An argument is valid if and only if the truth of premises entails the truth of conclusion. 1
Relationship with NTP
Another concept, necessarily truth-preserving (NTP), closely resembles validity, but validity demands more. An argument is valid solely due to its structure. 1 While this distinction is non-exist in formal logic language, it arise in natural languages. Consider the following argument:
The above argument is NTP only because we have the knowledge that water is
Validity Test
There are various way to test the validity of an argument such as:
- truth table - only works in propositional logic and can become unwieldy with numerous basic propositions due to combinatorial explosion
- truth tree (semantic tableaux) - can often be more efficient than a truth table and also works in predicate logic
- model checking - systematically enumerates all possible states of a system to verify properties. Only works with finite domains
- direct proofs
- natural deduction
- SAT solvers
Also, if we can get a counterexample where premises are true but the conclusion is false, we can immediately prove that an argument is invalid.
Relationship with Soundness
Note that validity doesn’t mean truth. If a promise is false, then even a valid argument can’t guarantee conclusion. On the other hand, even when the conclusion is true, we can’t guarantee that the promise is true. If a valid argument is also true, we say that it is sound.