Which Alice?

ALICE IN PUZZLE-LAND
THEN WHO DID STEAL THE PEPPER? Suppose the Gryphon
were guilty. Then he lied, which means the Mock Turtle is not
innocent (like the Gryphon said) but is guilty, so we would have two
guilty ones, which we don't have (as mentioned in the last problem).
Therefore the Gryphon is innocent. So his statement is true, hence
the Mock Turtle is innocent. Therefore the Mock Turtle's statement
is true, so the Lobster is guilty.
A METAPUZZLE For those who know the book, the Lobster
(unlike the Gryphon and the Mock Turtle) never really appeared in
Alice in Wonderland—rather he was a character in one of the poems
recited by Alice.
THE FOURTH TALE Suppose the Duchess stole the sugar.
Then she lied, which means that what she said about the Cook not
stealing the sugar was false—in other words the Cook must have
also stolen the sugar. But we are given that only one person stole
the sugar. So it is impossible that the Duchess stole it. Therefore the
Cook stole the sugar. (Incidentally, both must have been lying.)
THE FIFTH TALE If the Cheshire Cat ate the salt, then all
three are lying, so this possibility is out. If Bill ate the salt, then all
three are telling the truth, so this possibility is out. Therefore the
Caterpillar must have eaten the salt (hence also the first two
statements are lies and the third is the truth).
THE SIXTH TALE If the Frog-Footman stole it, then he and
the Knave both lied, so this is out. If the Fish-Footman stole it, then
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