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Mizar System
The Mizar system consists of a formal language for writing mathematical definitions and proofs, a proof assistant, which is able to mechanically check proofs written in this language, and a library of formalized mathematics, which can be used in the proof of new theorems. The system is maintained and developed by the Mizar Project, formerly under the direction of its founder Andrzej Trybulec. In 2009 the Mizar Mathematical Library was the largest coherent body of strictly formalized mathematics in existence. History The Mizar Project was started around 1973 by Andrzej Trybulec as an attempt to reconstruct mathematical vernacular so it can be checked by a computer. Its current goal, apart from the continual development of the Mizar System, is the collaborative creation of a large library of formally verified proofs, covering most of the core of modern mathematics. This is in line with the influential QED manifesto. Currently the project is developed and maintained by re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mizar System Logo
Mizar is a second-magnitude star in the handle of the Big Dipper asterism in the constellation of Ursa Major. It has the Bayer designation ζ Ursae Majoris ( Latinised as Zeta Ursae Majoris). It forms a well-known naked eye double star with the fainter star Alcor (a binary system consisting of Alcor A and Alcor B), and is itself a quadruple star system. The Mizar and Alcor system lies about 83 light-years away from the Sun, as measured by the Hipparcos astrometry satellite, and is part of the Ursa Major Moving Group. Nomenclature ''ζ Ursae Majoris'' ( Latinised to ''Zeta Ursae Majoris'' and abbreviated to ζ UMa or Zeta UMa) is Mizar's Bayer designation. It also has the Flamsteed designation 79 Ursae Majoris. The traditional name ''Mizar'' derives from the Arabic ' ' meaning 'apron; wrapper, covering, cover'. In 2016, the International Astronomical Union organized a Working Group on Star Names (WGSN) to catalog and standardize proper nam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Alberta
The University of Alberta (also known as U of A or UAlberta, ) is a public research university located in Edmonton, Alberta, Canada. It was founded in 1908 by Alexander Cameron Rutherford, the first premier of Alberta, and Henry Marshall Tory, the university's first president. It was enabled through the ''Post-secondary Learning Act.'' The university is considered a "comprehensive academic and research university" (CARU), which means that it offers a range of academic and professional programs that generally lead to undergraduate and graduate level credentials. The university comprises four campuses in Edmonton, an Augustana Campus in Camrose, Alberta, Camrose, and a staff centre in downtown Calgary. The original north campus consists of 150 buildings covering 50 city blocks on the south rim of the North Saskatchewan River valley parks system, North Saskatchewan River valley, across and west from downtown Edmonton. About 37,000 students from Canada and 150 other countries partici ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hahn–Banach Theorem
In functional analysis, the Hahn–Banach theorem is a central result that allows the extension of bounded linear functionals defined on a vector subspace of some vector space to the whole space. The theorem also shows that there are sufficient continuous linear functionals defined on every normed vector space in order to study the dual space. Another version of the Hahn–Banach theorem is known as the Hahn–Banach separation theorem or the hyperplane separation theorem, and has numerous uses in convex geometry. History The theorem is named for the mathematicians Hans Hahn and Stefan Banach, who proved it independently in the late 1920s. The special case of the theorem for the space C , b/math> of continuous functions on an interval was proved earlier (in 1912) by Eduard Helly, and a more general extension theorem, the M. Riesz extension theorem, from which the Hahn–Banach theorem can be derived, was proved in 1923 by Marcel Riesz. The first Hahn–Banach theore ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peer-review
Peer review is the evaluation of work by one or more people with similar competencies as the producers of the work ( peers). It functions as a form of self-regulation by qualified members of a profession within the relevant field. Peer review methods are used to maintain quality standards, improve performance, and provide credibility. In academia An academy (Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of tertiary education. The name traces back to Plato's school of philosophy, founded approximately 386 BC at Akademia, a sanctuary of Athena, the go ..., scholarly peer review is often used to determine an academic paper's suitability for publication. Peer review can be categorized by the type and by the field or profession in which the activity occurs, e.g., #Medical, medical peer review. It can also be used as a teaching tool to help students improve writing assignments. Henry Oldenburg (1619–1677) was a German-born British philosop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Economics
Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interactions of Agent (economics), economic agents and how economy, economies work. Microeconomics analyses what is viewed as basic elements within economy, economies, including individual agents and market (economics), markets, their interactions, and the outcomes of interactions. Individual agents may include, for example, households, firms, buyers, and sellers. Macroeconomics analyses economies as systems where production, distribution, consumption, savings, and Expenditure, investment expenditure interact; and the factors of production affecting them, such as: Labour (human activity), labour, Capital (economics), capital, Land (economics), land, and Entrepreneurship, enterprise, inflation, economic growth, and public policies that impact gloss ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms of probability, axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure (mathematics), measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event (probability theory), event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of determinism, non-deterministic or uncertain processes or measured Quantity, quantities that may either be single occurrences or evolve over time in a random fashion). Although it is no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automated Proof Checking
