Etymologie, Etimología, Étymologie, Etimologia, Etymology
UK Vereinigtes Königreich Großbritannien und Nordirland, Reino Unido de Gran Bretaña e Irlanda del Norte, Royaume-Uni de Grande-Bretagne et d'Irlande du Nord, Regno Unito di Gran Bretagna e Irlanda del Nord, United Kingdom of Great Britain and Northern Ireland
Logik, Lógica, Logique, Logica, Logic
mathematische Logik, Lógica matemática, Logique mathématique, Logica matematica, Mathematical logic
A
B
Boolean algebra (W3)
Die engl. "Boolean algebra", dt. "Boolesche Algebra", wurde nach dem britischen Mathematiker George Boole (1815 - 1864) benannt.
(E?)(L?) http://www.businessdictionary.com/terms-by-letter.php?letter=B
(E?)(L?) http://www.christianlehmann.eu/
(E?)(L?) http://193.175.207.139:8080/lido/Lido
Boolean algebra
(E?)(L?) http://foldoc.org/George+Boole
(E6)(L1) http://computer.howstuffworks.com/boolean.htm
(E?)(L?) http://www.oedilf.com/db/Lim.php?Word=Boolean%20algebra
Limericks on Boolean algebra
(E2)(L1) http://dictionary.reference.com/browse/Boolean+algebra
(E?)(L1) http://www-groups.dcs.st-and.ac.uk/~history/Glossary/
(E?)(L1) http://plato.stanford.edu/entries/boolalg-math/
The Mathematics of Boolean Algebra
First published Fri Jul 5, 2002; substantive revision Fri Feb 27, 2009
Boolean algebra is the algebra of two-valued logic with only sentential connectives, or equivalently of algebras of sets under union and complementation. The rigorous concept is that of a certain kind of algebra, analogous to the mathematical notion of a group. This concept has roots and applications in logic (Lindenbaum-Tarski algebras and model theory), set theory (fields of sets), topology (totally disconnected compact Hausdorff spaces), foundations of set theory (Boolean-valued models), measure theory (measure algebras), functional analysis (algebras of projections), and ring theory (Boolean rings). The study of Boolean algebras has several aspects: structure theory, model theory of Boolean algebras, decidability and undecidability questions for the class of Boolean algebras, and the indicated applications. In addition, although not explained here, there are connections to other logics, subsumption as a part of special kinds of algebraic logic, finite Boolean algebras and switching circuit theory, and Boolean matrices.
- •1. Definition and simple properties
- •2. The elementary algebraic theory
- •3. Special classes of Boolean algebras
- •4. Structure theory and cardinal functions on Boolean algebras
- •5. Decidability and undecidability questions
- •6. Lindenbaum-Tarski algebras
- •7. Boolean-valued models
- •Bibliography
- •Other Internet Resources
- •Related Entries
(E?)(L?) http://en.wikipedia.org/wiki/Stone%27s_representation_theorem_for_Boolean_algebras
Stone's representation theorem for Boolean algebras
(E6)(L1) http://mathworld.wolfram.com/BooleanAlgebra.html
(E?)(L?) http://wordcraft.infopop.cc/Archives/2004-2-Feb.htm
C
D
disjunction (W3)
Die engl. "disjunction", dt. "Disjunktion" bezeichnet das "einschliessende ODER". Bereits der Stoiker "Chrysippus of Soli" (280 BC - 206 BC) und seine Nachfolger diskutierten diese logische Beziehung.
Im Englischen ist dieser Begriff seit dem 16.Jh. für öffentlich zugängliche Werke nachgewiesen. (Die Fachleute schrieben noch lateinisch.) Im "OED" ist als Referenz "The Lawiers Logike, exemplifying the Praecepts of Logike by the Practise of the Common Lawe" von "Abraham Fraunce" (1588) und "A Defence of the Godlie Ministers" von "Dudley Fenner" (1587), aufgeführt.
Sprachlich geht engl. "disjunction" zurück auf lat. "dis-" = dt. "zer-", "ver-", "fort-", "weg-" und lat. "iungere" = dt. "verbinden".
