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Wim Blok
Willem Johannes "Wim" Blok (1947–2003) was a Dutch logician who made major contributions to algebraic logic, universal algebra, and modal logic. His important achievements over the course of his career include "a brilliant demonstration of the fact that various techniques and results that originated in universal algebra can be used to prove significant and deep theorems in modal logic." Blok began his career in 1973 as an algebraist investigating the varieties of interior algebras at the University of Illinois at Chicago. Following the 1976 completion of his Ph.D. on that topic, he continued on to study more general varieties of modal algebras. As an algebraist, Blok "was recognised by the modal logic community as one of the most influential modal logicians" by the end of the 1970s. He published many papers in the '' Reports on Mathematical Logic'', served as a member on their editorial board, and was one of their guest editors. Along with Don Pigozzi Don, don or DON and vari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logician
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually und ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2003 Deaths
3 (three) is a number, numeral and digit. It is the natural number following 2 and preceding 4, and is the smallest odd prime number and the only prime preceding a square number. It has religious or cultural significance in many societies. Evolution of the Arabic digit The use of three lines to denote the number 3 occurred in many writing systems, including some (like Roman and Chinese numerals) that are still in use. That was also the original representation of 3 in the Brahmic (Indian) numerical notation, its earliest forms aligned vertically. However, during the Gupta Empire the sign was modified by the addition of a curve on each line. The Nāgarī script rotated the lines clockwise, so they appeared horizontally, and ended each line with a short downward stroke on the right. In cursive script, the three strokes were eventually connected to form a glyph resembling a with an additional stroke at the bottom: ३. The Indian digits spread to the Caliphate in the 9th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leibniz Operator
In abstract algebraic logic, a branch of mathematical logic, the Leibniz operator is a tool used to classify deductive systems, which have a precise technical definition and capture a large number of logics. The Leibniz operator was introduced by Wim Blok and Don Pigozzi, two of the founders of the field, as a means to abstract the well-known Lindenbaum–Tarski process, that leads to the association of Boolean algebras to classical propositional calculus, and make it applicable to as wide a variety of sentential logics as possible. It is an operator that assigns to a given theory of a given sentential logic, perceived as a term algebra with a consequence operation on its universe, the largest congruence on the algebra that is compatible with the theory. Formulation In this article, we introduce the Leibniz operator in the special case of classical propositional calculus, then we abstract it to the general notion applied to an arbitrary sentential logic and, finally, we summarize ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modal Companion
In logic, a modal companion of a superintuitionistic (intermediate) logic ''L'' is a normal modal logic that interprets ''L'' by a certain canonical translation, described below. Modal companions share various properties of the original intermediate logic, which enables to study intermediate logics using tools developed for modal logic. Gödel–McKinsey–Tarski translation Let ''A'' be a propositional intuitionistic formula. A modal formula ''T''(''A'') is defined by induction on the complexity of ''A'': :T(p)=\Box p, for any propositional variable p, :T(\bot)=\bot, :T(A\land B)=T(A)\land T(B), :T(A\lor B)=T(A)\lor T(B), :T(A\to B)=\Box(T(A)\to T(B)). As negation is in intuitionistic logic defined by A\to\bot, we also have :T(\neg A)=\Box\neg T(A). ''T'' is called the Gödel translation or Gödel–McKinsey– Tarski translation. The translation is sometimes presented in slightly different ways: for example, one may insert \Box before every subformula. All such variants are prova ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Algebraic Logic
In mathematical logic, abstract algebraic logic is the study of the algebraization of deductive systems arising as an abstraction of the well-known Lindenbaum–Tarski algebra, and how the resulting algebras are related to logical systems.Font, 2003. History The archetypal association of this kind, one fundamental to the historical origins of algebraic logic and lying at the heart of all subsequently developed subtheories, is the association between the class of Boolean algebras and classical propositional calculus. This association was discovered by George Boole in the 1850s, and then further developed and refined by others, especially C. S. Peirce and Ernst Schröder, from the 1870s to the 1890s. This work culminated in Lindenbaum–Tarski algebras, devised by Alfred Tarski and his student Adolf Lindenbaum in the 1930s. Later, Tarski and his American students (whose ranks include Don Pigozzi) went on to discover cylindric algebra, whose representable instances algebraize al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Algebraic Logic
