A proof that p → q is true based on the fact that q is true, such proofs are known as ___________

The type of proof you are referring to is known as "modus ponens." Modus ponens is a form of argument where if we have a conditional statement $p \rightarrow q$ (if $p$ then $q$) and we know that $q$ is true, we can conclude that $p$ must also be true. This logical reasoning is fundamental in various fields, including mathematics and philosophy, and illustrates the process of deriving a conclusion based on premises.

In more formal terms, a proof using modus ponens involves the structure:

1. Premise 1: $p \rightarrow q$ (if $p$, then $q$)
2. Premise 2: $q$ is true
3. Conclusion: Therefore, $p$ is true.

This structure helps establish the validity of arguments and is a critical component in logical reasoning and deductive proofs.