(E?)(L1) http://www.alanwood.net/demos/ent4_frame.html
HTML 4.01 Character Entity References: logical disjunction ∨, ∨
(E?)(L2) http://www.britannica.com/
disjunction (logic) | inclusive disjunction (logic)
(E?)(L?) http://www.christianlehmann.eu/
(E?)(L?) http://193.175.207.139:8080/lido/Lido
(E?)(L?) http://www.cut-the-knot.org/arithmetic/funny/count.shtml#disjunction
(E?)(L1) http://www.fileformat.info/info/unicode/char/d.htm
Unicode Character 'LOGICAL OR' (U+2228): disjunction ∨
(E1)(L1) http://www.medterms.com/script/main/alphaidx.asp?p=m_dict
Meiotic nondisjunction | Mitotic nondisjunction | Nondisjunction
(E?)(L?) http://www.philosophypages.com/dy/ix1.htm
disjunction
(E2)(L1) http://dictionary.reference.com/
disjunction | nondisjunction
(E?)(L1) http://plato.stanford.edu/contents.html
disjunction (Ray Jennings)
(E6)(L?) http://www.unicode.org/charts/charindex.html
(E?)(L?) http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1018&context=onlinedictinvertzoology
disjunction | nondisjunction
(E6)(L1) http://mathworld.wolfram.com/letters/D.html
Disjunction | Exclusive Disjunction | Inclusive Disjunction
E
F
Formal logic (W3)
Engl. "formal logic" (1855) beschäftigt sich mit der "Form" nicht mit dem "Inhalt" von Aussagen.
(E?)(L2) http://www.britannica.com/EBchecked/topic/213716/formal-logic
formal logic
(E?)(L2) http://www.britannica.com/EBchecked/topic/213740/Formal-Logic-or-the-Calculus-of-Inference-Necessary-and-Probable
Formal Logic; or, the Calculus of Inference, Necessary and Probable (work by De Morgan)
(E?)(L?) http://www.christianlehmann.eu/
(E?)(L?) http://193.175.207.139:8080/lido/Lido
Designation Standard Language
- "formal logic" is std English
- "mathematische Logik" is std German
- "formale Logik" is non-std German
- "lógica formal" is std Portuguese
- "lógica matemática" is non-std Portuguese
(E2)(L1) http://dictionary.reference.com/browse/formal+logic
(E6)(L1) http://mathworld.wolfram.com/FormalLogic.html
SEE: Symbolic Logic
(E?)(L?) http://mathworld.wolfram.com/SymbolicLogic.html
The study of the meaning and relationships of statements used to represent precise mathematical ideas. Symbolic logic is also called formal logic.
SEE ALSO: Logic, Metamathematics
(E?)(L?) http://en.wikibooks.org/wiki/Category:Dewey/100
Formal Logic
(E?)(L?) http://en.wikipedia.org/wiki/List_of_English_words_of_German_origin#Mathematics_and_formal_logic
Mathematics and formal logic
- Ansatz (lit. "set down," roughly equivalent to "approach" or "where to begin", a starting assumption) - one of the most used German loan words in the English-speaking world of science.
- "Eigen-" in composita such as eigenfunction, eigenvector, eigenvalue, eigenform; in English "self-" or "own-". They are related concepts in the fields of linear algebra and functional analysis.
- Entscheidungsproblem
- Grossencharakter (German spelling: Größencharakter)
- Hauptmodul (the generator of a modular curve of genus 0)
- Hilbert's Nullstellensatz (without apostrophe in German)
- Ideal (originally "ideale Zahlen", defined by Ernst Kummer)
- Kernel (Ger.: Kern, translated as core)
- Krull's Hauptidealsatz (without apostrophe in German)
- Möbius band (Ger.: Möbiusband)
- quadratfrei
- Stützgerade
- Vierergruppe (also known as Klein four-group)
- "Neben-" in composita such as Nebentype
- "Z" from (ganze) Zahlen ((whole) numbers), the integers
(E1)(L1) http://ngrams.googlelabs.com/graph?corpus=0&content=Formal logic
Abfrage im Google-Corpus mit 15Mio. eingescannter Bücher von 1500 bis heute.
Engl. "Formal logic" taucht in der Literatur um das Jahr 1840 auf.
Erstellt: 2011-03
Fuzzylogik (W3)
Dass der Mensch sich selbst nicht gerade für logisch denkend hält kann man an der "Fuzzylogik" erkennen. Dabei handelt es sich um Methoden zur Nachahmung der menschlichen Denkweise.
Wenn man bedenkt, dass engl. "fuzzy" = "verschwommen" heißt, handelt es sich bei der "Fuzzylogik" also um eine "verschwommene Logik".
