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Stanisław Jaśkowski
Stanisław Jaśkowski (22 April 1906, in Warsaw – 16 November 1965, in Warsaw) was a Polish logician who made important contributions to proof theory and formal semantics. He was a student of Jan Łukasiewicz and a member of the Lwów–Warsaw School of Logic. Upon his death his name was added to the Genius Wall of Fame. He was the President (rector) of the Nicolaus Copernicus University in Toruń. Jaśkowski is considered to be one of the founders of natural deduction, which he discovered independently of Gerhard Gentzen in the 1930s. Gentzen's approach initially became more popular with logicians because it could be used to prove the cut-elimination theorem. However, Jaśkowski's is closer to the way that proofs are done in practice. He was also one of the first to propose a formal calculus of inconsistency-tolerant (or paraconsistent) logic. Furthermore, Jaśkowski was a pioneer in the investigation of both intuitionistic logic and free logic A free logic is a lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paraconsistent Logic
A paraconsistent logic is an attempt at a logical system to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing "inconsistency-tolerant" systems of logic which reject the principle of explosion. Inconsistency-tolerant logics have been discussed since at least 1910 (and arguably much earlier, for example in the writings of Aristotle); however, the term ''paraconsistent'' ("beside the consistent") was first coined in 1976, by the Peruvian philosopher Francisco Miró Quesada Cantuarias. The study of paraconsistent logic has been dubbed paraconsistency, which encompasses the school of dialetheism. Definition In classical logic (as well as intuitionistic logic and most other logics), contradictions entail everything. This feature, known as the principle of explosion or ''ex contradictione sequitur quodlibet'' (Latin, "from a contradiction, anything follows") can be expressed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicolaus Copernicus University In Toruń Faculty
Nicolaus is a masculine given name. It is a Latin, Greek and German form of Nicholas. Nicolaus may refer to: In science: * Nicolaus Copernicus, Polish astronomer who provided the first modern formulation of a heliocentric theory of the solar system * Nicolaus Otto (1832 – 1891), German engineer In mathematics: * Nicolaus I Bernoulli, Swiss mathematician * Nicolaus II Bernoulli, Swiss mathematician * Nicolaus Rohlfs, 18th-century German mathematics teacher who wrote astronomical calendars In literature: * Nicolaus Becker, German lawyer and writer, the author of the '' Rheinlied'' * Nicolaus of Damascus, Greek historical and philosophical writer who lived in the Augustan age In music: * Nicolaus Bruhns, German composer * Nicolaus Zacharie, Italian composer of the early Renaissance In Christianity: * Nicolaus Ludwig Zinzendorf, German religious and social reformer and bishop of the Moravian Church * Nicolaus Taurellus, German philosopher and theologian * Nicolaus of Antio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Warsaw Alumni
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the designation is reserved for colleges that have a graduate school. The word ''university'' is derived from the Latin ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". The first universities were created in Europe by Catholic Church monks. The University of Bologna (''Università di Bologna''), founded in 1088, is the first university in the sense of: *Being a high degree-awarding institute. *Having independence from the ecclesiastic schools, although conducted by both clergy and non-clergy. *Using the word ''universitas'' (which was coined at its foundation). *Issuing secular and non-secular degrees: grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polish Mathematicians
Polish may refer to: * Anything from or related to Poland, a country in Europe * Polish language * Poles Poles,, ; singular masculine: ''Polak'', singular feminine: ''Polka'' or Polish people, are a West Slavic nation and ethnic group, who share a common history, culture, the Polish language and are identified with the country of Poland in Cen ..., people from Poland or of Polish descent * Polish chicken * Polish brothers (Mark Polish and Michael Polish, born 1970), American twin screenwriters Polish may refer to: * Polishing, the process of creating a smooth and shiny surface by rubbing or chemical action ** French polishing, polishing wood to a high gloss finish * Nail polish * Shoe polish * Polish (screenwriting), improving a script in smaller ways than in a rewrite See also * * * Polonaise (other) {{Disambiguation, surname Language and nationality disambiguation pages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polish Logicians
Polish may refer to: * Anything from or related to Poland, a country in Europe * Polish language * Poles Poles,, ; singular masculine: ''Polak'', singular feminine: ''Polka'' or Polish people, are a West Slavic nation and ethnic group, who share a common history, culture, the Polish language and are identified with the country of Poland in Cen ..., people from Poland or of Polish descent * Polish chicken * Polish brothers (Mark Polish and Michael Polish, born 1970), American twin screenwriters Polish may refer to: * Polishing, the process of creating a smooth and shiny surface by rubbing or chemical action ** French polishing, polishing wood to a high gloss finish * Nail polish * Shoe polish * Polish (screenwriting), improving a script in smaller ways than in a rewrite See also * * * Polonaise (other) {{Disambiguation, surname Language and nationality disambiguation pages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Writers From Warsaw
