WFF 'N PROOF is a game of modern logic, developed to teach principles of
symbolic logic
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...
. It was developed by Layman E. Allen in 1962
a former professor of
Yale Law School
Yale Law School (Yale Law or YLS) is the law school of Yale University, a Private university, private research university in New Haven, Connecticut. It was established in 1824 and has been ranked as the best law school in the United States by ''U ...
and the
University of Michigan
, mottoeng = "Arts, Knowledge, Truth"
, former_names = Catholepistemiad, or University of Michigania (1817–1821)
, budget = $10.3 billion (2021)
, endowment = $17 billion (2021)As o ...
.
Rules
In the game, players must be able to recognize a "
well-formed formula
In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language. A formal language can be ...
" (WFF) in
Łukasiewicz notation, and to and use rules of logic to manipulate those WFFs into a
proof
Proof most often refers to:
* Proof (truth), argument or sufficient evidence for the truth of a proposition
* Alcohol proof, a measure of an alcoholic drink's strength
Proof may also refer to:
Mathematics and formal logic
* Formal proof, a con ...
.
Games are played in groups of two or three. The first player rolls the cubes and sets a WFF as a Goal. The goal is the conclusion of a proof. Each player then tries to construct a proof that ends with the goal. The Solution to the goal is the Premises which they started their proof with, and the Rules they used to get to the Goal.
Players take turns moving to the Essentials, Permitted Premises, or Permitted Rules sections of the mat. Any cube moved to Essentials must be used in any Solution, and must be an essential part of that solution; any cube in Permitted Premises may be used as part of a premise; any cube in Permitted Rules may be used as part of a Rule. Thus the players themselves shape the Solution, forcing one another to create new Solutions in response to moves.
At any point a player may challenge the last mover, if they feel the last mover has made a mistake. There are three types of Challenges. A-Flub means that the Challenger can make a Solution using the cubes in Required and Permitted and one more cube from Resources. P-Flub, or Challenge Impossible means the player believes the Mover cannot make a Solution using the cubes in Required, Permitted, and Resources. C-A-Flub means that the Challenger believes that the Mover, or some previous mover, missed an A-Flub. After a challenge, at least one player must show a correct Solution on paper.
The scoring goes like this:
The player who wins the challenge scores 10 points.
The loser of the challenge scores 6.
If there is a third player, he must side with or against the Challenger and scores points depending upon that decision.
Name
The name is a play on
Whiffenpoofs
The Yale Whiffenpoofs is a collegiate a cappella singing group. Established at Yale University in 1909, it is the oldest such group in the United States. The line-up is completely replaced each year: the group is always composed of rising senior ...
,
an a capella singing group established at Yale University in 1909.
See also
*
Academic Games
Academic Games is a competition in the U.S. in which players win by out-thinking each other in mathematics, language arts, and social studies. Formal tournaments are organized by local leagues, and on a national level by the Academic Games Leagu ...
*
First Order Logic
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...
References
Further reading
*
*
External links
* {{cite web , title=WFF 'N PROOF: The Game of Modern Logic , work=Games For Thinkers , date=2018 , url=https://www.gamesforthinkers.org/all/logic/wff-n-proof-the-game-of-modern-logic/ , access-date=2022-07-03 , url-status=live , archive-url=https://web.archive.org/web/20220703003134/https://gamesforthinkers.org/all/logic/wff-n-proof-the-game-of-modern-logic/ , archive-date=2022-07-03
Educational games
Formal languages
Metalogic
Syntax (logic)
Mathematical logic
Logical expressions