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.
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 $\text {KB}$.