The correct answer is: A. Resolution
Resolution is a rule of inference in propositional logic. It is used to prove the validity of a logical argument. The resolution rule states that if two clauses, $A$ and $\neg B$, are both true, then the clause $\neg A \lor B$ must also be true.
A propositional definite clause is a clause of the form $A \lor \neg B$, where $A$ and $B$ are propositional atoms. Propositional definite clauses can be used to represent knowledge about the world.
For example, the propositional definite clause “If it is raining, then the ground is wet” can be used to represent the knowledge that if it is raining, then the ground is wet.Resolution can be used to prove the validity of arguments involving propositional definite clauses. For example, the following argument is valid:
- If it is raining, then the ground is wet.
- It is raining.
- Therefore, the ground is wet.
This argument can be proved using resolution as follows:
- Resolve the first premise with the second premise to get the clause $\neg \neg R \lor W$.
- Simplify the clause $\neg \neg R \lor W$ to get the clause $R \lor W$.
- The clause $R \lor W$ is the conclusion of the argument.
Therefore, the argument is valid.
The other options are not closely related to propositional definite clauses.
- Inference is a general term for the process of drawing conclusions from premises. It is not a specific rule of inference like resolution.
- Conjunction is a logical connective that combines two propositions into a single proposition. It is not a rule of inference.
- First-order definite clauses are a type of clause that is used in first-order logic. They are not closely related to propositional definite clauses.