Question

Are the following arguments valid or not? Use resolution or resolution refutation to find out. Proceed in four steps:

• Extract the propositions from the argument and name them with single letters.

• Describe the hypotheses and the conclusion in propositional calculus.

• Convert these expressionsinto conjunctive normal form (CNF)suitable for resolution or resolution refutation (whichever method you decide to use).

• List the steps of the resolution (refutation) and state the result, that is, whether the argument is valid or not.

Statement:  If the AI lecture is boring, I will fall asleep. If I fall asleep, I will hit my head on the desk. If I hit my head on the desk, I will go to the hospital. I did not go to the hospital. Therefore, the AI lecture is not boring.  

Answer 1

Conjuctive Normal Form (CNF):

A formula is said to be in CNF if all the clauses are in conjunction and the symbols within that clauses are in disjunction.

Let p = AI lecture is boring

q = I will fall asleep

r = I will hit my head on the desk

s = I will go to hospital

So the first expression will be as follows

(p -> q)

(q -> r)

(r -> s)

(~p -> ~s)

So the formula will be,

(p -> q) ^ (q -> r) ^ (r -> s) ^ (~p -> ~s)

As we know p -> q = ~p v q

Applying to the above formula,

(~p v q) ^ (~q v r) ^ (~r v s) ^ (p v ~s)

So the above formula is in CNF as all clauses are in conjuction and literals within that clause are in disjunction