dr. Johannes Korbmacher

 

• Course coordinator
• Mathematical philosopher
• jkorbmacher.org

Logic?!

Rationale:

• Logic is about reasoning.
• Reasoning is intelligent behavior.

Some puzzles

Cards

• If 3 is blue or red, the rule doesn't fail.
• If 8 is not blue, the rule fails.
• If red is even, the rule fails.
• If blue is even or od, the rule doesn't fail.

Marriage

Two cases: 1. Ada is married, 2. Ada is unmarried.

1. A married person (Ada) is looking at an unmarried person (Alan).
2. A married person (Kurt) is looking at an unmarried person (Ada).

Linda

There are more situations in which Linda is a bank teller than where she's a feminist bank teller.

Three forms of inference we'll study in the course:

1. propositional (cards)
2. quantificational (marriage)
3. probabilistic (Linda)

Logical methods?

GenAI

Consider the following puzzle, the so-called Wason selection task:

You are shown a set of four cards placed on a table, each of which has a number on one side and a color on the other. The visible faces of the cards show 3, 8, blue and red. Which card(s) must you turn over in order to test that if a card shows an even number on one face, then its opposite face is blue?

Please use Python to calculate the correct answer. Don't use ordinary reasoning or explain your solution or hard-code the result, just analyze the problem and calculate the solution.

Outlook?

• What is logic?
• How is it used in AI today?