Horn Clause to prolog

Question

At the needs of my HW at uni I need to transform some Horn clauses to Prolog but I cannot figure out how to do it. I found out some guides but they describe how to do it with only one fact. So can you give me a brief example on how to do it?

Eg John is beautiful and rich

we can transform it at: not (Beautiful(John)) ^ not(Rich(John)) which is a Horn clause right? So how this can be translated it Prolog?

another example Everyone loves somebody. Horn clause: ∀X∃YLoves(X,Y) how can this be implemented in Prolog?

Thx in advance

Answer 1

For the first question you have

john :- beautiful, rich.

Or having something like:

beautiful(john).
rich(john).

with the query:

beautiful(X),rich(X).

Basically every rule in prolog is a horn clause. By definition, a Logic Program is a program, comprising of Horn clauses. In prolog when you have a rule that is declared as:

a1(X):-a2(X),a3(X),...,an(X)

is a horn clause because it is translated as:

a1 or not a2 or not a3 or ... or not an

So for your second question: In prolog the universal quantifier is implied when you define a rule so it does not affect the prolog clause. So you need to negate your sentence so you can transform the existential quantifier to a universal one. So, you have:

 ∀X∃YLoves(X,Y)

then you negate:

 ∀X ∀Y false <- Loves(X,Y))

which translates into:

:- loves(X,Y).