# First Order Logic to CNF for Knowledge Base

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.

• Are you sure you don't mean Conjunctive Normal Form? – John Douma Apr 5 '19 at 3:10
• Yes that is what i mean – Felauras Apr 5 '19 at 3:26

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)


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

• So that is changed, what about the CNF conversion? – Felauras Apr 5 '19 at 3:45

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:

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

• Oh lol duh, how is the CNF conversion though? – Felauras Apr 5 '19 at 3:42
• Thought for CNF conversion for a knowledge base that it has to be in the form of an implication? – Felauras Apr 5 '19 at 4:20
• @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. – Bram28 Apr 5 '19 at 12:00
• 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. – Felauras Apr 5 '19 at 20:33