# Theorem Proving Definitions

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*Warning*: This post has not been modified for over 2 years. For technical posts, make sure that it is still relevant.

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) |

Negation-Complete | Either $\phi$ or $\neg \phi$ can be proved in the system. |

Consistent | For any provable formula $\phi$, the negation ($\neg \phi$) cannot be provable. (Cannot derive a contradiction) |

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.