The fact that it’s the same phrasing used in the literature is really concerning, because it means the interpretation the literature gives is wrong: Many subjects may in fact be generating a mental model (based on deductive reasoning, no less!) which is entirely compatible with the problem-as-stated and yet which produces a different answer than the one the researchers expected.
One could certainly write ‘(Ace is present OR King is present) XOR (Queen is present OR Ace is present)’ which trivially reduces to ‘(King is present OR Queen is present) AND (Ace is not present)‘, but that gives the game away a bit—as perhaps it should! The fact that phrasing the knowledge formally rather than in ad-hoc English makes the correct answer so much more obvious is a strong indicator that this is a deficiency in the original researchers’ grasp of idiomatic English, not in their research subjects’ grasp of logic.
It’s difficult for me to look at the problem with fresh eyes, so I can’t be entirely certain whether the added ‘black box’ note helps. It doesn’t look helpful.
What would be really useful would be a physical situation in which the propositional-logic reading of the statements is the only correct interpretation. There is luckily a common silly-logic-puzzle trope which evokes this:
The dealer-robot has two heads, one of which always lies and one of which always tells the truth. You don’t know which is which.
After dealing the hand, but before showing it to you, the robot dealer takes a peek.
One of the robot’s heads has told you that the dealt hand contains either a king or an ace (or both).
The robot’s other head has told you that the dealt hand contains either a queen or an ace (or both).
The fact that it’s the same phrasing used in the literature is really concerning, because it means the interpretation the literature gives is wrong: Many subjects may in fact be generating a mental model (based on deductive reasoning, no less!) which is entirely compatible with the problem-as-stated and yet which produces a different answer than the one the researchers expected.
One could certainly write ‘(Ace is present OR King is present) XOR (Queen is present OR Ace is present)’ which trivially reduces to ‘(King is present OR Queen is present) AND (Ace is not present)‘, but that gives the game away a bit—as perhaps it should! The fact that phrasing the knowledge formally rather than in ad-hoc English makes the correct answer so much more obvious is a strong indicator that this is a deficiency in the original researchers’ grasp of idiomatic English, not in their research subjects’ grasp of logic.
It’s difficult for me to look at the problem with fresh eyes, so I can’t be entirely certain whether the added ‘black box’ note helps. It doesn’t look helpful.
What would be really useful would be a physical situation in which the propositional-logic reading of the statements is the only correct interpretation. There is luckily a common silly-logic-puzzle trope which evokes this: