AxAy Smoker(x) & Friends(y,x) => Smoker(y)
AxAy Friends(x,y) => Friends(y,x)
Assume we perform forward-chaining starting from this KB (with all of the rules
and facts already loaded) and show the specific conclusions added in their
exact order as rules are matched and fired. Assume rules and facts are always
matched in the exact order given above and that newly inferred facts are
immediately added to the end of the list.
AxAyAz Parent(x,y) & Parent(x,z) & y!=z => Sibling(y,z)
AxAyAz Sibling(v,w) & Parent(w,u) & Male(u) => Nephew(u,v)
Parent(Bob,Mary), Male(Bob), Female(Mary), Parent(Bob,Fred), Male(Fred), Parent(Mary,Tom), Male(Tom), Parent(Mary,Ann), Female(Ann)
Assume backward-chaining rule-based inference
is used to try to answer the query: Nephew(s,Fred). Show the trace of the
search conducted and the subgoals generated like that shown on page 16 of the
lecture notes on "Inference in First Order Logic," giving all answers
retrieved. Assume that the infix predicate "!=" (not equal) is evaluated
procedurally (i.e. handled externally by a program that directly computes the
correct truth value).
Ex (Barber(x) & In(x,Town) & Ay [(Man(y) & In(y,Town) & ~Shave(y,y)) <=>
Ax (Barber(z) => Man(z))
Show this statement is contradictory using resolution. See the previous year's
Homework 2 solution for the format to present the proof.