1. Show that the clause $(\lnot P_1 \lor \cdots \lor \lnot P_m \lor Q)$ is logically equivalent to the implication sentence $(P_1 \land \cdots \land P_m) {\;{\Rightarrow}\;}Q$.

2. Show that every clause (regardless of the number of positive literals) can be written in the form $(P_1 \land \cdots \land P_m) {\;{\Rightarrow}\;}(Q_1 \lor \cdots \lor Q_n)$, where the $P$s and $Q$s are proposition symbols. A knowledge base consisting of such sentences is in implicative normal form or

**Kowalski form**Kowalski:1979.

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

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

1. Show that the clause $(\lnot P_1 \lor \cdots \lor \lnot P_m \lor Q)$
is logically equivalent to the implication sentence
$(P_1 \land \cdots \land P_m) {\;{\Rightarrow}\;}Q$.

2. Show that every clause (regardless of the number of
positive literals) can be written in the form
$(P_1 \land \cdots \land P_m) {\;{\Rightarrow}\;}(Q_1 \lor \cdots \lor Q_n)$,
where the $P$s and $Q$s are proposition symbols. A knowledge base
consisting of such sentences is in implicative normal form or **Kowalski
form** Kowalski:1979.

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