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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, knowledge representation and natural language semantics, and functional programming with a focus on foundations and type theories... Education De Paiva earned a bachelor's degree in mathematics in 1982, a master's degree in 1984 (on pure algebra) and completed a doctorate at the University of Cambridge in 1988, under the supervision of Martin Hyland. UCAM-CL-TR-213 Her thesis introduced Dialectica spaces, a categorical way of constructing models of linear logic, based on Kurt Gödel's Dialectica interpretation . Career and research She worked for nine years at PARC in Palo Alto, California, and also worked at Rearden Commerce and Cuil before joining Nuance. She is an honorary research fellow in computer science at the University of Birmingham. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semantics
Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ..., linguistics and computer science. History In English, the study of meaning in language has been known by many names that involve the Ancient Greek word (''sema'', "sign, mark, token"). In 1690, a Greek rendering of the term ''semiotics'', the interpretation of signs and symbols, finds an early allusion in John Locke's ''An Essay Concerning Human Understanding'': The third Branch may be called [''simeiotikí'', "semiotics"], or the Doctrine of Signs, the most usual whereof being words, it is aptly enough ter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
DLMPST
The International Union of History and Philosophy of Science and Technology is one of the members of the International Science Council (ISC). It was founded in 1955 by merging the ''International Union of History of Science'' (IUHS) and the ''International Union of Philosophy of Science'' (IUPS), and consists of two divisions, the ''Division of History of Science and Technology'' (DHST) and the ''Division of Logic, Methodology and Philosophy of Science and Technology'' (DLMPST). Structure and governance The IUHPST does not have its own membership structure and governance, but is an umbrella organisation for its two Divisions, DHST and DLMPST. It is governed by the officers of the two Divisions in a rotational system where the Presidency of the Union rotates between the Presidents of the two Divisions. The current IUHPST President is Nancy Cartwright (President of DLMPST), the current IUHPST Vice President is Marcos Cueto (President of DHST), the current IUHPST Secretary General is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Research Fellow
A research fellow is an academic research position at a university or a similar research institution, usually for academic staff or faculty members. A research fellow may act either as an independent investigator or under the supervision of a principal investigator. Although research fellow positions vary in different countries and academic institutions, it is in general that they are junior researchers who try to develop their research careers under the guidance of senior researchers. United Kingdom In many universities this position is a career grade of a ''Research Career Pathway'', following on from a postdoctoral position such as research associate, and may be open-ended, subject to normal probation regulations. Within such a path, the next two higher career grades are usually senior research fellow and professorial fellow. Although similar to the position of a research fellow, these two positions are research only posts, with the rise of the career grade there will normal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cuil
Cuil ( ) was a search engine that organized web pages by content and displayed relatively long entries along with thumbnail pictures for many results. Cuil said it had a larger index than any other search engine, with about 120 billion web pages.Liedtke, Michael"Ex-Google engineers debut 'Cuil' way to search" Associated Press, 28 July 2008, retrieved 13 December 2009 It went live on July 28, 2008. Cuil's servers were shut down on September 17, 2010, with later confirmations the service had ended. Cuil was managed and developed largely by former employees of Google, Anna Patterson and Russell Power. The CEO and co-founder, Tom Costello, has worked for IBM and others. Cuil's privacy policy, unlike that of other search engines, said it did not store users' search activity or IP addresses.Your privacy Cuil, Last Modif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Palo Alto, California
Palo Alto (; Spanish language, Spanish for "tall stick") is a charter city in the northwestern corner of Santa Clara County, California, United States, in the San Francisco Bay Area, named after a Sequoia sempervirens, coastal redwood tree known as El Palo Alto. The city was established in 1894 by the American industrialist Leland Stanford when he founded Stanford University in memory of his son, Leland Stanford Jr. Palo Alto includes portions of Stanford University and borders East Palo Alto, California, East Palo Alto, Mountain View, California, Mountain View, Los Altos, California, Los Altos, Los Altos Hills, California, Los Altos Hills, Stanford, California, Stanford, Portola Valley, California, Portola Valley, and Menlo Park, California, Menlo Park. At the 2010 United States Census, 2020 census, the population was 68,572. Palo Alto is one of the most expensive cities in the United States in which to live, and its residents are among the most educated in the country. Howeve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dialectica Interpretation
In proof theory, the Dialectica interpretation is a proof interpretation of intuitionistic arithmetic (Heyting arithmetic) into a finite type extension of primitive recursive arithmetic, the so-called System T. It was developed by Kurt Gödel to provide a consistency proof of arithmetic. The name of the interpretation comes from the journal ''Dialectica'', where Gödel's paper was published in a 1958 special issue dedicated to Paul Bernays on his 70th birthday. Motivation Via the Gödel–Gentzen negative translation, the consistency of classical Peano arithmetic had already been reduced to the consistency of intuitionistic Heyting arithmetic. Gödel's motivation for developing the dialectica interpretation was to obtain a relative consistency proof for Heyting arithmetic (and hence for Peano arithmetic). Dialectica interpretation of intuitionistic logic The interpretation has two components: a formula translation and a proof translation. The formula translation describes how ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kurt Gödel
Kurt Friedrich Gödel ( , ; April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel had an immense effect upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell,For instance, in their "Principia Mathematica' (''Stanford Encyclopedia of Philosophy'' edition). Alfred North Whitehead, and David Hilbert were using logic and set theory to investigate the foundations of mathematics, building on earlier work by the likes of Richard Dedekind, Georg Cantor and Frege. Gödel published his first incompleteness theorem in 1931 when he was 25 years old, one year after finishing his doctorate at the University of Vienna. The first incompleteness theorem states that for any ω-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (for example P ... [...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] |
Dialectica Space
Dialectica spaces are a categorical way of constructing models of linear logic. They were introduced by Valeria de Paiva, Martin Hyland's student, in her doctoral thesis, as a way of modeling both linear logic and Gödel's Dialectica interpretation—hence the name. Given a category ''C'' and a specific object ''K'' of ''C'' with certain (logical) properties, one can construct the category of Dialectica spaces over ''C'', whose objects are pairs of objects of ''C'', related by a ''C''-morphism into ''K''. Morphisms of Dialectica spaces are similar to Chu space morphisms, but instead of an equality condition, they have an inequality condition, which is read as a logical implication Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid logical argument is one ...: the first object implies the second. Refe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term ''abstract algebra'' was coined in the early 20th century to distinguish this area of study from older parts of algebra, and more specifically from elementary algebra, the use of variables to represent numbers in computation and reasoning. Algebraic structures, with their associated homomorphisms, form mathematical categories. Category theory is a formalism that allows a unified way for expressing properties and constructions that are similar for various structures. Universal algebra is a related subject that studies types of algebraic structures as single objects. For example, the structure of groups is a single object in universal algebra, which is called the ''variety of groups''. History Before the nineteenth century, algebra meant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joint Policy Board For Mathematics
The Joint Policy Board for Mathematics (JPBM) consists of the American Mathematical Society, the American Statistical Association, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics. The Board has nearly 55,000 mathematicians and scientists who are members of the four organizations. Each April, the JPBM celebrateMathematics and Statistics Awareness Month(previously, the month was called Mathematics Awareness Month) to increase public understanding of and appreciation for mathematics and statistics. The event was renamed by the JPBM in 2017. To simplify coordination efforts, the JPBM also decided in 2017 that there will no longer be an annual assigned theme for the month. This celebration of mathematics, and now mathematics and statistics, began as Mathematics Awareness Week in 1986. JPBM Communications Award Each January at the Joint Mathematics Meeting the JPBM gives its Communications Award to a journalist or other communicator for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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