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notebook/notes/formal-system/proof-system/index.md

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Reorganize types of logic and formal systems.
2024-07-21 12:16:08 +00:00
---
title: Proof Systems
TARGET DECK: Obsidian::STEM
FILE TAGS: formal-system
tags:
- formal-system
- logic
---
## Overview
A deductive system found in certain formal systems. Proof systems are syntactic in nature. Proofs are sequences of WFFs, each of which are entailed from previous ones in the sequence. A theorem is then the last WFF in any valid sequence of WFFs.
%%ANKI
Basic
*Why* do we say formal systems using proof systems are purely syntactic?
Back: No meaning is attached to the WFFs of the formal language.
Reference: “Formal System,” in _Wikipedia_, May 10, 2024, [https://en.wikipedia.org/w/index.php?title=Formal_system](https://en.wikipedia.org/w/index.php?title=Formal_system&oldid=1223254138).
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END%%
%%ANKI
Cloze
Proof systems are {syntactic}, not {semantic}.
Reference: “Formal System,” in _Wikipedia_, May 10, 2024, [https://en.wikipedia.org/w/index.php?title=Formal_system](https://en.wikipedia.org/w/index.php?title=Formal_system&oldid=1223254138).
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END%%
%%ANKI
Basic
How is it purely syntactic proof systems can produce theorems?
Back: Inference rules define how to produce theorems from sequences of WFFs.
Reference: “Formal System,” in _Wikipedia_, May 10, 2024, [https://en.wikipedia.org/w/index.php?title=Formal_system](https://en.wikipedia.org/w/index.php?title=Formal_system&oldid=1223254138).
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END%%
%%ANKI
Basic
What kind of deductive system is natural deduction usually categorized as?
Back: A proof system.
Reference: “Formal System,” in _Wikipedia_, May 10, 2024, [https://en.wikipedia.org/w/index.php?title=Formal_system](https://en.wikipedia.org/w/index.php?title=Formal_system&oldid=1223254138).
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END%%
%%ANKI
Basic
Formal systems and hashing.
2024-07-27 13:02:30 +00:00
In a formal system, a proof is a sequence of what?
Back: Well-formed formulas.
Reorganize types of logic and formal systems.
2024-07-21 12:16:08 +00:00
Reference: “Formal System,” in _Wikipedia_, May 10, 2024, [https://en.wikipedia.org/w/index.php?title=Formal_system](https://en.wikipedia.org/w/index.php?title=Formal_system&oldid=1223254138).
Formal systems and hashing.
2024-07-27 13:02:30 +00:00
<!--ID: 1721561534235-->
Reorganize types of logic and formal systems.
2024-07-21 12:16:08 +00:00
END%%
%%ANKI
Basic
Formal systems and hashing.
2024-07-27 13:02:30 +00:00
In a proof system, a proof is used to produce what?
Back: A theorem.
Reorganize types of logic and formal systems.
2024-07-21 12:16:08 +00:00
Reference: “Formal System,” in _Wikipedia_, May 10, 2024, [https://en.wikipedia.org/w/index.php?title=Formal_system](https://en.wikipedia.org/w/index.php?title=Formal_system&oldid=1223254138).
Formal systems and hashing.
2024-07-27 13:02:30 +00:00
<!--ID: 1721561534230-->
Reorganize types of logic and formal systems.
2024-07-21 12:16:08 +00:00
END%%
%%ANKI
Basic
Formal systems and hashing.
2024-07-27 13:02:30 +00:00
In a proof system, what mechanism is used to produce WFFs from one another?
Back: Inference rules.
Reorganize types of logic and formal systems.
2024-07-21 12:16:08 +00:00
Reference: “Formal System,” in _Wikipedia_, May 10, 2024, [https://en.wikipedia.org/w/index.php?title=Formal_system](https://en.wikipedia.org/w/index.php?title=Formal_system&oldid=1223254138).
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END%%
## Bibliography
* “Formal System,” in _Wikipedia_, May 10, 2024, [https://en.wikipedia.org/w/index.php?title=Formal_system](https://en.wikipedia.org/w/index.php?title=Formal_system&oldid=1223254138).