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Martin Hyland
(John) Martin Elliott Hyland is professor of mathematical logic at the University of Cambridge and a fellow of King's College, Cambridge. His interests include mathematical logic, category theory, and theoretical computer science. Education Hyland was educated at the University of Oxford where he was awarded a Doctor of Philosophy degree in 1975 for research supervised by Robin Gandy. Research and career Martin Hyland is best known for his work on category theory applied to logic ( proof theory, recursion theory), theoretical computer science (lambda-calculus and semantics) and higher-dimensional algebra. In particular he is known for work on the effective topos (within topos theory) and on game semantics. His former doctoral students include Eugenia Cheng and Valeria de Paiva Valeria Correa Vaz de Paiva is a Brazilian mathematician, logician, and computer scientist. Her work includes research on logical approaches to computation, especially using category theory, knowl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge
Cambridge ( ) is a College town, university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cambridge became an important trading centre during the Roman and Viking ages, and there is archaeological evidence of settlement in the area as early as the Bronze Age. The first Town charter#Municipal charters, town charters were granted in the 12th century, although modern city status was not officially conferred until 1951. The city is most famous as the home of the University of Cambridge, which was founded in 1209 and consistently ranks among the best universities in the world. The buildings of the university include King's College Chapel, Cambridge, King's College Chapel, Cavendish Laboratory, and the Cambridge University Library, one of the largest legal deposit libraries in the world. The city's skyline is dominated by several Colleg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Theory
Proof theory is a major branchAccording to Wang (1981), pp. 3–4, proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. Barwise (1978) consists of four corresponding parts, with part D being about "Proof Theory and Constructive Mathematics". of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of the logical system. Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature. Some of the major areas of proof theory include structural proof theory, ordinal analysis, provability logic, reverse mathematics, proof mining, automated theorem proving, and proof complexity. Much research also focuses ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
English Mathematicians
English usually refers to: * English language * English people English may also refer to: Peoples, culture, and language * ''English'', an adjective for something of, from, or related to England ** English national identity, an identity and common culture ** English language in England, a variant of the English language spoken in England * English languages (other) * English studies, the study of English language and literature * ''English'', an Amish term for non-Amish, regardless of ethnicity Individuals * English (surname), a list of notable people with the surname ''English'' * People with the given name ** English McConnell (1882–1928), Irish footballer ** English Fisher (1928–2011), American boxing coach ** English Gardner (b. 1992), American track and field sprinter Places United States * English, Indiana, a town * English, Kentucky, an unincorporated community * English, Brazoria County, Texas, an unincorporated community ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fellows Of King's College, Cambridge
{{disambiguation ...
Fellows may refer to Fellow, in plural form. Fellows or Fellowes may also refer to: Places *Fellows, California, USA *Fellows, Wisconsin, ghost town, USA Other uses *Fellows Auctioneers, established in 1876. *Fellowes, Inc., manufacturer of workspace products *Fellows, a partner in the firm of English canal carriers, Fellows Morton & Clayton *Fellows (surname) See also *North Fellows Historic District, listed on the National Register of Historic Places in Wapello County, Iowa *Justice Fellows (other) Justice Fellows may refer to: *Grant Fellows Grant Fellows (April 13, 1865 – July 16, 1929) was an American jurist. Born in Hudson Township, Lenawee County, Michigan, Fellows went to Hudson High School in Hudson, Michigan. Fellows studied la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Year Of Birth Missing (living People)
A year or annus is the orbital period of a planetary body, for example, the Earth, moving in its orbit around the Sun. Due to the Earth's axial tilt, the course of a year sees the passing of the seasons, marked by change in weather, the hours of daylight, and, consequently, vegetation and soil fertility. In temperate and subpolar regions around the planet, four seasons are generally recognized: spring, summer, autumn and winter. In tropical and subtropical regions, several geographical sectors do not present defined seasons; but in the seasonal tropics, the annual wet and dry seasons are recognized and tracked. A calendar year is an approximation of the number of days of the Earth's orbital period, as counted in a given calendar. The Gregorian calendar, or modern calendar, presents its calendar year to be either a common year of 365 days or a leap year of 366 days, as do the Julian calendars. For the Gregorian calendar, the average length of the calenda ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic Notes In Theoretical Computer Science
