5.10. Example of Argument Validation

Try these first

1. 1.

   Define what a clause is in propositional logic.

   Hint

   Think about how literals combine to form more complex expressions.

2. 2.

   What is the resolution rule used for?

   Hint

   Consider how it helps in logic-based systems.

3. 3.

   What does the resolution rule allow you to do?

   • Form new clauses
   • Reject old clauses
   • Add literals

   Hint

   Consider how clauses interact with each other.

4. 4.

   True or False: The empty clause indicates that a set of clauses is satisfiable.

   • True
   • False

   Hint

   Think about what inconsistency implies.

5. 5.

   Given premises (A → B), (C → D), (¬A), (C), and the conclusion (B), show through resolution refutation that it is valid.

   Hint

   Follow the paths of resolution through the premises carefully.

6. 6.

   Construct a resolution tree for the clauses: (A ∨ B), (¬A ∨ C), (¬B ∨ D), (¬C) and determine if the empty clause is present.

   Hint

   Identify the steps leading towards the contradictions.