How Do You Stack Up Against Spock, Holmes, Wolf, Moriarity…? Selmer Bringsjord Professor of Logic, Philosophy, Cognitive Science, Computer Science Department of Cognitive Science (Chair) Department of Computer Science Director, Rensselaer AI & Reasoning Laboratory Rensselaer Polytechnic Institute Troy NY USA selmer@rpi.edu www.rpi.edu/~brings

What is Logic? The science of reasoning. The only invincible subject there is. The basis for all things intellectual, from engineering to computer science to philosophy. The most challenging subject there is. A key to riches. The key to divining the meaning of life (and other such big questions). The better way to program computers (9.20 lunch). One of two fundamental approaches to studying minds, and replicating/simulating minds in machines… The thing many creatures of fiction have mastered – have you (as a New Yorker)?… …

Number Sense 5 3 1 11 7 9 4 Vicky’s secret number is inside the triangle. It is outside the square. It is greater than 7 but less than 10. Vicky’s secret number is… 9

Simple Selection Task E T 4 7 Suppose I claim that the following rule is true. If a card has a vowel on one side, it has an even number on the other side. Which card or cards should you turn over in order to try to decide whether the rule is true or false?

“NYS 1” Given the statements a  b b c  a which one of the following statements must also be true? c b c h a none of the above

“NYS 2” Which one of the following statements is logically equivalent to the following statement: “If you are not part of the solution, then you are part of the problem.” If you are part of the solution, then you are not part of the problem. If you are not part of the problem, then you are part of the solution. If you are part of the problem, then you are not part of the solution. If you are not part of the problem, then you are not part of the solution.

“NYS 3” Given the statements c c  a a  b b  d (d  e) which one of the following statements must also be true? c e h a all of the above

J-L 1 Suppose that the following premise is true: If there is a king in the hand, then there is an ace in the hand, or else if there isn’t a king in the hand, then there is an ace. What can you infer from this premise? There is an ace in the hand. NO! NO! In fact, what you can infer is that there isn’t an ace in the hand!

Problem Given Selmer on Train Everyone loves anyone who loves someone. Alvin loves Bill. Can you infer that everyone loves Bill? ANSWER: JUSTIFICATION:

Problem Given Selmer on Train Everyone loves anyone who loves someone. Alvin loves Bill. Can you infer that everyone loves Bill? ANSWER: Yup. JUSTIFICATION: See proof just given.

Harder Variants Everyone loves anyone who loves someone. Alvin loves Bill. Can you infer that Cath loves Bill? Can you infer that Cath loves Dave? ANSWER: JUSTIFICATION:

Harder Variants Everyone loves anyone who loves someone. Alvin loves Bill. Can you infer that Cath loves Bill? Can you infer that Cath loves Dave? ANSWER: Yup JUSTIFICATION: ??

Bringsjord 1 If Billy helped, Doreen helped. (1) The following three assertions are either all true or all false: If Billy helped, Doreen helped. If Doreen helped, Frank did as well. If Frank helped, so did Emma. (2) The following assertion is definitely true: Billy helped. Can it be inferred from (1) and (2) that Emma helped? YUP!

The Dreadsbury Mansion Mystery Someone who lives in Dreadsbury Mansion killed Aunt Agatha. Agatha, the butler, and Charles live in Dreadsbury Mansion, and are the only people who live therein. A killer always hates his victim, and is never richer than his victim. Charles hates no one that Aunt Agatha hates. Agatha hates everyone except the butler. The butler hates everyone not richer than Aunt Agatha. The butler hates everyone Agatha hates. No one hates everyone. Agatha is not the butler. Now, given the above clues, there is a bit of disagreement between three (competent?) Norwegian detectives. Inspector Bjorn is sure that Charles didn’t do it. Is he right? Inspector Reidar is sure that it was a suicide. Is he right? Inspector Olaf is sure that the butler, despite conventional wisdom, is innocent. Is he right? See Hyperproof...

Last Brain Teaser Explorations... Is the following assertion true or false? Prove that you are correct. There exists something which is such that if it’s a bird, then everything is a bird. Explorations...

“Show me the $” Problem If one of the following assertions is true then so is the other: (1) There is a king in the hand if and only if there is an ace in the hand. (2) There is a king in the hand. Which is more likely to be in the hand, if either: the king or the ace?