WFF 'N PROOF: The Game of Modem Logic

By Layman E. Allen
Professor of Law and Senior Research Scientist
University of Michigan

The original 21-game kit teaches symbolic logic, the rules of inference, logical proof and formal systems. Beginning games can be mastered by young children. Advanced versions will challenge intelligent adults. Studies show that three weeks of intensive WFF 'N PROOF play have been accompanied by average increases in nonverbal I.Q. scores of more than 20 points. These are excellent games for anyone who wishes to increase ability in abstract reasoning and precise thinking. The games are for 2 or more players ages 6 to adult.

This page includes rules that define Basic WFF 'N PROOF, the 18 basic derived rules and their proofs, strategies for playing Adventurous WFF 'N PROOF, the Tarski Short Cut, Network WFF 'N PROOF, and Network EQUATIONS.

Adventurous WFF 'N PROOF

With deeply felt appreciation to my brother, Bob Allen, whose keen sense of the subtleties of the strategies of play has significantly informed this version of Adventurous WFF 'N PROOF.

The following five rules which were added to Basic WFF 'N PROOF, define Adventurous WFF 'NPROOF.

A1 Derived Rule

Any player who has the burden of proof (hereafter, a BoP player) can use in sustaining that burden, any new derived rule that the BoP player can prove when called upon to do so.

A2 Proof Bet Rule.

Any player who does not have the burden of proof can make a 4-point bet with any BoP player that the BoP player cannot prove the new derived rule that the BoP player has used in the BoP player's solution.


(a) In a 3-player match there are the following five different betting situations.

Number of Solutions (1) (2) (3) (4) (5)
Number of BoP Players
Number of Bettors

(b) If there is no bet by a non-BoP player (Situations 2 and 5), then the BoP player does not have to prove the new derived rule used in the BoP player's solution. Thus, in Adventurous WFF 'N PROOF the door is opened to some imaginative bluffing. However, deeper knowledge of logic of WFF 'N PROOF can curb the effectiveness of such strategies.

(c) Notice that in Situation 1 by Rule A4 it is possible for a bettor to get a bet score of 8 where that bettor bets both BoP players and neither proves the new derived rule used in her solution (and also possible to get a -8 bet score where both proves her new derived rule). Similarly, it is possible in Situation 3 for a BoP player to get 8 or ̄8 bet scores against two bettors by succeeding or failing to prove the new derived rule used.

A3 Solution and Proving Rule

The Detroit graduating seniors participating in the 2001 National Academic Games Tournament made significant contributions to the refinement and improvement of this rule. In constructing a Solution or in proving new derived rule, a BoP player can use any of the 11 assumed rules of inference of WFF 'N PROOF (Ki, Ko, Ci, Co, R, Ai, Ao, Ni, No, Ei, and Eo) and also any of the 18 basic derived rules of WFF 'N PROOF (AoAi, AoCi, AoNKi, AoNo, CoAi, CoCi, CoNKi, CoNo, KoKi, KoNAi, KoNCi, NAoKi, NCoKi, NKoAi, NKoCi, NNi, NNo, and Rp), but no other rules.


In regular Adventurous WFF 'N PROOF the Tarski Short Cut is not an acceptable proof; however, other Adventurous variations could either (a) accept it as a proof of a new derived rule or (b) make it the only acceptable proof of such.

A4 Proof Bet Scoring Rule

If the BoP player proves the new derive rule used in his solution, he gets a bet score of 4 and the bettor gets a bet score of ̄ 4, but if the BoP player does not prove the new derived rule used, the BoP player gets a bet score of  ̄ 4 and the bettor gets a bet score of 4. Comment In Adventurous WFF 'N PROOF a player's total score is her regular score (0, 6, 8, 10, or 16) plus her bet score
( ̄ 8, ̄ 4, 0, 4, or 8).

A5 Multiple R Rule (A5 is a superfluous rule. As of January 1, 2002, it is no longer in effect and cannot be used.)

If there is an R cube available as an Essential resource when players have the burden of proof, then for every R that is available for use to sustain that burden those players may (but need not) use another extra R in sustaining their burden of proof.


Thus, on an A-flub challenge if there is already an R cube in the Rules section of the Permitted Playing Mat, then players who have the burden of proof and choose to use a remaining R as an Essential R will have available in sustaining their burden of proof, 1,2,3, or 4 Rs - whichever they choose.

Criteria for Resolving Ambiguities, Vagueness, and Gaps in Game Rules

For purposes of resolving a dispute that arises in the play of WFF 'N PROOF where the game rules are imprecise or incomplete and judges are called in to decide, the dominant consideration for such decisions should be the effect upon all players' learning; judges should pick the alternative that contributes most to such learning. (And if you wish to be especially helpful and contribute to possible refinement of the rules that define WFF 'N PROOF, send the author an email message about the situation at this address:

Last update November 22, 2010