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Unformatted text preview: truth value under τ. If B is a tautological consequence of A 1 ,…,A n , then B is a logical consequence of A 1 ,…,A n . (Recall: B is a logical consequence of A 1 ,…,A n if and only if it is impossible for all of A 1 ,…,A n to be true but B to be false.) Examples: Tet(a) Tet(a) . Cube(b) . Dodec(d) , Dodec(d) . Cube(d) Cube(d) Two sentences A,B are logically equivalent if and only if there is no logically possible circumstance in which A, B have different truth values. Examples: . (Tet(a) . Small(a)) . Tet(a) . . Small(a) . Cube(b) . (Dodec(c) . Tet(d)) (Cube(b) . Dodec(c)) . (Cube(b) . Dodec(c)) (a = b) . ( b = c) (a =b) . ( b = c) . ( a = c) These two sentences are logically equivalent but they are not tautologically equivalent....
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 Spring '08
 KNIGHT
 Logic, truth value assignment

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