|
Jean-Yves Girard
Jean-Yves Girard (; born 1947) is a French logician working in proof theory. He is a research director (emeritus) at the mathematical institute of University of Aix-Marseille, at Luminy. Biography Jean-Yves Girard is an alumnus of the École normale supérieure de Saint-Cloud. He made a name for himself in the 1970s with his proof of strong normalization in a system of second-order logic called System F. This result gave a new proof of Takeuti's conjecture, which was proven a few years earlier by William W. Tait, Motō Takahashi and Dag Prawitz. For this purpose, he introduced the notion of "reducibility candidate" ("candidat de réducibilité"). He is also credited with the discovery of Girard's paradox, linear logic, the geometry of interaction, ludics, and (satirically) the mustard watch. He obtained the CNRS Silver Medal in 1983 and is a member of the French Academy of Sciences. Bibliography * * * * Jean-Yves Girard (2011). ''The Blind Spot: Lectures on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lyon
Lyon (Franco-Provençal: ''Liyon'') is a city in France. It is located at the confluence of the rivers Rhône and Saône, to the northwest of the French Alps, southeast of Paris, north of Marseille, southwest of Geneva, Switzerland, northeast of Saint-Étienne. The City of Lyon is the List of communes in France with over 20,000 inhabitants, third-largest city in France with a population of 522,250 at the Jan. 2021 census within its small municipal territory of , but together with its suburbs and exurbs the Lyon Functional area (France), metropolitan area had a population of 2,308,818 that same year, the second largest in France. Lyon and 58 suburban municipalities have formed since 2015 the Lyon Metropolis, Metropolis of Lyon, a directly elected metropolitan authority now in charge of most urban issues, with a population of 1,424,069 in 2021. Lyon is the Prefectures in France, prefecture of the Auvergne-Rhône-Alpes Regions of France, region and seat of the Departmental co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emeritus
''Emeritus/Emerita'' () is an honorary title granted to someone who retires from a position of distinction, most commonly an academic faculty position, but is allowed to continue using the previous title, as in "professor emeritus". In some cases, the term is conferred automatically upon all persons who retire at a given rank, but in others, it remains a mark of distinguished performance (usually in the area of research) awarded selectively on retirement. It is also used when a person of distinction in a profession retires or hands over the position, enabling their former rank to be retained in their title. The term ''emeritus'' does not necessarily signify that a person has relinquished all the duties of their former position, and they may continue to exercise some of them. In descriptions of deceased professors emeriti listed at U.S. universities, the title ''emeritus'' is replaced by an indication of the years of their appointments, except in obituaries, where it may be us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessment to form Cambridge University Press and Assessment under Queen Elizabeth II's approval in August 2021. With a global sales presence, publishing hubs, and offices in more than 40 countries, it published over 50,000 titles by authors from over 100 countries. Its publications include more than 420 academic journals, monographs, reference works, school and university textbooks, and English language teaching and learning publications. It also published Bibles, runs a bookshop in Cambridge, sells through Amazon, and has a conference venues business in Cambridge at the Pitt Building and the Sir Geoffrey Cass Sports and Social Centre. It also served as the King's Printer. Cambridge University Press, as part of the University of Cambridge, was a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French Academy Of Sciences
The French Academy of Sciences (, ) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefront of scientific developments in Europe in the 17th and 18th centuries, and is one of the earliest Academy of Sciences, Academies of Sciences. Currently headed by Patrick Flandrin (President of the academy), it is one of the five Academies of the . __TOC__ History The Academy of Sciences traces its origin to Colbert's plan to create a general academy. He chose a small group of scholars who met on 22 December 1666 in the King's library, near the present-day Bibliothèque nationale de France, Bibliothèque Nationale, and thereafter held twice-weekly working meetings there in the two rooms assigned to the group. The first 30 years of the academy's existence were relatively informal, since no statutes had as yet been laid down for the ins ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ludics
In proof theory, ludics is an analysis of the principles governing inference rules of mathematical logic. Key features of ludics include notion of compound connectives, using a technique known as ''focusing'' or ''focalisation'' (invented by the computer scientist Jean-Marc Andreoli), and its use of ''locations'' or ''loci'' over a base instead of propositions. More precisely, ludics tries to retrieve known logical connectives and proof behaviours by following the paradigm of interactive computation, similarly to what is done in game semantics to which it is closely related. By abstracting the notion of formulae and focusing on their concrete uses—that is distinct occurrences—it provides an abstract syntax for computer science, as loci can be seen as pointers on memory. The primary achievement of ludics is the discovery of a relationship between two natural, but distinct notions of type, or proposition. The first view, which might be termed the proof-theoretic or Gentzen-st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry Of Interaction
In proof theory, the Geometry of Interaction (GoI) was introduced by Jean-Yves Girard shortly after his work on linear logic. In linear logic, proofs can be seen as various kinds of networks as opposed to the flat tree structures of sequent calculus. To distinguish the real proof nets from all the possible networks, Girard devised a criterion involving trips in the network. Trips can in fact be seen as some kind of operator acting on the proof. Drawing from this observation, Girard described directly this operator from the proof and has given a formula, the so-called ''execution formula'', encoding the process of cut elimination at the level of operators. Subsequent constructions by Girard proposed variants in which proofs are represented as flows, or operators in von Neumann algebras. Those models were later generalised by Seiller's Interaction Graphs models. One of the first significant applications of GoI was a better analysis of Lamping's algorithm for optimal reduction for th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Logic
