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Base Case (recursion)
Recursion occurs when the definition of a concept or process depends on a simpler or previous version of itself. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics and computer science, where a function being defined is applied within its own definition. While this apparently defines an infinite number of instances (function values), it is often done in such a way that no infinite loop or infinite chain of references can occur. A process that exhibits recursion is ''recursive''. Video feedback displays recursive images, as does an infinity mirror. Formal definitions In mathematics and computer science, a class of objects or methods exhibits recursive behavior when it can be defined by two properties: * A simple ''base case'' (or cases) — a terminating scenario that does not use recursion to produce an answer * A ''recursive step'' — a set of rules that reduces all successive cases ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cantor Ternary Set
In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of unintuitive properties. It was discovered in 1874 by Henry John Stephen Smith and mentioned by German mathematician Georg Cantor in 1883. Through consideration of this set, Cantor and others helped lay the foundations of modern point-set topology. The most common construction is the Cantor ternary set, built by removing the middle third of a line segment and then repeating the process with the remaining shorter segments. Cantor mentioned this ternary construction only in passing, as an example of a perfect set that is nowhere dense. More generally, in topology, a Cantor space is a topological space homeomorphic to the Cantor ternary set (equipped with its subspace topology). The Cantor set is naturally homeomorphic to the countable product ^ of the discrete two-point space \underline 2 . By a theorem of L. E. J. Brouwer, this is equivalent to being perfect, nonempty, compact, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinite Regress
Infinite regress is a philosophical concept to describe a series of entities. Each entity in the series depends on its predecessor, following a recursive principle. For example, the epistemic regress is a series of beliefs in which the justification of each belief depends on the justification of the belief that comes before it. An infinite regress argument is an argument against a theory based on the fact that this theory leads to an infinite regress. For such an argument to be successful, it must demonstrate not just that the theory in question entails an infinite regress but also that this regress is ''vicious''. There are different ways in which a regress can be vicious. The most serious form of viciousness involves a contradiction in the form of ''metaphysical impossibility''. Other forms occur when the infinite regress is responsible for the theory in question being implausible or for its failure to solve the problem it was formulated to solve. Traditionally, it was of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circular Definition
A circular definition is a type of definition that uses the term(s) being defined as part of the description or assumes that the term(s) being described are already known. There are several kinds of circular definition, and several ways of characterising the term: pragmatic, lexicographic and linguistic Linguistics is the scientific study of language. The areas of linguistic analysis are syntax (rules governing the structure of sentences), semantics (meaning), Morphology (linguistics), morphology (structure of words), phonetics (speech sounds .... Circular definitions are related to circular reasoning in that they both involve a self-referential approach. Circular definitions may be unhelpful if the audience must either already know the meaning of the key term, or if the term to be defined is used in the definition itself. In linguistics, a circular definition is a description of the meaning of a lexeme that is constructed using one or more synonymous lexemes that are al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Production (computer Science)
In computer science, a production or production rule is a rewrite rule that replaces some symbols with other symbols. A finite set of productions P is the main component in the specification of a formal grammar (specifically a generative grammar). The other components are a finite set N of nonterminal symbols, a finite set (known as an alphabet) \Sigma of terminal symbols that is disjoint from N and a distinguished symbol S \in N that is the ''start symbol''. In an unrestricted grammar, a production is of the form u \to v, where u and v are arbitrary strings of terminals and nonterminals, and u may not be the empty string. If v is the empty string, this is denoted by the symbol \epsilon, or \lambda (rather than leaving the right-hand side blank). So productions are members of the cartesian product :V^*NV^* \times V^* = (V^*\setminus\Sigma^*) \times V^*, where V := N \cup \Sigma is the ''vocabulary'', ^ is the Kleene star operator, V^*NV^* indicates concatenation, \cup deno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Grammar
A formal grammar is a set of Terminal and nonterminal symbols, symbols and the Production (computer science), production rules for rewriting some of them into every possible string of a formal language over an Alphabet (formal languages), alphabet. A grammar does not describe the semantics, meaning of the strings — only their form. In applied mathematics, formal language theory is the discipline that studies formal grammars and languages. Its applications are found in theoretical computer science, theoretical linguistics, Formal semantics (logic), formal semantics, mathematical logic, and other areas. A formal grammar is a Set_(mathematics), 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 grammatical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recursive Grammar
