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.

Word | Definition |
---|---|

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) |

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) |

Hopefully, I’ll come back and add more terms as I get confused.