Representation of Boolean Functions Using Binary Trees

This Demonstration shows representations of Boolean functions of two, three or four arguments using binary trees.
Abbreviations: CNF = canonical normal form, DNF = disjunctive normal form, BDT = binary decision tree, ANF = algebraic normal form, BFF = Boolean function form.

Details

The first use of binary trees to represent Boolean functions were Macfarlane's diagrams that he called "logical spectra"[5, p. 44]. The representation is more compact than using truth tables.

References

[1] R. Audi, ed., The Cambridge Dictionary of Philosophy, Cambridge: Cambridge University Press, 1995 pp. 780–782.
[2] L. Borkowski, Elementy logiki formalnej (Elements of Formal Logic, in Polish), 3rd ed., Warsaw: Wyd, 1976.
[3] L. Carroll, Symbolic Logic and the Game of Logic, New York: Dover, 1958.
[4] I. M. Copi and C. Cohen, Introduction to Logic, 9th ed., New York: Macmillan, 1994 pp. 214–218.
[5] M. Gardner, Logic Machines, Diagrams and Boolean Algebra, New York: Dover Publications, 1968.

External Links

Boolean Function (Wolfram MathWorld)
Boolean Algebra (Wolfram MathWorld)
Interactive Venn Diagrams
Venn Diagrams and Syllogisms
Venn Diagrams
Lewis Carroll's Bilateral Diagram
Lewis Carroll's Diagram and Categorical Syllogisms
Euler Circles for Categorical Syllogisms
The Ontological Table

Permanent Citation

Izidor Hafner
​
​"Representation of Boolean Functions Using Binary Trees"​
​http://demonstrations.wolfram.com/RepresentationOfBooleanFunctionsUsingBinaryTrees/​
​Wolfram Demonstrations Project​
​Published: September 20, 2016