Linear logic is a substructural logic proposed by French logician Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the dualities of the former with many of the constructive properties of the latter. Although the logic has also been studied for its own sake, more broadly, ideas from linear logic have been influential in fields such as programming languages, game semantics, and quantum physics (because linear logic can be seen as the logic of quantum information theory), as well as linguistics, particularly because of its emphasis on resource-boundedness, duality, and interaction. Linear logic lends itself to many different presentations, explanations, and intuitions. Proof-theoretically, it derives from an analysis of classical sequent calculus in which uses of (the structural rules) contraction and weakening are carefully controlled. Operationally, this means that logical deduction is no longer merely about an ever-expanding collection of pe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Girard's Paradox
In mathematical logic, System U and System U− are pure type systems, i.e. special forms of a typed lambda calculus with an arbitrary number of sorts, axioms and rules (or dependencies between the sorts). System U was proved inconsistent by Jean-Yves Girard in 1972 (and the question of consistency of System U− was formulated). This result led to the realization that Martin-Löf's original 1971 type theory was inconsistent, as it allowed the same "Type in Type" behaviour that Girard's paradox exploits. Formal definition System U is defined as a pure type system with * three sorts \; * two axioms \; and * five rules \. System U− is defined the same with the exception of the (\triangle, \ast) rule. The sorts \ast and \square are conventionally called “Type” and “ Kind”, respectively; the sort \triangle doesn't have a specific name. The two axioms describe the containment of types in kinds (\ast:\square) and kinds in \triangle (\square:\triangle). Intuitively, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dag Prawitz
Dag Prawitz (born 1936, Stockholm) is a Swedish philosopher and logician. He is best known for his work on proof theory and the foundations of natural deduction, and for his contributions to proof-theoretic semantics. Prawitz is a member of the Norwegian Academy of Science and Letters, of the Royal Swedish Academy of Letters and Antiquity and the Royal Swedish Academy of Science. Prawitz was awarded the Rolf Schock Prize in Logic and Philosophy in 2020. References External links Prawitz's web page at Stockholm University 1936 births Living people Swedish logicians Mathematical logicians Swedish philosophers Members of the Royal Swedish Academy of Sciences Members of the Norwegian Academy of Science and Letters Proof theorists 20th-century Swedish philosophers People from Stockholm {{Europe-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William W
William is a masculine given name of Germanic origin. It became popular in England after the Norman conquest in 1066,All Things William"Meaning & Origin of the Name"/ref> and remained so throughout the Middle Ages and into the modern era. It is sometimes abbreviated "Wm." Shortened familiar versions in English include Will or Wil, Wills, Willy, Willie, Bill, Billie, and Billy. A common Irish form is Liam. Scottish diminutives include Wull, Willie or Wullie (as in Oor Wullie). Female forms include Willa, Willemina, Wilma and Wilhelmina. Etymology William is related to the German given name ''Wilhelm''. Both ultimately descend from Proto-Germanic ''*Wiljahelmaz'', with a direct cognate also in the Old Norse name ''Vilhjalmr'' and a West Germanic borrowing into Medieval Latin ''Willelmus''. The Proto-Germanic name is a compound of *''wiljô'' "will, wish, desire" and *''helmaz'' "helm, helmet".Hanks, Hardcastle and Hodges, ''Oxford Dictionary of First Names'', Oxfor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Takeuti's Conjecture
In mathematics, Takeuti's conjecture is the conjecture of Gaisi Takeuti that a sequent formalisation of second-order logic has cut-elimination (Takeuti 1953). It was settled positively: * By Tait, using a semantic technique for proving cut-elimination, based on work by Schütte (Tait 1966); * Independently by Prawitz (Prawitz 1968) and Takahashi by a similar technique (Takahashi 1967), although Prawitz's and Takahashi's proofs are not limited to second-order logic, but concern higher-order logics in general; * It is a corollary of Jean-Yves Girard's syntactic proof of strong normalization for System F. Takeuti's conjecture is equivalent to the 1-consistency of second-order arithmetic in the sense that each of the statements can be derived from each other in the weak system of primitive recursive arithmetic (PRA). It is also equivalent to the strong normalization of the Girard/Reynold's System F. See also * Hilbert's second problem References * Dag Prawitz, 1968. Hauptsa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second-order Logic
In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and type theory. First-order logic quantifies only variables that range over individuals (elements of the domain of discourse); second-order logic, in addition, quantifies over relations. For example, the second-order sentence \forall P\,\forall x (Px \lor \neg Px) says that for every formula ''P'', and every individual ''x'', either ''Px'' is true or not(''Px'') is true (this is the law of excluded middle). Second-order logic also includes quantification over sets, functions, and other variables (see section below). Both first-order and second-order logic use the idea of a domain of discourse (often called simply the "domain" or the "universe"). The domain is a set over which individual elements may be quantified. Examples First-order logic can quantify over individuals, but no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
