Five Islanders and Their Conditionals

Five islanders A, B, C, D and E are each a knight (always truthful) or a knave (always lying). Each makes one statement, read as an ordinary "if ... then ..." claim (it is false only when the first part is true and the second part false): - A: "If B is a knight, then I am a knave." - B: "If C is a knight, then E is a knight." - C: "If E is a knight, then A is a knight." - D: "If I am a knave, then B is a knight." - E: "If I am a knave, then D is a knight." How many of the five are knaves? Give a single integer.

• conditional probability

Source: Original puzzle in the knights-and-knaves tradition; conditional statements are classical in Smullyan's collections. Statement written for AxiomIQ.