Appendix C: A Logic Puzzle

The following puzzle is I have adapted from Smullyan []. It's the kind of puzzle that would be used in the proposed study. (Note that I have connected it to ``real life" at Rensselaer.) The solution (a proof in the propositional calculus) follows on the next page -- but don't look: get it on your own.

``The time has come," Professor Peabody announced, ``to run a simulation of our AI-controlled VR system. Strap your helmet on, my man, and fire up our peraflop machine!"

``I'm afraid that isn't possible," Max said. ``Our supercomputer has been stolen from the catacombs of the VCC."

``What!? Only rats and the two of us dare tread there - at least that's what I thought. Who, by god, stole it?" Peabody asked.

``If I knew that, Professor, I would have had it back for our momentous test, no? Do you think I relish facing the wrath of ARPA?"

Peabody called campus security; they searched all over Capitaland and beyond for the missing supercomputer (which allowed people to park ticketlessly on campus for the first time since Henry Ford invented the Model T). Soon it was found -- but divided into three parts. One part was found in Renssleaer-retired Dr. Demento's house, one in the house of Munch (an infamous RPI hacker), and the third part was found in the house of MIT's President, Skurvy. All three were arrested and interrogated.

At the interrogation, Sherlock Hemlock announced that he would get to the bottom of the mess.

``Did you by any chance steal the supercomputer?" Hemlock asked Dr. Demento.

``I most certainly did not," Demento replied.

``What about you?" Sherlock Hemlock snapped at Munch. ``Are you by any chance the culprit?"

Munch said: ``One of us stole it, but it wasn't me!"

Hemlock wheeled around, his cape cutting through the air. ``And what about you?" he said to the cringing third suspect, Skurvy. ``What do you have to say about this crime against Technology? Did Dr. Demento and Munch both tell the truth?"

``At least one of them did," Skurvy replied.

As subsequent investigation revealed, Demento and Skurvy were not both speaking the truth.

Who stole the supercomputer?

The following is a compressed derivation which gives the solution, with obvious predicates for `telling the truth' and `stole the computers,' and obvious constants for the characters involved.

1. [as.]
2. [as.]
3. [as.]
4. [as.]
5. [2]
6. [5]
7. [6]
8. [7]
9. [8, 1]
10. [do sub-proof]
11. [10]
12. [11]
13. Ts [12, 3]
14. [4]
15. [13, 14]
16. Sd [15, 1]