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Situation Theory
Situation theory provides the mathematical foundations to situation semantics, and was developed by writers such as Jon Barwise and Keith Devlin in the 1980s. Due to certain foundational problems, the mathematics was framed in a non-well-founded set theory. One could think of the relation of situation theory to situation semantics as like that of type theory to Montague semantics. Basic types Types in the theory are defined by applying two forms of type abstraction, starting with an initial collection of basic types. Basic types: *TIM: the type of a temporal location *LOC: the type of a spatial location *IND: the type of an individual *RELn: the type of an n-place relation *SIT: the type of a situation *INF: the type of an infon *TYP: the type of a type *PAR: the type of a parameter *POL: the type of a polarity (i.e. 0 or 1) Infons are made of basic types. For instance: If l is a location, then l is of type LOC, and the infon is a fact. See also * State of affairs (philosophy) R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Situation Semantics
In situation theory, situation semantics (pioneered by Jon Barwise and John Perry in the early 1980s) attempts to provide a solid theoretical foundation for reasoning about common-sense and real world situations, typically in the context of theoretical linguistics, theoretical philosophy, or applied natural language processing, Barwise and Perry Situations, unlike worlds, are not complete in the sense that every proposition or its negation holds in a world. According to ''Situations and Attitudes'', meaning is a relation between a discourse situation, a connective situation and a described situation. The original theory of ''Situations and Attitudes'' soon ran into foundational difficulties. A reformulation based on Peter Aczel's non-well-founded set theory was proposed by Barwise before this approach to the subject petered out in the early 1990s. HPSG Situation semantics is the first semantic theory that was used in head-driven phrase structure grammar (HPSG). Kratzer Bar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jon Barwise
Kenneth Jon Barwise (; June 29, 1942 – March 5, 2000) was an American mathematician, philosopher and logician who proposed some fundamental revisions to the way that logic is understood and used. Education and career Born in Independence, Missouri to Kenneth T. and Evelyn Barwise, Jon was a precocious child. A pupil of Solomon Feferman at Stanford University, Barwise started his research in infinitary logic. After positions as assistant professor at Yale University and the University of Wisconsin, during which time his interests turned to natural language, he returned to Stanford in 1983 to direct the Center for the Study of Language and Information. He began teaching at Indiana University in 1990. He was elected a Fellow of the American Academy of Arts and Sciences in 1999. In his last year, Barwise was invited to give the 2000 Gödel Lecture; he died prior to the lecture. Philosophical and logical work Barwise contended that, by being explicit about the context in whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Keith Devlin
Keith J. Devlin (born 16 March 1947) is a British mathematician and popular science writer. Since 1987 he has lived in the United States. He has dual British-American citizenship.Curriculum vitae Profkeithdevlin.com, accessed 3 February 2014. Biography He was born and grew up in England, in . There he attended a local primary school followed by Greatfield High School in Hull. In the last school year he was appointed head boy. Devlin earned a BSc (special) in mathem ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-well-founded Set Theory
Non-well-founded set theories are variants of axiomatic set theory that allow sets to be elements of themselves and otherwise violate the rule of well-foundedness. In non-well-founded set theories, the foundation axiom of ZFC is replaced by axioms implying its negation. The study of non-well-founded sets was initiated by Dmitry Mirimanoff in a series of papers between 1917 and 1920, in which he formulated the distinction between well-founded and non-well-founded sets; he did not regard well-foundedness as an axiom. Although a number of axiomatic systems of non-well-founded sets were proposed afterwards, they did not find much in the way of applications until Peter Aczel’s hyperset theory in 1988. The theory of non-well-founded sets has been applied in the logical modelling of non-terminating computational processes in computer science (process algebra and final semantics), linguistics and natural language semantics (situation theory), philosophy (work on the Liar Paradox), an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Theory
In mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that were proposed as foundations are Alonzo Church's typed λ-calculus and Per Martin-Löf's intuitionistic type theory. Most computerized proof-writing systems use a type theory for their foundation. A common one is Thierry Coquand's Calculus of Inductive Constructions. History Type theory was created to avoid a paradox in a mathematical foundation based on naive set theory and formal logic. Russell's paradox, which was discovered by Bertrand Russell, existed because a set could be defined using "all possible sets", which included itself. Between 1902 and 1908, Bertrand Russell proposed various "theories of type" to fix the problem. By 1908 Russell arrived at a "ramified" theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Montague Semantics
__notoc__ Montague grammar is an approach to natural language semantics, named after American logician Richard Montague. The Montague grammar is based on mathematical logic, especially higher-order predicate logic and lambda calculus, and makes use of the notions of intensional logic, via Kripke models. Montague pioneered this approach in the 1960s and early 1970s. Overview Montague's thesis was that natural languages (like English) and formal languages (like programming languages) can be treated in the same way: There is in my opinion no important theoretical difference between natural languages and the artificial languages of logicians; indeed, I consider it possible to comprehend the syntax and semantics of both kinds of language within a single natural and mathematically precise theory. On this point I differ from a number of philosophers, but agree, I believe, with Chomsky and his associates. ("Universal Grammar" 1970) Montague published what soon became known as Montague g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
State Of Affairs (philosophy)
In philosophy, a state of affairs (german: Sachverhalt), also known as a situation, is a way the actual world must be in order to make some given ''proposition'' about the actual world true; in other words, a state of affairs is a ''truth-maker'', whereas a proposition is a ''truth-bearer''. Whereas states of affairs either ''obtain'' or ''fail-to-obtain'', propositions are either ''true'' or ''false''. Some philosophers understand the term "states of affairs" in a more restricted sense as a synonym for "fact". In this sense, there are no states of affairs that do not obtain. David Malet Armstrong is well known for his defence of a factualism, a position according to which the world is a world of facts and not a world of things. Overview States of affairs are complex entities: they are built up from or constituted by other entities. Atomic states of affairs are constituted by one particular and one property exemplified by this particular. For example, the state of affairs that Socr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edward N
Edward is an English given name. It is derived from the Anglo-Saxon name ''Ēadweard'', composed of the elements '' ēad'' "wealth, fortune; prosperous" and '' weard'' "guardian, protector”. History The name Edward was very popular in Anglo-Saxon England, but the rule of the Norman and Plantagenet dynasties had effectively ended its use amongst the upper classes. The popularity of the name was revived when Henry III named his firstborn son, the future Edward I, as part of his efforts to promote a cult around Edward the Confessor, for whom Henry had a deep admiration. Variant forms The name has been adopted in the Iberian peninsula since the 15th century, due to Edward, King of Portugal, whose mother was English. The Spanish/Portuguese forms of the name are Eduardo and Duarte. Other variant forms include French Édouard, Italian Edoardo and Odoardo, German, Dutch, Czech and Romanian Eduard and Scandinavian Edvard. Short forms include Ed, Eddy, Eddie, Ted, Teddy and Ned ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |