13 This exercise looks into the relationship between clauses and implication sentences.

a. Show that the clause (￢P1 ∨ ・ ・ ・ ∨ ￢Pm ∨ Q) is logically equivalent to the implication sentence (P1 ∧ ・ ・ ・ ∧ Pm) ⇒ Q.

b. Show that every clause (regardless of the number of positive literals) can be written in the form (P1 ∧ ・ ・ ・ ∧ Pm) ⇒ (Q1 ∨ ・ ・ ・ ∨ Qn), where the Ps and Qs are proposition symbols. A knowledge base consisting of such sentences is in implicative normal form or Kowalski IMPLICATIVE form (Kowalski, 1979).

NORMAL FORM

c. Write down the full resolution rule for sentences in implicative normal form.