mirror of
https://github.com/Brandon-Rozek/website.git
synced 2024-11-28 18:13:35 -05:00
21 lines
1.3 KiB
Markdown
21 lines
1.3 KiB
Markdown
---
|
|
title: "Theorem Proving Definitions"
|
|
date: 2019-12-29T11:21:07-05:00
|
|
draft: false
|
|
images: []
|
|
math: true
|
|
medium_enabled: 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) |
|
|
| 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.
|