5.3. Understanding the Resolution Rule

Try these first

1. 1.

   Define the resolution rule in your own words.

   Hint

   Think about how combining clauses might simplify expressions.

2. 2.

   What does a 'valid argument form' imply?

   Hint

   Focus on the relationship between premises and conclusion.

3. 3.

   What is the resolution rule?

   • A way to write logical expressions
   • A mechanism to derive new clauses from existing ones
   • A method of simplifying single propositions

   Hint

   Focus on clause interactions.

4. 4.

   True or False: A valid argument form always leads to a true conclusion.

   • True
   • False

   Hint

   Consider what 'valid' means in this context.

5. 5.

   Given the clauses A ∨ B, ¬A ∨ C, and ¬B ∨ ¬C, prove whether C can be concluded using the resolution rule.

   Hint

   Focus on systematically eliminating possibilities.

6. 6.

   Construct a resolution tree for the clauses: (P ∨ Q), (¬Q), and (R ∨ ¬P). How do these relate to proving the validity of a conclusion?

   Hint

   Ensure to apply the resolution rule step by step across clauses.