Algebra Booleana (logica)

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

Algebra Booleana, seu logica Booleana, est logicae calculus, medio saeculo undevicensimo a Georgio Boole propositus, qui ad valores veritatis computandas adhibetur. Fundamenta eius sunt operationes coniunctio x ∧ y, disiunctio x ∨ y, et negatio ¬x. Haec algebrae numerorum realum dissimilia non sunt, quae multiplicatione xy et additione x + y utitur. Operationes Booleanae sunt etiam omnes aliae operationes quae ex his operationibus primitivis creari possunt, velut x∧(y∨z). 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.

Nexus interni

• Algebra universalis
• Calculus propositionum
• Diagramma Vennianum
• Dominium Booleanum
• Electronica digitalis
• Functio Booleana
• Functio Booleana finitaria
• Functio valita Booleana^?
• Functiones Booleanae ad syntactica explicandum
• Graphicum logicale
• Informatica
• Index rerum algebrae Booleanae
• Java (lingua programmandi)
• Leges formae
• Leges De Morganiana
• Logica trinaria
• Logica propositionalis
• Logicam minimi facere
• Minimus negationis operator
• Porta logica
• Statistica
• 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). Amstelodami: 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). Bloomingtoniae in Indiana: Indiana University Press. ISBN 978-0-253-37204-8 
• Schröder, Ernestus (1890–1910). Vorlesungen über die Algebra der Logik (exakte Logik), I–III. Lipsiae: 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.). Berolini: 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 3: 183–198.
• "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.^?