Given the propositions:
(I) (P&Q) -> R
(II) R -> S
(III) Q & ~S
(IV) ~P
- Write the truth table for statement (I).
- Use the rules of logic in Figure 6.13 in the book (p. 172) to show that (IV) follows from (I), (II) and (III).
You have the following predicates: HeadOf(h,x), Horse(x), Animal(x) Write the logical formula corresponding to the statement: "The head of a horse is the head of an animal" and "Horses are animals".
- Convert the statement into CNF.
- Prove that "The head of a horse is the head of an animal" follows from "Horses are animals" using resolution and the statements you have in part A.
Assume the following facts:
Steve only likes easy courses.
Science courses are hard.
All the courses in the basketweaving department are easy.
BK101 is a basketweaving course.
Susan likes the same courses as Steve.
(a) Translate these sentences into predicate logic. (You will need to add commonsense axioms to make the proof possible, Also, there are several ways to represent "only likes"; find one that will work in the proof.)
(b) Convert the formulas into CNF.
(c) Prove that Steve likes BK101 by resolution (don't forget to negate the conclusion).
Consider the following joint probability distribution: