Algebraic Logic
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Home > Art, Film & Photography > Algebraic Logic: Kleene Algebra, Boolean Algebra, Canonical Form, Relation Algebra, Higher-Dimensional Algebra, Predicate Functor Logic
Algebraic Logic: Kleene Algebra, Boolean Algebra, Canonical Form, Relation Algebra, Higher-Dimensional Algebra, Predicate Functor Logic

Algebraic Logic: Kleene Algebra, Boolean Algebra, Canonical Form, Relation Algebra, Higher-Dimensional Algebra, Predicate Functor Logic


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About the Book

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 31. Chapters: Kleene algebra, Boolean algebra, Canonical form, Relation algebra, Higher-dimensional algebra, Predicate functor logic, Residuated Boolean algebra, Abstract algebraic logic, Action algebra, Leibniz operator, MV-algebra, Monadic Boolean algebra, Cylindric algebra, Lindenbaum-Tarski algebra, De Morgan algebra, Polyadic algebra. Excerpt: Boolean algebra, as developed in 1854 by George Boole in his book An Investigation of the Laws of Thought, is a variant of ordinary elementary algebra differing in its values, operations, and laws. Instead of the usual algebra of numbers, Boolean algebra is the algebra of truth values 0 and 1, or equivalently of subsets of a given set. The operations are usually taken to be conjunction, disjunction, and negation -, with constants 0 and 1. And the laws are definable as those equations that hold for all values of their variables, for example x (y x) = x. Applications include mathematical logic, digital logic, computer programming, set theory, and statistics. Boole's algebra predated the modern developments in abstract algebra and mathematical logic; it is however seen as connected to the origins of both fields. In an abstract setting, Boolean algebra was perfected in the late 19th century by Jevons, Schroder, Huntington, and others until it reached the modern conception of an (abstract) mathematical structure. For example, the empirical observation that one can manipulate expressions in the algebra of sets by translating them into expressions in Boole's algebra is explained in modern terms by saying that the algebra of sets is a Boolean algebra (note the indefinite article). In fact, M. H. Stone proved in 1936 that every Boolean algebra is isomorphic to a field of sets. In the 1930s, while studying switching circuits, Claude Shannon observed that one could also apply the rules of Boo...


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Product Details
  • ISBN-13: 9781155856100
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 108
  • Spine Width: 6 mm
  • Weight: 209 gr
  • ISBN-10: 1155856104
  • Publisher Date: 29 Aug 2011
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Kleene Algebra, Boolean Algebra, Canonical Form, Relation Algebra, Higher-Dimensional Algebra, Predicate Functor Logic
  • Width: 189 mm


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