(E6)(L1) http://www.anglizismenindex.de/
(E?)(L?) http://en.wikipedia.org/wiki/Fuzzing
(E?)(L?) http://www.owasp.org/index.php/JBroFuzz
JBroFuzz is a stateless network protocol fuzzer that emerged from the needs of penetration testing. Written in Java, it allows for the identification of certain classess of security vulnerabilities, by means of creating malformed data and having the network protocol in question consume the data.
G
H
I
Informal logic (W3)
Die Bezeichnung engl. "Informal logic" kam in den 1970er Jahren durch "Leo Groarke" auf. Der Google "Books Ngram Viewer" findet "Informal logic" allerdings bereits ab 1940.
(E?)(L1) http://plato.stanford.edu/contents.html
informal logic - see logic: informal
(E1)(L1) http://ngrams.googlelabs.com/graph?corpus=0&content=Informal logic
Abfrage im Google-Corpus mit 15Mio. eingescannter Bücher von 1500 bis heute.
Engl. "Informal logic" taucht in der Literatur um das Jahr 1940 auf.
J
K
L
logic (W3)
Das griech "logikê" bedeutete etwa "Wissenschaft des Denkens", "vernünftiges Denken" (griech. "lógos" = "Rede", "Wort", "Vernunft"). Es wurde von den Stoikern benutzt und umfasste viele philosophische Bereiche (die heute nicht mehr zur Logik gezählt werden).
Das Wort engl. "logic" erhielt seine moderne Bedeutung im 3.Jh. in den Kommentaren des "Alexander von Aphrodisias" zu den Werken des Aristoteles (384-322 v.u.Z.). Die logischen Schriften des Aristoteles dienten seinen Schülern als Hilfsmittel zur Wahrheitserkenntnis und wurde unter dem Begriff "Organon" zusammengefasst.
Im Mittelalter war "Logik" eine der drei Wissenschaften des "Trivium", neben "Rhetorik" und "Grammatik".
Das weiterführende "Quadrium" umfasste die Wissenschaften "Arithmetik", "Geometrie", "Astronomie" und "Musik".
Das "OED" weist als ersten Nachweis des Wortes "logic" auf "Chaucer’s: Canterbury Tales" im Jahr 1362 hin.
Die moderne Logik wird von Augustus de Morgan (1806-1871) und "George Boole" (1815-1864) eingeläutet.
Diese beiden Begriffe wurden von "De Morgan (1847) und John Venn (1881) als Buchtitel benutzt.
Von anderen Autoren wurden im 19.Jh. die Bezeichnungen "Deductive logic" und "Inductive logic" benutzt.
(E?)(L?) http://jeff560.tripod.com/mathsym.html
Eine Übersicht mathematischer Symbole inklusive der logischen Symbole und ihres ersten Auftretens findet man auf der Seite "Earliest Uses of Symbols of Set Theory and Logic" von "Jeff Miller".
(E?)(L?) http://jeff560.tripod.com/set.html
Earliest Uses of Symbols of Set Theory and Logic
Last updated: Sept. 1, 2010
The study of logic goes back more than two thousand years and in that time many symbols and diagrams have been devised. Around 300 BC Aristotle introduced letters as term-variables, a "new and epoch-making device in logical technique." The modern era of mathematical notation in logic began with George Boole (1815-1864), although none of his notation survives. Set theory came into being in the late 19th and early 20th centuries, largely a creation of Georg Cantor (1845-1918). See MacTutor's A history of set theory or, for more detail, Set theory from the Stanford Encyclopedia of Philosophy.
...
