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How do I state the sentences for KB ∧ ¬ α when I already have KB.

KB:

∀xTourist(x) => Person(x): Every tourist is a person.

∀xTourist(x) ∧ visits(x, Malaysia) => walksCanopy(x): Every tourist who visits Malaysia walks the canopy.

∀xPerson(x) ∧ has(x, Acrophobia) => fallSick(x, walksCanopy): Every person who has acrophobia falls sick when they walk the canopy.

∃xPerson(x) => has(x, Acrophobia): There are some people who have acrophobia.

Friend(Abu, Bill): Abu and Bill are friends.

Person(Abu) => livesIn(Abu, Malaysia): Abu is a person who lives in Malaysia.

Person(Bill) => livesIn(Bill, Canada): Bill is a person who lives in Canada.

∀xFriend(x) ∧ Friend(Bill, x) ∧ visitsCountry(Bill, x): Bill visits the countries of all his friends.

has(Bill, Acrophobia): Bill has acrophobia.

Prove that "Bill will fall sick".

I already looked at my lecture notes and even looked it up online but I can't seem to understand what KB ∧ ¬ α is.

Thanks.

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  • $\begingroup$ You need the formula $\alpha$. $\endgroup$ – Mauro ALLEGRANZA Apr 12 at 7:45
  • $\begingroup$ Then you have to negate it and add to the four formulas of KB. $\endgroup$ – Mauro ALLEGRANZA Apr 12 at 7:46
  • $\begingroup$ Having said that, maybe you can add detials about the problem you are working on... $\endgroup$ – Mauro ALLEGRANZA Apr 12 at 7:47
  • $\begingroup$ Maybe you are working with Resolution ? $\endgroup$ – Mauro ALLEGRANZA Apr 12 at 8:06
  • $\begingroup$ @MauroALLEGRANZA Hi, I've edited my question and changed my KB. If I am understanding it correctly α is "Bill will fall sick"? $\endgroup$ – Mike Mann Apr 12 at 9:21
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Let $\text {KB}$ a set of sentences and $\alpha$ a sentence.

In order to prove that $\text {KB} \vDash \alpha$ we consider $\text {KB} \cup \{ \lnot \alpha \}$ and apply the Resolution proof-procedure for predicate logic.

If we succeed deriving the empty clause, we have shown that $\text {KB} \cup \{ \lnot \alpha \}$ is unsatisfiable, that is equivalent to $\text {KB} \vDash \alpha$.


In your example, you are asked to prove that "Bill will fall sick" is implied by $\text {KB}$.

This means that "Bill will fall sick" is "your $\alpha$" and thus you have to add "Bill will not fall sick" to $\text {KB}$.

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  • $\begingroup$ So basically if I have to state my sentences for KB it'd be: ∀xTourist(x) => Person(x) ∧ ¬ fallSick(Bill): Every tourist is a person and Bill will not fall sick. and so on. Is that right? $\endgroup$ – Mike Mann Apr 12 at 14:11
  • $\begingroup$ @MikeMann - Yes $\lnot \alpha$ is ¬ fallSick(Bill). $\endgroup$ – Mauro ALLEGRANZA Apr 12 at 14:14
  • $\begingroup$ thanks! I'm gonna work on CNF conversion and resolution now and see if I can figure it out. $\endgroup$ – Mike Mann Apr 12 at 14:23

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