Marquand's Representation of Boolean Functions

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This Demonstration shows Marquand's rectangular representation of Boolean functions of two to six arguments.



CNF = canonical normal form

DNF = disjunctive normal form

BDT = binary decision tree

ANF = algebraic normal form


Contributed by: Izidor Hafner (September 2016)
Open content licensed under CC BY-NC-SA



The first published suggestion for rectangular presentation of Boolean algebra of proposition was [1] as mentioned in [6, p. 43–44].


[1] A. Marquand, "On Logical Diagrams for Terms," Philosophical Magazine Series 5, 12(75), 1881 pp. 266–270. doi:10.1080/14786448108627104.

[2] R. Audi, ed., The Cambridge Dictionary of Philosophy, Cambridge: Cambridge University Press, 1995 pp. 780–782.

[3] L. Borkowski, Elementy logiki formalnej (Elements of Formal Logic, in Polish), 3rd ed., Warsaw: Wyd, 1976.

[4] L. Carroll, Symbolic Logic and the Game of Logic, New York: Dover, 1958.

[5] I. M. Copi and C. Cohen, Introduction to Logic, 9th ed., New York: Macmillan, 1994 pp. 214–218.

[6] M. Gardner, Logic Machines, Diagrams and Boolean Algebra, New York: Dover Publications, 1968.

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