When I look into a new field, sometimes I get confused by the whole new set of vocab terms I need to encounter. This post will serve to keep me straight with the terms involved in theorem proving.
| Modus Ponens | If $P$ implies $Q$ and $P$ is asserted to be true, then $Q$ must be true. |
| Complete | If every formula having the property can be derived using the system. (i.e The system does not miss a result) |
| Negation-Complete | Either $\phi$ or $\neg \phi$ can be proved in the system. |
| Decidable | An effective method exists for deriving the correct answer in a finite time. |
| Sound | Every formula that can be proved in the system is logically valid with respect to the semantics of the system. (i.e The system does not produce a wrong result) |