(E?)(L?) http://www-history.mcs.st-andrews.ac.uk/Search/historysearch.cgi?TOPICS=1&WORD=logic
History Topics
- Bolzano's manuscripts references
- Bolzano publications.html
- Set theory references
- Jaina mathematics references
- Mathematical games references
- U of St Andrews History
- Mathematical games references
- Ledermann interview
- Jaina mathematics references
- Christianity and Mathematics
- Word problems
- Set theory
- Measurement
- function concept
- Mathematical games
- Amusements.html
- Infinity
- Squaring the circle
- Calculus history
- Greek astronomy
- 20th century time references
- Topology history references
- Classical time references
- Infinity references
- Real numbers 3 references
- Real numbers 2 references
- 20th century time references
- Topology history references
- Classical time references
- Infinity references
- Real numbers 3 references
- Real numbers 2 references
- Bolzano's manuscripts
- Harriot's manuscripts
(E?)(L?) http://plato.stanford.edu/entries/alexander-aphrodisias/
(E?)(L?) http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Aristotle.html
(E?)(L?) http://plato.stanford.edu/entries/aristotle-logic/
(E?)(L?) http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/De_Morgan.html
(E?)(L?) http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Boole.html
(E?)(L?) http://plato.stanford.edu/entries/logic-informal/
(E?)(L?) http://plato.stanford.edu/entries/stoicism/
- •1. Sources of our information on the Stoics
- •2. Philosophy and life
- •3. Physical Theory
- •4. Logic
- •5. Ethics
- •6. Influence
- •Bibliography
- •Other Internet Resources
- •Related Entries
(E?)(L?) http://www.economics.soton.ac.uk/staff/aldrich/logic.htm
(E?)(L?) http://members.aol.com/jeff570/set.html
M
Mathematical logic (W3)
Der italienischer Mathematiker Giuseppe Peano benutzte den Ausdruck engl. "Mathematical logic" (1855) (auch engl. "symbolic logic") zur Bezeichnung dieser "neuen" Wissenschaft, bzw. zur Unterscheidung des "Logik"-Begriffs von der traditionellen Logik.
(E?)(L?) http://www.bubl.ac.uk/link/m/mathematicallogic.htm
(E?)(L?) http://www.businessdictionary.com/definition/mathematical-logic.html
(E?)(L?) http://www.christianlehmann.eu/
(E?)(L?) http://193.175.207.139:8080/lido/Lido
"mathematical logic" is non-std English
(E?)(L?) http://world.logic.at/
Mathematical Logic Around the World (Univ Bonn)
(E2)(L1) http://dictionary.reference.com/browse/mathematical+logic
(E?)(L?) http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Peano.html
Peano was the founder of "symbolic logic" and his interests centred on the foundations of mathematics and on the development of a formal logical language.
...
(E?)(L?) http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Peano.html
...
In 1888 Peano published the book Geometrical Calculus which begins with a chapter on "mathematical logic". This was his first work on the topic that would play a major role in his research over the next few years and it was based on the work of Schröder, Boole and Charles Peirce.
...
(E?)(L?) http://en.wikibooks.org/wiki/Category:Dewey/100
Mathematical Logic
(E1)(L1) http://ngrams.googlelabs.com/graph?corpus=0&content=Mathematical logic
Abfrage im Google-Corpus mit 15Mio. eingescannter Bücher von 1500 bis heute.
Engl. "Mathematical logic" taucht in der Literatur um das Jahr 1890 auf.
Erstellt: 2011-03
N
O
P
Q
R
S
Symbolic logic (W3)
Als Gründer der engl. "symbolic logic" (auch "formal logic", "mathematical logic") gilt Giuseppe Peano (1858-1932).
Die Grundlagen dieses Wissenschaftszweiges legten Gottfried Wilhelm Leibniz (1646-1716) und Friedrich Ludwig Gottlob Frege (1848-1925). Die mathematischen Philosophen Alfred North Whitehead (1861-1947) und Bertrand Arthur William Russell (1872-1970) entwickelten die "symbolische Logik" in ihrem Werk "Principia Mathematica", das im Jahr 1910 erschien, weiter.
