5.7. Example of Resolution Tree

Try these first

1. 1.

   What is a resolvent?

   Hint

   Think of the definition you learned earlier.

2. 2.

   List the conditions needed to apply the resolution rule.

   Hint

   What does 'positive' and 'negative' forms refer to?

3. 3.

   What do we call the new clause formed by applying the resolution rule?

   • Compound Clause
   • Resolvent
   • Disjunction

   Hint

   Remember the terminology used!

4. 4.

   True or False: The existence of an empty clause in your resolution tree indicates a valid argument.

   • True
   • False

   Hint

   What does 'empty' represent in logic?

5. 5.

   Using the initial premises {P → Q, ¬P, R → Q}, demonstrate whether R can be logically concluded using resolution. Provide a resolution tree.

   Hint

   Follow the resolution sequence methodically and observe connections.

6. 6.

   Explain how the properties of resolution and unsatisfiability could apply in real-world scenarios, like conflict resolution.

   Hint

   Consider how arguments in discussions can mirror logical propositions.