Marquand's Representation of Boolean Functions

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.