An Issue on default logic
We have the following sentences which I translated them to FOL by using the language:
Att(x) for "x attended the ceremony"
Likes(x,y) for "x likes y"
Rel(x,y) for "x is a relative of y"
Ab(x) for "x is an abnormal relative"
(a) Only all the normal relatives attended the wedding ceremony.
a) ∀x Att(x) ------ > ¬ Ab(x)
(b) Everybody who attended the ceremony was either a relative of the groom or a relative of the bride.
b) ∀x∀y∀z Att(x) -------> Rel (X, groom) \/ Rel (x, bride)
(c) Groom’s relatives normally like the groom.
c) ∀x Rel (x, Groom) /\ ¬ Ab(x) ------ > Like (x,groom)
(d) Bride’s relatives normally like the bride.
d) ∀z Rel (z, Groom) ¬ Ab(z) ------ > Like (z,groom)
(e) Peter does not like bride.
e) ¬ Likes (Peter, bride)
I suppose my translation is correct.
Now the are three questions:
(1) How can I show, by using FOL rules, that Peter likes the groom or he did not attend the ceremony.
(2) Check if the claim, that Peter does not like groom, is entailed by the knowledge base under GCWA.
(3) Show, that if the sentence “All the relatives of the groom are abnormal” was added to the knowledge base, it would follow, under the GCWA, that Peter does not like the groom.
Any idea? Thanks