Question

These questions concern concern issues with substitution and skolemization.

a. given the premise ∀ x ∃ y p(x,y), it is not valid to conclude that ∃ q p(q,q). give an example of a predicate p where the first is true but the second is false.

b. suppose that an inference engine is incorrectly written with the occurs check omitted, so that it allows a literal like p(x,f(x)) to be unified with p(q,q). (as mentioned, most standard implementations of prolog actually do allow this.) show that such an inference engine will allow the conclusion ∃ y p(q,q) to be inferred from the premise ∀ x ∃ y p(x,y)

Answer 1

what is skolemization