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Tutorial 1. Logic and AI

Exercise sheet

Definitions

Note: A definition needs to fully explain the meaning of a concept. This is typically done by saying under which precise conditions the concept applies. That is, the answer should have the form like “A valid inference is an inference such that…” or “An inference is valid just in case …”.

a.) Inference

Give a definition of inference. Include examples (where your definition applies) and non-examples (where it does not). Make sure to explain why your definition applies or not.

b.) Validity

Give a definition of deductive and inductive inference. Include examples and non-examples with explanations.

Indicators  

Give at least 5 additional examples of:

a.)

premise indicators,

b.)

inference indicators.

Solution

a.) Since, because, since, for, whereas, as.

b.) It follows that, thus, hence, consequently, we know that.

Validity  

Which of the following inferences is valid? Specify whether the inference is deductively or inductively valid.

a.)

Every attempt so far has failed. So the next attempt will also fail.

b.)

Well, I didn’t not cause the bug. So, I caused the bug.

c.)

If you did that, pigs can fly. So, you didn’t do it.

d.)

All software has bugs. So, this software has bugs, too.

e.)

A thinking computer is not a computer anymore. So it’s impossible to teach a computer how to think.

Solution
Deductive and inductive inference

Provide an argument that every deductively valid inference is also inductively valid. Does the converse also hold?

Expert systems
Thinking, Fast and Slow

Give at least 3 new examples of:

a.)

System 1

b.)

System 2

Research

Note: These questions require you to do your own research, using reliable academic sources. You need to reference your sources!

Decidability

Are all logical systems undecidable?

Symbolic AI

Give 2 examples of existing expert systems, one that “failed” and one that’s still in use today. Explain why the first one failed.

Discussion

Note: The following questions require argumentative writing, i.e. you’re asked to take an informed view on the question, clearly state your position, and the reasons for it.

a.) Logic and system 2

Is all logical thinking system 2 thinking?

b.) Minds and machines

Does Gödel’s theorem show that we cannot build a logic-based AGI?