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On Boolean algebra and its importance for the computer sciences
Author(s) -
Löwdin PerOlov
Publication year - 1992
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560420412
Subject(s) - boolean algebra , two element boolean algebra , boolean algebras canonically defined , class (philosophy) , branching (polymer chemistry) , free boolean algebra , complete boolean algebra , algebra over a field , point (geometry) , stone's representation theorem for boolean algebras , relation algebra , boolean expression , computer science , boolean circuit , boolean domain , boolean function , mathematics , theoretical computer science , discrete mathematics , pure mathematics , algebra representation , chemistry , geometry , organic chemistry , artificial intelligence
A brief survey is given of the abstract contentless Boolean algebra and its realizations to logic, class theory, and electric circuits as well as its applications to the software and hardware of the modern electronic computers. It is shown that three relations, 1 + 1 = 1, 1 + 1 = 0, and 1 + 1 = 10, correspond to three different realizations of the algebra, and that they, hence, represent an elementary example of a Gödelian branching point in the abstract Boolean algebra.