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## NetLogo User Community Models

## WHAT IS IT?

This is based on the classic logic board game, "WFF 'N PROOF". WFF 'N Proof is actually a series of over 21 games of increasing difficult. To play, you must first understand what a "WFF" is - a WFF is a Well Formed Formula in propositional logic, using a new notation with the letters p, q, r, s, C, A, K, E, and N.

A given expression is a WFF if and only if:
1. it is a 'p', 'q', 'r', or 's'; or
2. it is a two-unit expression in which the first unit is an 'N' and the second unit is a WFF; or
3. it is a three-unit expression in which the first unit is a 'C', 'A', 'K', or 'E' and the second and third units are WFFs.

This program can tell you whether any combination of these letters is, in fact, a WFF or not. It has two game play modes: you can either let the program generate a random combination of these letters and answer "YES, this is a WFF" or "NO, this is not a WFF". Or, you can create your own expressions and click the "Next Question/Answer" button to see if it is a WFF or not. How many answers you get right or wrong are recorded.

Finally, you can also run a simulation to generate a list of correct WFF's by clicking the "Generate WFFs" button. I have already done this, generating a list of 19,771 unique WFF's between length 1 and 7 characters long, after 1 million trials. This is contained in the variable "permanent_list."

To be able to generate well-formed formulas, you don't need to know what the letters mean, but they do correspond to logical oeprators. The lower-case letters p, q, r, and s stand for simple sentences (e.g. "I am happy.").

TRANSLATION CODE:

Kpq = [p] AND [q]
Apq = [p] OR [q]
Cpq = IF [p] THEN [q]
Epq = [p] IF AND ONLY IF [q]
Np = IT IS NOT SO THAT [p]

Several studies have shown that playing WFF 'N Proof improved IQ scores by as much as 20 points! See references below.

## HOW IT WORKS
See the code for more details and copious notes. This isn't an agent-based model.

## HOW TO USE IT

There are two game play modes. If you check your own expression, enter your string in the field "expression" and click "Next Question/Answer." In the other game mode, you *first* click "Next Question/Answer" and then answer by clicking Yes or No.

## THINGS TO NOTICE

After awhile, you get the pattern.

## CREDITS AND REFERENCES

The game is available at http://www.gamesforthinkers.org/ .
Here are some citations:
Allen, Laymen E., Robert W. Allen, and Joan Ross. 1970. "The Virtues of NonSimulation Games" in Simulation & Games, September, 319-326.
Allen, Laymen E., Robert W. Allen, and Joan Ross. 1966. "Programmed games and thel learning of problem-solving skills: the WFF'N PROOF example." Journal of Educational Research 60: 22-26.