A writer is a person who uses written words in different writing styles and techniques to communicate ideas. Writers produce different forms of literary art and creative writing such as novels, short stories, books, poetry, travelogues, plays, screenplays, teleplays, songs, and essays as well as other reports and news articles that may be of interest to the general public. Writers' texts are published across a wide range of media. Skilled writers who are able to use language to express ideas well, often contribute significantly to the cultural content of a society. The term "writer" is also used elsewhere in the arts and music, such as songwriter or a screenwriter, but also a stand-alone "writer" typically refers to the creation of written language. Some writers work from an oral tradition. Writers can produce material across a number of genres, fictional or non-fictional. Other writers use multiple media such as graphics or illustration to enhance the communication of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1965 Deaths
Events January–February * January 14 – The Prime Minister of Northern Ireland and the Taoiseach of the Republic of Ireland meet for the first time in 43 years. * January 20 ** Lyndon B. Johnson is Second inauguration of Lyndon B. Johnson, sworn in for a full term as President of the United States. ** Indonesian President Sukarno announces the withdrawal of the Indonesian government from the United Nations. * January 30 – The Death and state funeral of Winston Churchill, state funeral of Sir Winston Churchill takes place in London with the largest assembly of dignitaries in the world until the 2005 funeral of Pope John Paul II. * February 4 – Trofim Lysenko is removed from his post as director of the Institute of Genetics at the Russian Academy of Sciences, Academy of Sciences in the Soviet Union. Lysenkoism, Lysenkoist theories are now treated as pseudoscience. * February 12 ** The African and Malagasy Republic, Malagasy Common Organization ('; OCA ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1906 Births
Events January–February * January 12 – Persian Constitutional Revolution: A nationalistic coalition of merchants, religious leaders and intellectuals in Persia forces the shah Mozaffar ad-Din Shah Qajar to grant a constitution, and establish a national assembly, the Majlis. * January 16–April 7 – The Algeciras Conference convenes, to resolve the First Moroccan Crisis between French Third Republic, France and German Empire, Germany. * January 22 – The strikes a reef off Vancouver Island, Canada, killing over 100 (officially 136) in the ensuing disaster. * January 31 – The 1906 Ecuador–Colombia earthquake, Ecuador–Colombia earthquake (8.8 on the Moment magnitude scale), and associated tsunami, cause at least 500 deaths. * February 7 – is launched, sparking a Anglo-German naval arms race, naval race between Britain and Germany. * February 11 ** Pope Pius X publishes the encyclical ''Vehementer Nos'', denouncing the 1905 French law on t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Logic
A free logic is a logic with fewer existential presuppositions than classical logic. Free logics may allow for terms that do not denote any object. Free logics may also allow models that have an empty domain. A free logic with the latter property is an inclusive logic. Explanation In classical logic there are theorems that clearly presuppose that there is something in the domain of discourse. Consider the following classically valid theorems. :1. \forall xA \Rightarrow \exists xA :2. \forall x \forall rA(x) \Rightarrow \forall rA(r) :3. \forall rA(r) \Rightarrow \exists xA(x) A valid scheme in the theory of equality which exhibits the same feature is :4. \forall x(Fx \rightarrow Gx) \land \exists xFx \rightarrow \exists x(Fx \land Gx) Informally, if F is '=y', G is 'is Pegasus', and we substitute 'Pegasus' for y, then (4) appears to allow us to infer from 'everything identical with Pegasus is Pegasus' that something is identical with Pegasus. The problem comes from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intuitionistic Logic
Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems of intuitionistic logic do not assume the law of the excluded middle and double negation elimination, which are fundamental inference rules in classical logic. Formalized intuitionistic logic was originally developed by Arend Heyting to provide a formal basis for L. E. J. Brouwer's programme of intuitionism. From a proof-theoretic perspective, Heyting’s calculus is a restriction of classical logic in which the law of excluded middle and double negation elimination have been removed. Excluded middle and double negation elimination can still be proved for some propositions on a case by case basis, however, but do not hold universally as they do with classical logic. The standard explanation of intuitionistic logic is the BHK interpreta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cut-elimination Theorem
The cut-elimination theorem (or Gentzen's ''Hauptsatz'') is the central result establishing the significance of the sequent calculus. It was originally proved by Gerhard Gentzen in his landmark 1934 paper "Investigations in Logical Deduction" for the systems LJ and LK formalising intuitionistic and classical logic respectively. The cut-elimination theorem states that any judgement that possesses a proof in the sequent calculus making use of the cut rule also possesses a cut-free proof, that is, a proof that does not make use of the cut rule. The cut rule A sequent is a logical expression relating multiple formulas, in the form , which is to be read as proves , and (as glossed by Gentzen) should be understood as equivalent to the truth-function "If (A_1 and A_2 and A_3 …) then (B_1 or B_2 or B_3 …)." Note that the left-hand side (LHS) is a conjunction (and) and the right-hand side (RHS) is a disjunction (or). The LHS may have arbitrarily many or few formulae; when the L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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