In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human–machine collaboration. This involves some sort of interactive proof editor, or other User interface, interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer. A recent effort within this field is making these tools use artificial intelligence to automate the formalization of ordinary mathematics. System comparison * ACL2 – a programming language, a first-order logical theory, and a theorem prover (with both interactive and automatic modes) in the Boyer–Moore tradition. * Rocq (software), Rocq (formerly known as ''Coq'') – Allows the expression of mathematical assertions, mechanically checks proofs of these assertions, helps to find formal proofs, and extracts a certified program from the constructive proof ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ASCII
ASCII ( ), an acronym for American Standard Code for Information Interchange, is a character encoding standard for representing a particular set of 95 (English language focused) printable character, printable and 33 control character, control characters a total of 128 code points. The set of available punctuation had significant impact on the syntax of computer languages and text markup. ASCII hugely influenced the design of character sets used by modern computers; for example, the first 128 code points of Unicode are the same as ASCII. ASCII encodes each code-point as a value from 0 to 127 storable as a seven-bit integer. Ninety-five code-points are printable, including digits ''0'' to ''9'', lowercase letters ''a'' to ''z'', uppercase letters ''A'' to ''Z'', and commonly used punctuation symbols. For example, the letter is represented as 105 (decimal). Also, ASCII specifies 33 non-printing control codes which originated with ; most of which are now obsolete. The control cha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Declarative Programming
In computer science, declarative programming is a programming paradigm—a style of building the structure and elements of computer programs—that expresses the logic of a computation without describing its control flow. Many languages that apply this style attempt to minimize or eliminate side effects by describing ''what'' the program must accomplish in terms of the problem domain, rather than describing ''how'' to accomplish it as a sequence of the programming language primitives (the ''how'' being left up to the language's implementation). This is in contrast with imperative programming, which implements algorithms in explicit steps. Declarative programming often considers programs as theories of a formal logic, and computations as deductions in that logic space. Declarative programming may greatly simplify writing parallel programs. Common declarative languages include those of database query languages (e.g., SQL, XQuery), regular expressions, logic programming ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Logic
Classical logic (or standard logic) or Frege–Russell logic is the intensively studied and most widely used class of deductive logic. Classical logic has had much influence on analytic philosophy. Characteristics Each logical system in this class shares characteristic properties: Gabbay, Dov, (1994). 'Classical vs non-classical logic'. In D.M. Gabbay, C.J. Hogger, and J.A. Robinson, (Eds), ''Handbook of Logic in Artificial Intelligence and Logic Programming'', volume 2, chapter 2.6. Oxford University Press. # Law of excluded middle and double negation elimination # Law of noncontradiction, and the principle of explosion # Monotonicity of entailment and idempotency of entailment # Commutativity of conjunction # De Morgan duality: every logical operator is dual to another While not entailed by the preceding conditions, contemporary discussions of classical logic normally only include propositional and first-order logics. Shapiro, Stewart (2000). Classical Logic. In St ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Formalized Reasoning
The ''Journal of Formalized Reasoning'' is a peer-reviewed open access academic journal established in 2009. It publishes formalization efforts in any area, including classical mathematics, constructive mathematics, formal algorithms, and program verifications. It is maintained by ''AlmaDL'', the digital library of the University of Bologna. Abstracting and indexing The journal is abstracted and indexed in Scopus, MathSciNet, and ''Zentralblatt MATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastru ...''. External links * Computer science journals Open access journals Reasoning Academic journals established in 2008 Biannual journals University of Bologna English-language journals Mathematics journals {{compu-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Automated Reasoning
The ''Journal of Automated Reasoning'' was established in 1983 by Larry Wos, who was its editor in chief until 1992. It covers research and advances in automated reasoning, mechanical verification of theorems, and other deductions in classical and non-classical logic. The journal is published by Springer Science+Business Media. As of 2021, the editor-in-chief is Jasmin Blanchette, a professor of theoretical computer science at the Ludwig-Maximilians-Universität München. The journal's 2019 impact factor is 1.431, and it is indexed by several science indexing services, including the Science Citation Index Expanded and Scopus. References External links * {{Official website, 1=https://www.springer.com/computer/theoretical+computer+science/journal/10817 Computer science journals Logic journals English-language journals Academic journals established in 1983 Logic in computer science Formal methods publications Springer Science+Business Media academic journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