In mathematical logic, abstract algebraic logic is the study of the algebraization of deductive systems arising as an abstraction of the well-known Lindenbaum–Tarski algebra, and how the resulting algebras are related to logical systems.Font, 2003. History The archetypal association of this kind, one fundamental to the historical origins of algebraic logic and lying at the heart of all subsequently developed subtheories, is the association between the class of Boolean algebras and classical propositional calculus. This association was discovered by George Boole in the 1850s, and then further developed and refined by others, especially C. S. Peirce and Ernst Schröder, from the 1870s to the 1890s. This work culminated in Lindenbaum–Tarski algebras, devised by Alfred Tarski and his student Adolf Lindenbaum in the 1930s. Later, Tarski and his American students (whose ranks include Don Pigozzi) went on to discover cylindric algebra, whose representable instances algebraize al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Don Pigozzi
Don, don or DON and variants may refer to: Places *County Donegal, Ireland, Chapman code DON * Don (river), a river in European Russia *Don River (other), several other rivers with the name *Don, Benin, a town in Benin * Don, Dang, a village and hill station in Dang district, Gujarat, India *Don, Nord, a ''commune'' of the Nord ''département'' in northern France *Don, Tasmania, a small village on the Don River, located just outside Devonport, Tasmania *Don, Trentino, a commune in Trentino, Italy * Don, West Virginia, a community in the United States *Don Republic, a temporary state in 1918–1920 *Don Jail, a jail in Toronto, Canada People Role or title * Don (honorific), a Spanish, Portuguese, and Italian title, given as a mark of respect *Don, a crime boss, especially in the Mafia , ''Don Konisshi'' (コニッシー) *Don, a resident assistant at universities in Canada and the U.S. *University don, in British and Irish universities, especially at Oxford, Cambridge, S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Logic
In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables. What is now usually called classical algebraic logic focuses on the identification and algebraic description of models appropriate for the study of various logics (in the form of classes of algebras that constitute the algebraic semantics for these deductive systems) and connected problems like representation and duality. Well known results like the representation theorem for Boolean algebras and Stone duality fall under the umbrella of classical algebraic logic . Works in the more recent abstract algebraic logic (AAL) focus on the process of algebraization itself, like classifying various forms of algebraizability using the Leibniz operator . Calculus of relations A homogeneous binary relation is found in the power set of ''X'' × ''X'' for some set ''X'', while a heterogeneous relation is found in the power set of ''X'' × ''Y'', where ''X'' ≠ ''Y''. Whether a g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reports On Mathematical Logic
A report is a document that presents information in an organized format for a specific audience and purpose. Although summaries of reports may be delivered orally, complete reports are almost always in the form of written documents. Usage In modern business scenario, reports play a major role in the progress of business. Reports are the backbone to the thinking process of the establishment and they are responsible, to a great extent, in evolving an efficient or inefficient work environment. The significance of the reports includes: * Reports present adequate information on various aspects of the business. * All the skills and the knowledge of the professionals are communicated through reports. * Reports help the top line in decision making. * A rule and balanced report also helps in problem solving. * Reports communicate the planning, policies and other matters regarding an organization to the masses. News reports play the role of ombudsman and levy checks and balances on the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Studia Logica
''Studia Logica'' (full name: Studia Logica, An International Journal for Symbolic Logic), is a scienific journal publishing papers employing formal tools from Mathematics and Logic. The scope of papers published in Studia Logica covers all scientific disciplines; the key criterion for published papers is not their topic but their method: they are required to contain significant and original results concerning formal systems and their properties. The journal offers papers on topics in general logic and on applications of logic to methodology of science, linguistics, philosophy, and other branches of knowledge. The journal is published by the Institute of Philosophy and Sociology of the Polish Academy of Sciences and Springer publications. History The name Studia Logica appeared for the first time in 1934, but only one volume (edited by Jan Łukasiewicz) has been published that time. It had been published continuously since December 1953 in changing frequency by the Polish Acade ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