In computer science, a grammar is informally called a recursive grammar if it contains production rules that are recursive, meaning that expanding a non-terminal according to these rules can eventually lead to a string that includes the same non-terminal again. Otherwise it is called a non-recursive grammar.. For example, a grammar for a context-free language is left recursive if there exists a non-terminal symbol ''A'' that can be put through the production rules to produce a string with ''A'' (as the leftmost symbol). All types of grammars in the Chomsky hierarchy can be recursive and it is recursion that allows the production of infinite sets of words. Properties A non-recursive grammar can produce only a finite language; and each finite language can be produced by a non-recursive grammar. For example, a straight-line grammar produces just a single word. A recursive context-free grammar that contains no useless rules necessarily produces an infinite language. This proper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Language Semantics
Semantics is the study of linguistic meaning. It examines what meaning is, how words get their meaning, and how the meaning of a complex expression depends on its parts. Part of this process involves the distinction between sense and reference. Sense is given by the ideas and concepts associated with an expression while reference is the object to which an expression points. Semantics contrasts with syntax, which studies the rules that dictate how to create grammatically correct sentences, and pragmatics, which investigates how people use language in communication. Lexical semantics is the branch of semantics that studies word meaning. It examines whether words have one or several meanings and in what lexical relations they stand to one another. Phrasal semantics studies the meaning of sentences by exploring the phenomenon of compositionality or how new meanings can be created by arranging words. Formal semantics relies on logic and mathematics to provide precise framewor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-reference
Self-reference is a concept that involves referring to oneself or one's own attributes, characteristics, or actions. It can occur in language, logic, mathematics, philosophy, and other fields. In natural or formal languages, self-reference occurs when a sentence, idea or formula refers to itself. The reference may be expressed either directly—through some intermediate sentence or formula—or by means of some encoding. In philosophy, self-reference also refers to the ability of a subject to speak of or refer to itself, that is, to have the kind of thought expressed by the first person nominative singular pronoun "I" in English. Self-reference is studied and has applications in mathematics, philosophy, computer programming, second-order cybernetics, and linguistics, as well as in humor. Self-referential statements are sometimes paradoxical, and can also be considered recursive. In logic, mathematics and computing In classical philosophy, paradoxes were created b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pirahã Language
Pirahã (also spelled ''Pirahá, Pirahán''), or Múra-Pirahã, is the indigenous language of the Pirahã people of Amazonas, Brazil. The Pirahã live along the Maici River, a tributary of the Amazon River. Pirahã is the only surviving dialect of the Mura language; all others having died out in the last few centuries as most groups of the Mura people have shifted to Portuguese. Due to this, Pirahã can be considered its own language now, as no other Mura dialects have survived. Suspected relatives, such as Matanawi, are also extinct. Pirahã is estimated to have between 250 and 380 speakers. It is not in immediate danger of extinction, as its use is vigorous and the Pirahã community is mostly monolingual. The Pirahã language is the subject of various controversial claims; for example, that it provides evidence against linguistic relativity. The controversy is compounded by the difficulty of learning the language; the number of linguists with field experience in Pirah� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel Everett
Daniel Leonard Everett (born July 26, 1951) is an American linguist and author best known for his study of the Amazon basin's Pirahã people and their language. Everett is currently Trustee Professor of Cognitive Sciences at Bentley University in Waltham, Massachusetts. From July 1, 2010, to June 30, 2018, Everett served as Dean of Arts and Sciences at Bentley. Prior to Bentley University, Everett was chair of the Department of Languages, Literatures and Cultures at Illinois State University in Normal, Illinois. He has taught at the University of Manchester and is former chair of the Linguistics Department of the University of Pittsburgh. Some of his claims about the Pirahã language have beecontested by other linguists. Early life Everett was raised near the Mexican border in Holtville, California. His father was an occasional cowboy, mechanic, and construction worker. His mother was a waitress at a local restaurant. Everett played in rock bands from the time he was 11 yea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noam Chomsky
Avram Noam Chomsky (born December 7, 1928) is an American professor and public intellectual known for his work in linguistics, political activism, and social criticism. Sometimes called "the father of modern linguistics", Chomsky is also a major figure in analytic philosophy and one of the founders of the field of cognitive science. He is a laureate professor of linguistics at the University of Arizona and an institute professor emeritus at the Massachusetts Institute of Technology (MIT). Among the most cited living authors, Chomsky has written more than 150 books on topics such as linguistics, war, and politics. In addition to his work in linguistics, since the 1960s Chomsky has been an influential voice on the American Left, American left as a consistent critic of U.S. foreign policy, Criticism of capitalism, contemporary capitalism, and Corporate influence on politics in the United States, corporate influence on political institutions and the media. Born to Ashkenazi Jew ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
