5.9. Proof by Resolution Refutation

Try these first

1. 1.

   What does the resolution rule allow us to do?

   Hint

   Think about how conclusions can be derived from premises.

2. 2.

   Define what a resolvent is.

   Hint

   Consider the new information created from resolving clauses.

3. 3.

   What does the resolution rule allow?

   • It combines clauses
   • It cancels common literals
   • It adds new clauses

   Hint

   Focus on the key action that the resolution rule performs.

4. 4.

   Does an empty clause indicate a valid argument?

   • True
   • False

   Hint

   Consider what it means if you reach no clauses.

5. 5.

   Given the premises: 'If A, then B' (A → B), 'If B, then C' (B → C) and 'A', show through resolution refutation that the conclusion 'C' is valid.

   Hint

   Focus on deriving new clauses step-by-step and watch for the empty clause.

6. 6.

   Create a proof by resolution refutation for the premises: 'X ∨ Y' and '¬X', concluding 'Y'.

   Hint

   Combine the premises carefully and track resolutions leading to your conclusion.