Algebra Booleana (logica)

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Algebra Booleana seu Logica Booleana est logicalis calculus valorum veritatis, decennio 184 a Georgio Boole creavitur. Est similis algebrae numerorum realum, sed operationes coniunctio x ∧ y, disiunctio x ∨ y, et negatio ¬x sunt pro multiplicatione xy, additione x + y, et negatione −x. Operationes Booleanae sunt illae etiam omnes aliae operationes quae ex his creari possunt, e.g. x∧(y∨z). Illae operationes sunt aequa copiae omnium operationum super copia {0,1} quae numerum argumentorum finitum habent; sunt 2²ⁿ illorum operationum n argumenta habentum.

Leges algebrae Booleanae aequationibus quae axiomates dicuntur et consecutionibus logicalibus eorum quae theoremas dicuntur, aut semantica — aequationibus quae omni adsignatione argumentorum eorum sunt verae — definisse potest. Axiomatibus definire est sanum et perfectum, id est, axiomatibus definire nec plurem (sanum) nec pauciorem (perfectum) leges probat quam semantica.

Vide etiam

• Algebra Booleana (introductio)
• Algebra Booleana (structura)
• Algebra Heyting
• Algebra Lindenbaum–Tarski
• Algebra universalis
• Calculus propositionum
• Cancelli (ordo)
• Diagramma Venn
• Dominium Booleanum
• Functio Booleana
• Functio Booleana finitary
• Functio valita Booleana
• Functiones Booleanae ad syntactica explicandum
• Graphicum logicale
• Index rerum algebrae Booleanae
• Leges Formae
• Logica trinaria
• Logicam minimi facere
• Minimus negationis operator
• Porta logica
• Tabula veritatis

Bibliographia

• 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 

Nexus externi

• Georgius Boole, 1848, "The Calculus of Logic," Cambridge and Dublin Mathematical Journal III: 183-98.
• Logical Formula Evaluator (for Windows), a software which calculates all possible values of a logical formula
• How Stuff Works - Boolean Logic
• Maiki & Boaz BDD-PROJECT, a Web Application for BDD reduction and visualization.