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20 lines
1.3 KiB
Markdown
20 lines
1.3 KiB
Markdown
---
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title: "Theorem Proving Definitions"
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date: 2019-12-29T11:21:07-05:00
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draft: false
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images: []
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math: true
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---
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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.
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| Word | Definition |
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| ----------------- | ------------------------------------------------------------ |
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| Modus Ponens | If $P$ implies $Q$ and $P$ is asserted to be true, then $Q$ must be true. |
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| Complete | If every formula having the property can be derived using the system. (i.e The system does not miss a result) |
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| Negation-Complete | Either $\phi$ or $\neg \phi$ can be proved in the system. |
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| Consistent | For any provable formula $\phi$, the negation ($\neg \phi$) cannot be provable. (Cannot derive a contradiction) |
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| Decidable | An effective method exists for deriving the correct answer in a finite time. |
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| 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) |
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Hopefully, I'll come back and add more terms as I get confused.
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