|
Jean-Yves Girard
Jean-Yves Girard (; born 1947) is a French logician working in proof theory. He is the research director ( emeritus) at the mathematical institute of the 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,, ; Occitan: ''Lion'', hist. ''Lionés'' also spelled in English as Lyons, is the third-largest city and second-largest metropolitan area of 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, northeast of Saint-Étienne. The City of Lyon proper had a population of 522,969 in 2019 within its small municipal territory of , but together with its suburbs and exurbs the Lyon metropolitan area had a population of 2,280,845 that same year, the second most populated in France. Lyon and 58 suburban municipalities have formed since 2015 the Metropolis of Lyon, a directly elected metropolitan authority now in charge of most urban issues, with a population of 1,411,571 in 2019. Lyon is the prefecture of the Auvergne-Rhône-Alpes region and seat of the Departmental Council of Rhône (whose jurisdiction, however, no longer extends over the Metropolis of Lyo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Aix-Marseille
Aix-Marseille University (AMU; french: Aix-Marseille Université; formally incorporated as ''Université d'Aix-Marseille'') is a public research university located in the Provence region of southern France. It was founded in 1409 when Louis II of Anjou, Count of Provence, petitioned the Pisan Antipope Alexander V to establish the University of Provence, making it one of the oldest university-level institutions in France. The institution came into its current form following a reunification of the University of Provence, the University of the Mediterranean and Paul Cézanne University. The reunification became effective on 1 January 2012, resulting in the creation of the largest university in the French-speaking world, with about 80,000 students. AMU has the largest budget of any academic institution in the Francophone world, standing at €750 million. It is consistently ranked among the top 200 universities in the world and is ranked within the top 4 universities in France accord ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing house specializing in monographs and scholarly journals. Most are nonprofit organizations and an integral component of a large research university. They publish work that has been reviewed by schola ... in the world. It is also the King's Printer. Cambridge University Press is a department of the University of Cambridge and is both an academic and educational publisher. It became part of Cambridge University Press & Assessment, following a merger with Cambridge Assessment in 2021. With a global sales presence, publishing hubs, and offices in more than 40 Country, countries, it publishes over 50,000 titles by authors from over 100 countries. Its publishing includes more than 380 academic journals, monographs, reference works, school and uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French Academy Of Sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, 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 Institut de France. 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 Nationals, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CNRS Silver Medal
The CNRS Silver Medal is a scientific award given every year to about fifteen researchers by the French National Centre for Scientific Research The French National Centre for Scientific Research (french: link=no, Centre national de la recherche scientifique, CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,63 ... (CNRS). It is awarded to a researcher for "the originality, quality and importance of their work, recognised on a national and international level". It is part of the "CNRS Talents" medals, along with the CNRS gold medal, which rewards a whole scientific career, the CNRS bronze medal, which rewards young researchers, the Innovation medal, which honours remarkable work in the technological, therapeutic, economic or societal fields, and the CNRS Crystal medal, which rewards research support staff. Notable recipients * Gabriel Peyré (mathematics) (2021) * Marie-Hélène Verlhac (biol ... [...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-s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Logic
Linear logic is a substructural logic proposed by 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 persistent "truths", ... [...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). They were both proved inconsistent by Jean-Yves Girard in 1972. 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, the sorts describe a hierarchy in the ''nature'' of the terms. # ... [...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. 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 The Rolf Schock Prizes were established and endowed by bequest of philosopher and artist Rolf Schock (1933–1986). The prizes were first awarded in Stockholm, Sweden, in 1993 and, since 2005, are awarded every three years. Each recipient current ... 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 {{Eu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William W
William is a male given name of Germanic origin.Hanks, Hardcastle and Hodges, ''Oxford Dictionary of First Names'', Oxford University Press, 2nd edition, , p. 276. It became very popular in the English language after the Norman conquest of England 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, Wills, Willy, Willie, Bill, and Billy. A common Irish form is Liam. Scottish diminutives include Wull, Willie or Wullie (as in Oor Wullie or the play ''Douglas''). Female forms are Willa, Willemina, Wilma and Wilhelmina. Etymology William is related to the given name ''Wilhelm'' (cf. Proto-Germanic ᚹᛁᛚᛃᚨᚺᛖᛚᛗᚨᛉ, ''*Wiljahelmaz'' > German ''Wilhelm'' and Old Norse ᚢᛁᛚᛋᛅᚼᛅᛚᛘᛅᛋ, ''Vilhjálmr''). By regular sound changes, the native, inherited English form of the name should b ... [...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 (Takahashi 1967) 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 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. Hauptsatz for higher order log ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.jpg "Click for more on -> Lyon")