''Electronic Notes in Theoretical Computer Science'' is an electronic computer science journal published by Elsevier, started in 1995. Its issues include many post-proceedings for workshops, etc. The journal is abstracted and indexed in Scopus and Science Citation Index The Science Citation Index Expanded – previously entitled Science Citation Index – is a citation index originally produced by the Institute for Scientific Information (ISI) and created by Eugene Garfield. It was officially launched in 1964 .... Electronic Notes in Theoretical Computer Science has been discontinued as of 2021. References Computer science journals Elsevier academic journals Publications established in 1995 {{comp-sci-theory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Semantics
Game semantics (german: dialogische Logik, translated as ''dialogical logic'') is an approach to Formal semantics (logic), formal semantics that grounds the concepts of truth or Validity (logic), validity on game theory, game-theoretic concepts, such as the existence of a winning strategy for a player, somewhat resembling Socratic dialogues or medieval theory of Obligationes. History In the late 1950s Paul Lorenzen was the first to introduce a game semantics for logic, and it was further developed by Kuno Lorenz. At almost the same time as Lorenzen, Jaakko Hintikka developed a model-theoretical approach known in the literature as ''GTS'' (game-theoretical semantics). Since then, a number of different game semantics have been studied in logic. Shahid Rahman (Lille) and collaborators developed dialogical logic into a general framework for the study of logical and philosophical issues related to logical pluralism. Beginning 1994 this triggered a kind of renaissance with lasting conseq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topos Theory
In mathematics, a topos (, ; plural topoi or , or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally: on a site). Topoi behave much like the category of sets and possess a notion of localization; they are a direct generalization of point-set topology. The Grothendieck topoi find applications in algebraic geometry; the more general elementary topoi are used in logic. The mathematical field that studies topoi is called topos theory. Grothendieck topos (topos in geometry) Since the introduction of sheaves into mathematics in the 1940s, a major theme has been to study a space by studying sheaves on a space. This idea was expounded by Alexander Grothendieck by introducing the notion of a "topos". The main utility of this notion is in the abundance of situations in mathematics where topological heuristics are very effective, but an honest topological space is lacking; it is sometimes possible to find a topos formal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Effective Topos
In mathematics, the effective topos is a topos In mathematics, a topos (, ; plural topoi or , or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally: on a site). Topoi behave much like the category of sets and possess a notio ... introduced by , based on Kleene's notion of recursive realizability, that captures the idea of effectivity in mathematics. References * * * * Topos theory {{cattheory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Higher-dimensional Algebra
In mathematics, especially ( higher) category theory, higher-dimensional algebra is the study of categorified structures. It has applications in nonabelian algebraic topology, and generalizes abstract algebra. Higher-dimensional categories A first step towards defining higher dimensional algebras is the concept of 2-category of higher category theory, followed by the more 'geometric' concept of double category. A higher level concept is thus defined as a category of categories, or super-category, which generalises to higher dimensions the notion of category – regarded as any structure which is an interpretation of Lawvere's axioms of the '' elementary theory of abstract categories'' (ETAC). Ll. , Thus, a supercategory and also a super-category, can be regarded as natural extensions of the concepts of meta-category, multicategory, and multi-graph, ''k''-partite graph, or colored graph (see a color figure, and also its definition in graph theory). Supercategories ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semantics Of Programming Languages
In programming language theory, semantics is the rigorous mathematical study of the meaning of programming languages. Semantics assigns computational meaning to valid string (computer science), strings in a programming language syntax. Semantics describes the processes a computer follows when Execution (computing), executing a program in that specific language. This can be shown by describing the relationship between the input and output of a program, or an explanation of how the program will be executed on a certain computer platform, platform, hence creating a model of computation. History In 1967, Robert W. Floyd publishes the paper ''Assigning meanings to programs''; his chief aim is "a rigorous standard for proofs about computer programs, including formal verification, proofs of correctness, equivalence, and termination". Floyd further writes: A semantic definition of a programming language, in our approach, is founded on a Syntax (programming languages), syntactic defini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
