5.6. Resolving More than Two Clauses

Try these first

1. 1.

   Define a clause in propositional logic.

   Hint

   Think of it as an OR statement in logic.

2. 2.

   What do we mean by the resolvent of two clauses?

   Hint

   It's the result after doing some 'cancellation'.

3. 3.

   What is a resolution in propositional logic?

   • A method for creating arguments
   • A way to cancel out literals
   • A type of proof
   • A definition of clauses

   Hint

   Think about what happens during the process.

4. 4.

   True or False: The resolution tree must contain every clause from the original set.

   • True
   • False

   Hint

   Consider the flexibility of choosing pairs for resolution.

5. 5.

   Demonstrate the validity of the argument A ∨ B, ¬A, C → D using proof by resolution refutation.

   Hint

   Track your negations closely for coherence.

6. 6.

   Given clauses: ¬P ∨ R, P ∨ Q, Q → ¬R. Create a resolution tree to show if Q can lead to a conclusion.

   Hint

   Order of clauses matters in resolution!