The psychology of knights and knaves

Knight-knave brain teasers are about a realm in which some people, knights, tell only truths, whereas all others, knaves, tell only lies. For example, suppose person A says, "I am a knight and B is a knight," and person B says, "A is a knave." Is A a knight or a knave? Is B a knight or a knave? In a pilot study, we asked subjects to think aloud while solving problems like these. Their statements suggested that they were making assumptions about the knight/knave status of the characters and drawing deductive inferences from these assumptions to test their consistency. This encouraged us to model the process by means of a simulation based on an earlier natural-deduction theory of reasoning. The model contains a set of deduction rules in the form of productions and a working memory that holds a proof of the correct answer. The greater the number of steps (assumptions and inferences) in the proof, the greater the predicted difficulty of the puzzle. The experiments reported here confirmed this prediction by showing that subjects were more likely to make mistakes (Experiment 1) and take longer to solve (Experiment 2) puzzles associated with a larger number of proof steps.