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Algebra Booleana (logica)

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Pars fenestrae ex ecclesia cathedrali, Lindi, ubi natus est Georgius Boole

Algebra Booleana seu Logica Booleana est logicae calculus, decennio 184 a Georgio Boole creatus, qui ad valores veritatis computandas adhibetur. Fundamenta eius sunt operationes coniunctio xy, disiunctio xy, et negatio ¬x. Hoc non est dissimilis algebrae numerorum realum, quae multiplicatione xy et additione x + y utitur. Operationes Booleanae sunt etiam omnes aliae operationes quae ex his operationibus primitivis creari possunt, velut x∧(yz). Copia illarum operationum aequivalet copiae omnium operationum super copia {0,1} quae numerum argumentorum finitum habent; sunt 22n illorum operationum n argumenta habentum.

Leges De Morgan sunt principia algebrae Booleanae

Leges algebrae Booleanae aequationibus quae systema axiomatum dicuntur et consecutionibus logicis eorum quae theoremata dicuntur, aut semantica — aequationibus quae omni adsignatione argumentorum eorum sunt verae — definiri possunt. Axiomatibus definire est sanum et perfectum, id est, axiomatibus definire nec plurem (sanum) nec pauciorem (perfectum) leges probat quam semantica.

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Bibliographia[recensere | fontem recensere]

  • Boole, George (2003) [1854]. An Investigation of the Laws of Thought. Prometheus Books. ISBN 978-1-59102-089-9 
  • Dwinger, Philip (1971). Introduction to Boolean algebras. Würzburg: Physica Verlag 
  • Givant, Steven; Halmos, Paul (2009). Introduction to Boolean Algebras. Undergraduate Texts in Mathematics, Springer. ISBN 978-0-387-40293-2 .
  • Koppelberg, Sabine (1989). "General Theory of Boolean Algebras". Handbook of Boolean Algebras, Vol. 1 (ed. J. Donald Monk with Robert Bonnet). Amsterdam: North Holland. ISBN 978-0-444-70261-6 
  • Peirce, Carolus Sanders (1989). Writings of Charles S. Peirce: A Chronological Edition: 1879–1884 (ed. Christian J. W. Kloesel). Bloomington, IN: Indiana University Press. ISBN 978-0-253-37204-8 
  • Schröder, Ernestus (1890–1910). Vorlesungen über die Algebra der Logik (exakte Logik), I–III. Leipzig: B.G. Teubner 
  • Shannon, Claudius (1938). "The Symbolic Analysis of Relay and Switching Circuits". Trans. Am. Inst. Electrical Eng. 38: 713 
  • Shannon, Claudius (1949). "The Synthesis of Two-Terminal Switching Circuits". Bell System Technical Journal 28: 59–98 
  • Sikorski, Romanus (1969). Boolean Algebras (3/e ed.). Berlin: Springer-Verlag. ISBN 978-0-387-04469-9 
  • Stone, Marshall (1936). "The Theory of Representations for Boolean Algebras". Transactions of the American Mathematical Society (Transactions of the American Mathematical Society, Vol. 40, No. 1) 40 (1): 37–111 
  • Tarski, Alfredus (1929). "Sur les classes closes par rapport à certaines opérations élémentaires". Fundamenta Mathematicae 16: 195–197 
  • Tarski, Alfredus (1935). "Zur Grundlegung der Booleschen Algebra, I". Fundamenta Mathematicae 24: 177–198 
  • Vladimirov, D.A. (1969). булевы алгебры (Boolean algebras, in Russian, German translation Boolesche Algebren 1974). Nauka (German translation Akademie-Verlag) 
  • Zhegalkin, Ivan Ivanovich (1927). "On the Technique of Calculating Propositions in Symbolic Logic". Mat. Sb 43: 9–28 

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