(E?)(L?) http://www.aslonline.org/index.htm
Association of Symbolic Logic
(E?)(L?) http://www.aslonline.org/othersites.htm
Links to Other Sites
Organizations
- American Association for the Advancement of Science (AAAS)
- American Mathematical Society (AMS)
- American Philosophical Association (APA)
- Association for Computing Machinery (ACM)
- Conference Board of the Mathematical Sciences (CBMS)
- Cognitive Science Society
- European Association for Computer Science Logic (EACSL)
- European Association for Logic, Language and Information (FoLLI)
- Gödel Society
- Institute of Electrical and Electronics Engineers, Inc. (IEEE)
- International Mathematical Olympiad (IMO)
- Linquistic Society of America
- Logic in Computer Science (LICS)
- London Mathematical Society
- Mathematical Association of America (MAA)
- The Danish Network for Philosophical Logic and Its Applications Newsletter (PHINEWS)
- Society for Industrial and Applied Mathematics (SIAM)
- The Philosophy of Science Association
Research Institutes
- Fields Institute for Research in Mathematical Sciences
- Fuzziness and Uncertainty Modelling Research Group
- Institute for Logic, Language, and Computation (ILLC)
- Institute for Mathematics and its Applications (IMA)
- Mathematical Institutes and Centers (Site organized by AMS)
- Mathematical Sciences Research Institute (MSRI)
Scholarly Resources
- http://www.nd.edu/~cholak/computability/computability.html - Bibiliographic Site for Computability Theory
- http://wwwagr.informatik.uni-kl.de/~akademie/contents.html - Bibliography of Mathematical Logic and Related Fields
- http://www.math.ufl.edu/~jal/set_theory.html - Bibliographic Site for Set Theory
- http://dblp.uni-trier.de/db/index.html - Computer Science Bibliography
- http://directory.google.com/Top/Science/Math/Logic_and_Foundations/ - Google Web Directory for Logic and Foundations
- http://www.jstor.org/ - JSTOR - Scholarly Journal Archive
- http://www.cirs-tm.org - International Center for Scientific Research (CIRS)
- http://xxx.lanl.gov/archive/math - Los Alamos National Laboratory Mathematics Archive
- http://www-groups.dcs.st-and.ac.uk/~history/index.html - The MacTutor History of Mathematics Archive
- http://dmoz.org/Science/Math/Logic_and_Foundations/ - Open Directory Project
- http://www.math.uu.se/logik/logic-server/ - Research Groups in Logic and Theoretical Computer Science (Maintained by the Upsala Group for Mathematical Logic)
- http://www.sosig.ac.uk/philosophy/logic/ - Social Sciences Information Gateway - Logic Resources
(E?)(L?) http://www.businessdictionary.com/definition/symbolic-logic.html
(E?)(L?) http://www.christianlehmann.eu/
(E?)(L?) http://193.175.207.139:8080/lido/Lido
(E?)(L1) http://www.gutenberg.org/browse/authors/c
Carroll, Lewis, 1832-1898: Symbolic Logic, 1897
(E?)(L?) http://www.philosophypages.com/dy/ix3.htm
(E?)(L?) http://www.philosophypages.com/dy/s9.htm#sylo
(E2)(L1) http://dictionary.reference.com/browse/symbolic+logic
(E?)(L?) http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Peano.html
Peano was the founder of "symbolic logic" and his interests centred on the foundations of mathematics and on the development of a formal logical language.
...
(E?)(L?) http://mathworld.wolfram.com/SymbolicLogic.html
The study of the meaning and relationships of statements used to represent precise mathematical ideas. "Symbolic logic" is also called "formal logic".
SEE ALSO: Logic, Metamathematics
(E1)(L1) http://ngrams.googlelabs.com/graph?corpus=0&content=Symbolic logic
Abfrage im Google-Corpus mit 15Mio. eingescannter Bücher von 1500 bis heute.
Engl. "Symbolic logic" taucht in der Literatur um das Jahr 1890 auf.
Erstellt: 2011-03
T
U
V
W
X
Y
Z
Buecher zur Kategorie:
Etymologie, Etimología, Étymologie, Etimologia, Etymology
UK Vereinigtes Königreich Großbritannien und Nordirland, Reino Unido de Gran Bretaña e Irlanda del Norte, Royaume-Uni de Grande-Bretagne et d'Irlande du Nord, Regno Unito di Gran Bretagna e Irlanda del Nord, United Kingdom of Great Britain and Northern Ireland
Logik, Lógica, Logique, Logica, Logic
amazon - Logik, Lógica, Logique, Logica, Logic
Logica (IT)
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
Smith, Peter (Author)
An Introduction to Formal Logic
(E?)(L1) http://www.amazon.ca/exec/obidos/ASIN/0521008042/etymologporta-20
(E?)(L1) http://www.amazon.de/exec/obidos/ASIN/0521008042/etymologety0f-21
(E?)(L1) http://www.amazon.fr/exec/obidos/ASIN/0521008042/etymologetymo-21
(E?)(L1) http://www.amazon.it/exec/obidos/ASIN/0521008042/etymologporta-21
(E?)(L1) http://www.amazon.co.uk/exec/obidos/ASIN/0521008042/etymologety0d-21
(E?)(L1) http://www.amazon.com/exec/obidos/ASIN/0521008042/etymologpor09-20
Paperback: 366 pages
Publisher: Cambridge University Press (6 Nov 2003)
Language English
Product Description
Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.
Book Description
This book introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages. It will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.
Erstellt: 2011-03
T
U
V
W
X
Y
Z