5.5. Proof of Validity of Resolution

Try these first

1. 1.

   Define the resolution rule in your own words.

   Hint

   Think about combining or cancelling out conflicting parts.

2. 2.

   What do we call the resulting clause after applying the resolution rule?

   Hint

   Remember this term is key when discussing outcomes of resolutions.

3. 3.

   What is the key benefit of the resolution rule?

   • It combines equations
   • It eliminates literals in contradictions
   • It establishes a valid conclusion from premises

   Hint

   Think about how the resolution impacts the truth of statements.

4. 4.

   Resolution is crucial in programming languages like PROLOG, True or False?

   • True
   • False

   Hint

   Consider where resolution is applied in logical reasoning.

5. 5.

   Prove that the argument composed of the premises 'A ∨ B' and '¬A ⟹ C' entails 'C' using resolution methods.

   Hint

   Consider all forms of transformation for complete coverage.

6. 6.

   Construct a resolution proof that shows if 'X ⟹ Y' and '¬Y' are true, what can be concluded?

   Hint

   Restructure to visualize clear paths between premises and conclusions.