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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, Wim Blok co-authored the ... [...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 study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to work." Premise ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2003 Deaths
This is a list of lists of deaths of notable people, organized by year. New deaths articles are added to their respective month (e.g., Deaths in ) and then linked below. 2025 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991 1990 1989 1988 1987 1986 Earlier years ''Deaths in years earlier than this can usually be found in the main articles of the years.'' See also * Lists of deaths by day * Deaths by year (category) {{DEFAULTSORT:deaths by year ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1947 Births
It was the first year of the Cold War, which would last until 1991, ending with the dissolution of the Soviet Union. Events January * January–February – Winter of 1946–47 in the United Kingdom: The worst snowfall in the country in the 20th century causes extensive disruption of travel. Given the low ratio of private vehicle ownership at the time, it is mainly remembered in terms of its effects on the railway network. * January 1 – The ''Canadian Citizenship Act, 1946, Canadian Citizenship Act'' comes into effect, providing a Canadian citizenship separate from British law. * January 4 – First issue of weekly magazine ''Der Spiegel'' published in Hanover, Germany, edited by Rudolf Augstein. * January 10 – The United Nations adopts a resolution to take control of the free city of Trieste. * January 15 – Elizabeth Short, an aspiring actress nicknamed the "Black Dahlia", is found brutally murdered in a vacant lot in Los Angeles; the mysterious case is never solv ... [...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 summariz ... [...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 pr ... [...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 algebra (structure), 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 Charles Sanders Peirce, C. S. Peirce and Ernst Schröder (mathematician), 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) we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Don Pigozzi
Don, don or DON and variants may refer to: Places *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 *DON, Chapman code for County Donegal, Ireland People and characters Role or title *Don (honorific), a Spanish, Portuguese, and Italian title, given as a mark of respect * Don (academia), a fellow or tutor of a college or university in the U.K. and elsewhere *Don, a crime boss, especially in the Mafia People with the name * Don (given name), a short form of the masculine given na ... [...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 and bound variables, free variables. What is now usually called classical algebraic logic focuses on the identification and algebraic description of model theory, models appropriate for the study of various logics (in the form of classes of algebras that constitute the algebraic semantics (mathematical logic), algebraic semantics for these deductive systems) and connected problems like Representation (mathematics), 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 for some set ''X'', while a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reports On Mathematical Logic
A report is a document or a statement that presents information in an organized format for a specific audience and purpose. Although summaries of reports may be delivered orally, complete reports are usually given in the form of written documents. Typically reports relay information that was found or observed. The credible report enhances the previous beliefs while dishonest information can question the agency preparing the report. Reports from IPCC as IPCC reports, World Health Report and Global Gender Gap Report from World Economic Forums are few examples of reports highlighting important worldly affairs. 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 bu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Studia Logica
''Studia Logica'' (full name: ''Studia Logica, An International Journal for Symbolic Logic'') is a scientific 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 Jan Łukasiewicz (; 21 December 1878 – 13 February 1956) was a Polish logician and philosopher who is best known for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
