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WFF 'N PROOF is a game of modern logic, developed to teach principles of symbolic logic. It was developed by Layman E. Allen in 1962 [ 1 ] [ 2 ] a former professor of Yale Law School and the University of Michigan .
A proof game is called a shortest proof game if no shorter solution exists. In this case the task is simply to construct a shortest possible game ending with the given position. When published, shortest proof games will normally present the solver with a diagram - which is the final position to be reached - and a caption such as "SPG in 9.0".
The theorem follows by induction on the length of the game from these two lemmas. Lemma 1. If s = 0, then t ≠ 0 no matter what move is made. Proof: If there is no possible move, then the lemma is vacuously true (and the first player loses the normal play game by definition).
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Perfect play for a game is known when the game is solved. [1] Based on the rules of a game, every possible final position can be evaluated (as a win, loss or draw). By backward reasoning, one can recursively evaluate a non-final position as identical to the position that is one move away and best valued for the player whose move it is. Thus a ...
For the purposes of the Sprague–Grundy theorem, a game is a two-player sequential game of perfect information satisfying the ending condition (all games come to an end: there are no infinite lines of play) and the normal play condition (a player who cannot move loses).
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