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I am doing some Homework for an Artificial Intelligence Course, we are covering some First Order Logic and Conjuctive Normal Form.

Here are the questions that I have to answer that I am having trouble with

Q10. [20] Suppose that the sentence A in Q9 is changed to:

A1. Some great chefs are French.

1) [6] Write it in the FOL sentence.

a. Existential(x): GC(x) and F(x)

2) [6] Convert 1) to the the definite clause in CNF, suitable for Knowledge_Base through Skolemization, etc. if necessary.

a. Existential(x): GC(x) and F(x)

b. ¬ (Existential(x): GC(x) and F(x))

c. Universal(x): ¬GC(x) or ¬F(x)

d. Universal(x): GC(x) therefore ¬F(x)

3) [8] Prove how the same query can be answered (or not). Justify your answer step by step.

So my question here is, I feel like I am doing the conversion from FOL here to CNF wrong unless you can actually have a negative predicate as a conclusion for CNF for the knowledge base. How would I go about changing this to make it work?

And then I have no idea how to approach #3 to answer the question.

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  • $\begingroup$ Are you sure you don't mean Conjunctive Normal Form? $\endgroup$ – John Douma Apr 5 '19 at 3:10
  • $\begingroup$ Yes that is what i mean $\endgroup$ – Felauras Apr 5 '19 at 3:26
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Q10. [20] Suppose that the sentence A in Q9 is changed to:

A1. Some great chefs are French.

1) [6] Write it in the FOL sentence.

a. Existential(x) Universal(y): GC(y) and F(x)

That says: "Everything is a great chef, and something is French."

You want to claim that there is a thing that is a great chef, and this same thing is also French.   So you must use the same token for it.

Existential(x): GC(x) and F(x)

$$\exists x:(\operatorname{GC}(x)\land \operatorname{F}(x))$$

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  • $\begingroup$ So that is changed, what about the CNF conversion? $\endgroup$ – Felauras Apr 5 '19 at 3:45
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Your symbolization of 'some great chefs are French' is wrong. That should simply be:

$\exists x (GC(x) \land F(x))$

After negation:

$\neg \exists x (GC(x) \land F(x))$

You get:

$\forall x \neg (GC(x) \land F(x))$

And thus:

$\forall x (\neg GC(x) \lor \neg F(x))$

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  • $\begingroup$ Oh lol duh, how is the CNF conversion though? $\endgroup$ – Felauras Apr 5 '19 at 3:42
  • $\begingroup$ Thought for CNF conversion for a knowledge base that it has to be in the form of an implication? $\endgroup$ – Felauras Apr 5 '19 at 4:20
  • $\begingroup$ @Felauras I am not sure what method you are being taught ... if you could speel that out in your post I can provide a more meaningful answer. $\endgroup$ – Bram28 Apr 5 '19 at 12:00
  • $\begingroup$ Sorry, I guess I was mistaken and was wrong. I misunderstood the lectures and realized that when I looked back at the lecture notes after you said this. $\endgroup$ – Felauras Apr 5 '19 at 20:33

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