Probability Logic Test

Requires a Wolfram Notebook System

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

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

This Demonstration presents a simple test for probability logic. The value of compound propositions is evaluated according to probability laws.


A simple two-dimensional area is occupied by white or gray triangles, squares, and pentagons. A disk indicates that the shape of the element is not known; in this case a proposition of type Shape() has value 1/3. A gray-white figure means that the color of the figure is not known; in this case a proposition of type Color(x) has value 1/2.


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



The procedure used should work on any propositional sentence. Using Mathematica's built-in function LogicalExpand eliminates all propositional connectives except ¬, ∧, and ∨. Negation is eliminated by rules, such as . Another application of LogicalExpand gives a disjunctive normal form without negations, that is a disjunction of conjunctions. There are special cases if the form reduces to a single conjunction, a single atomic statement, or True or False.

A conjunction is treated as a list of statements . In case the same figure appears with different shapes or colors, the probability of the conjunction is 0. (For instance: ) If no such case occurs, the set of statements is independent.

The shape and color of the same figure are independent of each other; the shapes of two different figures are independent, and so on. In these kinds of cases, and the basic formula for disjunction is .

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.