---
title: "Theorem Proving Definitions"
date: 2019-12-29T11:21:07-05:00
draft: false
images: []
math: true
---

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.