Rules of Basic WFF 'N PROOF

Summary of Rules

Comments

1. The Goal is the conclusion of a proof. After you have rolled the cubes, the symbols that appear on their upward faces are the Resources for that play of the game. When it is possible to set a Goal for which a Solution (a set of premisses and a set of names of rules of inference) can be built from the remaining Resources, then in order to avoid Flubbing you must set such a Goal, and you must not say "No Goal." For example, if no pair of one-letter WFFs appear as Resources, you may say "No Goal," without Flubbing; but if any pair one-letter WFFs appear as Resources along with other Resources that will permit the construction of the names of rules of inference that will justify the inference of one of those WFFs as a conclusion from the other as a premiss, you must set a Goal.
2. The Goal is a string of at most five cubes that is a WFF. Thus, the only the 'C', 'A', 'K', 'E', 'N', 'p', 'q', 'r', and 's' cubes may be used in the Goal. Some examples of permissible Goals are p, Nq, Crs, ANpNs, and KsErp. Expressions such as CK and pr are not permissible Goals because they are not WFFs.
3. In Basic WFF 'N PROOF, the Goal is not changed after it has been set.

• move a cube from Resources to the Premisses section of the Permitted Parts mat, or
• move a cube from Resources to the Rules section of the Permitted Parts mat, or
• move a cube from Resources to the Essential Parts mat.

Comments

1. By their moves, the players shape the Solution. Cubes are never moved after they have been placed on the playing mat.
2. Moving an 'R', 'i', or 'o' to the Premisses section of the Permitted Parts mat is, in effect, forbidding the use of those Resources in the Solution because all premisses are WFFs and these letters are not used in WFFs.
3. Moving a 'q', 'r', or 's' to the Rules section of the Permitted Parts mat is, in effect, forbiddng the use of those Resources in the Solution because those letters are not used in the names of rules of inference.

Comment

The Bonus Rule has the effect of allowing a mover to move two cubes to the playing mats, but the first cube moved must, in effect, be forbidden to be used in building the Solution.

• you must not use any of the cubes that have been forbidden;
• you may use as many of the cubes that have been permitted as you like;
• you must use all of the cubes that have been made essential in an essential manner in the Solution; and
• you may always use at least one cube from Resources; you may use at most one cube from Resources when there has been an A-claim challenge or a C-claim challenge that stems from a previous A-claim violation (see the Flubbing Rule in Section 3.5 below), and you may use as many Resources as you like when there has been a P-claim challenge, a C-claim challenge that stems from a previous P-claim violation, or a No-Goal challenge (note that on a No-Goal challenge you must set a Goal as well as build a Solution).

1. Since several Resource cubes may show the same symbol, it is possible to have one 'R' that is forbidden in the Premisses section of the Permitted Parts mat, a second 'R' that is permitted in the Rules section of the Permitted Parts mat, and a third 'R' that is essential on the Essential Parts mat.
2. In order for a Resource to be used essentially, the premiss or rule name in which the Resource is used cannot be deleted from the proposed Solution and the Goal still be deducible from the premisses and by means of the rule names that remain.

• you declare "No Goal" when, in fact, you could have set a Goal for which there was a Solution;
• by your move you violate one of the following C-A-P claims:
1. "C" I Cannot Correctly challenge on this turn.
2. "A" If possible, I am Avoiding by this move allowing a Solution to be built with at most one more cube from Resources.
3. "P" It is still Possible for the remaining Resources to be so played that a Solution can be built.

1. The P-claim means that you Flub if you make a move (P)revents all possibilities for building a Solution.
2. The A-claim means that you Flub if you make a move that (A)llows a Solution to be built with at most one more cube from Resources when you could have made a move that both avoided doing so and at the same time fulfilled the P-claim. Of course, when only two cubes are left in Resources, you may have to move one of them so that they are made permitted or essential and allow a Solution to be built with just one more cube from the Resources, because forbidding either cube violates the P-claim. This is a Force-Out situation rather than an A-claim violation, because in such circumstances it is not possible to avoid allowing a Solution to be built with just one more cube from the Resources without violating the P-claim.
3. The C-claim means that once a Flub is made, every subsequent move is a Flub because every subsequent mover could have (C)orrectly challenged. Since only the most recent Flub may be challenged, the C-claim makes it possible to win by laying a trap: make a deliberate Flub, and as soon as the next player moves, challenge him for failing to challenge you.

Comments

1. A challenge cannot be retracted once a player has said "Challenge."
2. To determine priority in those rare cases where two players say "Challenge" simultaneously, a coin (or other token) should be placed in the center of the table when the cubes are first rolled. The first of the simultaneously- challenging players to pick up the coin shall be the Challenger; the other player shall be the Third Party.

Comments

1. A Solution must, of course, satisfy the conditions imposed by the Solution rule and the previous plays of the cubes onto the Permitted Parts mat and the Essential Parts mat.
2. Sometimes the burden of proof will be upon the Challenger -- namely, when the Challenger alleges that there has been a Flub by virtue of a false No-Goal declaration, an A-claim violation, or a C-claim violation that stems from a previous A-claim violation. On the other hand, sometimes the burden will be upon the Mover -- namely, when the Challenger alleges that there has been a Flub by virtue of a P-claim violation or a C-claim violation that stems from a previous P-claim violation.
3. When a Challenger has alleged an A-claim violation or a C-claim violation that stems from a previous A-claim violation, he also has the burden of proving that there was an alternative move that (a) did not allow a Solution to be built with at most one more cube from the Resources, and (b) did not violate the P-claim.
4. If there has been a challenge of a No-Goal declaration, the burden of proof is upon the Challenger, who, from the Resources, must not only build a Solution but also set a Goal.

• she has the burden of proving the existence of a Solution and she sustains it (by writing one), or
• she does not have the burden of proving the existence of a Solution (somebody else has the burden), and nobody sustains that burden of proof.

• the Third Party (T) must join either the Challenger (C) or the Mover (M), and
• if the player that T joins has the burden of proving the existence of a Solution, then T must sustain the same burden of proof by independently writing a Solution, and
• if T is Correct, then T scores 8 points if he has joined C and 10 if he has joined M, and
• C's score depends on the kind of challenge:
1. C scores 16 if both
• she makes an A-flub and then
• she is correct on her CA-flub challenge of the move immediately following her A-flub move (Bold challenge), and
2. C scores 10 if she is correct on any other kind of challenge.
• M scores 10 if M is Correct, and
• if anyone is incorrect, then he scores 6.

1. If the game involves four or more players, then all of the players other than the Mover and the Challenger are Third Parties.
2. The effect of this scoring rule is usually (although not always) that one of the two players involved in a challenge scores 16, 10, or 8 and the other 6. In some circumstances, they both may wind up with 6. T can score 10 when he joins M. However, T can score at most 8 by joining C. This places a premium upon being the first player to challenge another's Flub.

• (A) if a player has declared Force-Out, meaning that a Solution can be built with one more cube from Resources, but that there is no Flub, then (1) each player who writes a Solution within the specified time limit (usually from one to two minutes) scores 8, and (2) if the player who has declared "Force-Out" cannot build a Solution, he scores 0, and (3) all other players score 6, and
• (B) if the first player has said that No Goal can be set, then each player scores 8.

Comment
The situation described in (A) will generally arise when there is only one cube left in Resources

• deciding whether to set a Goal or to declare "No Goal," or
• deciding whether to move a cube, to challenge, or to assert that a Solution can be built with one more cube from the Resources (Force-Out), or
• deciding whom to join after a challenge, or
• trying to build a Solution.