Lukasiewicz's Three-Valued Logic

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.