How Do You Stack Up Against Spock, Holmes, Wolf, Moriarity…?

Selmer BringsjordProfessor 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)• 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

9

1 11

47

3

5

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 onthe other side.

Which card or cards should you turn over in order to try to decideWhether the rule is true or false?

“NYS 1”Given the statements

a bbc a

which one of the following statements must also be true?

cbchanone of the above

“NYS 2”

Which one of the following statements is logically equivalent to thefollowing statement: “If you are not part of the solution, then youare 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 thesolution.

“NYS 3”Given the statementscc aa bb d(d e)

which one of the following statements must also be true?

cehaall 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 acein 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 doesn’t love 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 doesn’t love Bill.

Can you infer that Cath loves Bill?Can you infer that Cath loves Dave?

ANSWER: Yes x 2

JUSTIFICATION: See proof just given.

Bringsjord 1(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 definitelytrue: Billy helped.

Can it be inferred from (1) and (2) that Emma helped?

YUP!

The Dreadsbury Mansion MysterySomeone 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 disagreementbetween 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?

Email your answer with supporting proof

Last Brain Teaser

Is the following assertion true or false? Prove that you are correct.

There exists something which is such that if it’s a bird, theneverything is a bird.

Email your answer with supporting proof