in my semantics class we had two examples of invalid arguments:$$\begin{array}{rl} & p \lor q \\ & \neg p \\ \hline \therefore & \neg q \end{array}$$and$$\begin{array}{rl} & p \to q \\ \hline \therefore & \neg (r \to q) \end{array}.$$But there's a difference between both arguments, in the first you can't both satisfy the premises and the conclusion since $\{p \lor q, \neg p, \neg q\}$ is not simultaneously satisfiable and therefore you can't make the argument valid by adding more premises.
But in the second case you could simply add $r \land \neg q$ as an additional premise to make it valid.
Are there different names for invalid arguments that are logically inconsistent like in the first case and those where the premises are not strong enough to support the conclusion like in the second case?
Thanks in advance for your help.
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$\begingroup$Validity is not about satisfiability, save for it must me valid for all truth-value assignments to be assigned. To be valid, the conclusion must follow logically from the given premises. So yes, It the first case, the argument is a contradiction, and cannot be satisfied by any truth value assignment.
In the second case, if p and q true but r false, the premise is true, but the conclusion is false. Hence the implication is not valid.
We call an argument contingent., when its truth-value depends on the truth values of the literals.
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