distinguish one word from another. Most commonly, following the work of phonetician John C. Wells, a lexical set is a class of words in a language that share a certain vowel phoneme.
A phraseme, also called a set phrase, fixed expression, multiword expression (in computational linguistics), or idiom, [1] [2] [3] [citation needed] is a multi-word or multi-morphemic utterance whose components include at least one that is selectionally constrained [clarification needed] or restricted by linguistic convention such that it is not freely chosen. [4]
A set of sentences is called a (first-order) theory, which takes the sentences in the set as its axioms. A theory is satisfiable if it has a model M ⊨ T {\displaystyle {\mathcal {M}}\models T} , i.e. a structure (of the appropriate signature) which satisfies all the sentences in the set T {\displaystyle T} .
Chomsky uses this argument as well to motivate the establishment of distinct levels of linguistic analysis. [75] Chomsky then shows that a grammar which analyzes sentences up to the phrase structure level contains many constructional homonymities at the phrase structure level where the resulting ambiguities need to be explained at a higher level.
After all this, the version of the "set of all sets" paradox conceived by Bertrand Russell in 1903 led to a serious crisis in set theory. Russell recognized that the statement x = x is true for every set, and thus the set of all sets is defined by {x | x = x}. In 1906 he constructed several paradox sets, the most famous of which is the set of ...