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

a. Show that the clause (7P1 V . . . V TP, V Q) is logically equivalent to the implication sentence (PI A . A P,) + Q.

b. Show that every clause (regardless of the number of positive literals) can be written in the form (PI A . . . A P,) + (Q1 V . - . V Q,), where the Ps and Qs are proposition symbols. A knowledge base consisting of such sentences is in implicative normal IMPLICATIVE NORMAL FORM form or Kowalski form.

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