5.8. Key Properties of Resolution

Try these first

1. 1.

   Define the resolution rule in your own words.

   Hint

   Think about how we can combine two statements.

2. 2.

   What does the empty clause represent?

   Hint

   Consider what contradiction means in logic.

3. 3.

   What does the resolution rule allow us to do?

   • Derive new clauses
   • Create new propositions
   • Extend existing clauses

   Hint

   Focus on the main function of the resolution rule.

4. 4.

   If a set of clauses leads to the empty clause, what does it signify?

   • True
   • False

   Hint

   Think about what an empty result implies.

5. 5.

   Given clauses C1: (P ∨ Q) and C2: (¬P ∨ R), resolve these and provide the correct resolvent. Then explain why the notion of truth matters in determining the validity of the argument.

   Hint

   Look closely at the common literals before resolving.

6. 6.

   Construct a set of clauses that would lead to the empty clause. Then analyze what this implies regarding the arguments established.

   Hint

   Think about how contradictions function in logic.