Lukasiewicz's Three-Valued Logic

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This Demonstration presents a simple test for Kleene's three-valued logic. The values are: True, False, and Undefined (or Unknown or Undecided), with associated numerical values 1, 0, 1/2, respectively. The value of compound propositions is evaluated according Łukasiewicz truth tables.

Contributed by: Izidor Hafner (March 2011)
Open content licensed under CC BY-NC-SA


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A simple two-dimensional area is occupied by triangles, squares, and pentagons of three sizes and two colors. A disk-shaped figure means that the shape of the element is not known. In this case a proposition of type Shape() has value "unknown". Lukasiewicz's paper "On the Three-Valued Logic" was published in 1920. Kleene's three-valued logic (1938) differs from it by having U instead of T in the U, U row for and .

S. C. Kleene, Introduction to Metamathematics, Amsterdam: North Holland, 1952 pp. 332–335.



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