Representation in Prolog - Logic Programs : Artificial intelligence

If we impose some more constraints on first order logic, then we get to a representation language known as logic programs. The major limitation we impose is that all the knowledge we want to encode is represented such as Horn clauses. These are implications which containa head anda body, where the predicates in the body are conjoined and they imply the single predicate in the head. Horn clauses are entirely quantified over all the variables appearing in them. So, an instance Horn clause looks like this:

∀x, y, z ( b₁(x,y) ∧ b₂(x) ∧ ... ∧ b_n(x,y,z) -> h(x,y))

We see that the body contain of predicates bi and the head is h(x,y). We may make this look a lot more like the Prolog programs you are used to writing by making a few syntactic changes: firstly, we turn the implication around and write it as :- thus:

∀x, y, z (h(x,y) :- b₁(x,y) ∧ b₂(x) ... b_n(x,y,z))

next, we change the symbols to commas.

∀x, y, z (h(x,y) :- b₁(x,y), b₂(x), ..., b_n(x,y,z))

Lastly, we remove the universal quantification (it is assumed in Prolog), make the variables capital letters (Prolog requires this), and put a complete stop at the end:

h(X,Y) :- b1(X,Y), b2(X), ..., bn(X,Y,Z).

Note that we utilize the notation h/2 to indicate that predicate h has arity 2. Also, we call a set of Horn clauses  aslike a logic program. Representative knowledge with logic programs is less expressive than full first order logic, butstill it can express lots of types of information. In specific, disjunction can be gained by having different Horn clauses with the same head. So, this sentence in first -order logic:

∀x (a(x) ∨ b(x) -> c(x) ∧ d(x))

itcan be written as the following logic program:

c(x) :- a(x).

c(x) :- b(x).

d(x) :- a(x).

d(x) :- b(x).

We also permit ourselves to represent facts as atomic ground predicates. For instance, we can state that:

parent(georgedubya,georgesenior). colour(red). and so on.