Reorganize ARS and logic notes.

c-declarations
Joshua Potter 2024-07-19 03:35:22 -06:00
parent 9acf6ca60e
commit 0c34a108cb
10 changed files with 69 additions and 30 deletions

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@ -220,7 +220,7 @@
"encoding/index.md": "071cfa6a5152efeda127b684f420d438",
"c/strings.md": "aba6e449906d05aee98e3e536eb43742",
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@ -558,7 +558,7 @@
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},
"fields_dict": {
"Basic": [

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@ -9,6 +9,6 @@ title: "2024-06-22"
- [ ] Korean (Read 1 Story)
* Notes on [[beta-reduction#Normal Form|β-normal forms]].
* Very basic notes on [[ars|abstract rewriting systems]].
* Very basic notes on [[abstract-rewriting-systems/index|abstract rewriting systems]].
* Additional set theory definitions ([[functions#Restrictions|restrictions]] and [[functions#Images|images]]).
* Read chapters 2 ("Methodology") and 3 ("Properties") of "An Introduction to Ontology".

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@ -8,5 +8,5 @@ title: "2024-06-28"
- [ ] Sheet Music (10 min.)
- [ ] Korean (Read 1 Story)
* Notes on the [[beta-reduction#Church-Rosser Theorem|Church-Rosser theorem]] and [[ars#Confluence|confluence]] in general.
* Notes on the [[beta-reduction#Church-Rosser Theorem|Church-Rosser theorem]] and [[abstract-rewriting-systems/index#Confluence|confluence]] in general.
* Read chapter 7 "Time" and chapter 8 "Mereology" of "An Introduction to Ontology".

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@ -0,0 +1,9 @@
---
title: "2024-07-19"
---
- [ ] Anki Flashcards
- [x] KoL
- [x] OGS
- [ ] Sheet Music (10 min.)
- [ ] Korean (Read 1 Story)

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@ -91,4 +91,4 @@ END%%
* “Canonical Form,” in _Wikipedia_, January 7, 2024, [https://en.wikipedia.org/w/index.php?title=Canonical_form](https://en.wikipedia.org/w/index.php?title=Canonical_form&oldid=1194093963).
* “Confluence (Abstract Rewriting),” in _Wikipedia_, May 22, 2024, [https://en.wikipedia.org/w/index.php?title=Confluence](https://en.wikipedia.org/w/index.php?title=Confluence_(abstract_rewriting)&oldid=1225041322).
* Normal Form,” in _Wikipedia_, April 27, 2024, [https://en.wikipedia.org/w/index.php?title=Normal_form](https://en.wikipedia.org/w/index.php?title=Normal_form_(abstract_rewriting)&oldid=1221094193).
* Normal Form,” in _Wikipedia_, April 27, 2024, [https://en.wikipedia.org/w/index.php?title=Normal_form](https://en.wikipedia.org/w/index.php?title=Normal_form_(abstract_rewriting)&oldid=1221094193).

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@ -1,9 +1,9 @@
---
title: Normal Form
TARGET DECK: Obsidian::STEM
FILE TAGS: logic
FILE TAGS: ars::normal
tags:
- logic
- ars
---
## Overview
@ -12,7 +12,8 @@ An object is said to be in **normal form** if it cannot be reduced any further.
* [[truth-tables|Conjunctive Normal Form]]
* [[truth-tables|Disjunctive Normal Form]]
* [[quantification#Identifiers|Prenex Normal Form]]
* [[pred-logic#Identifiers|Prenex Normal Form]]
* [[beta-reduction#Normal Form|β-normal forms]]
%%ANKI
Basic

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@ -84,9 +84,14 @@ Reference: Gries, David. *The Science of Programming*. Texts and Monographs in
<!--ID: 1707317708633-->
END%%
* Associative Laws
* $E1 \textbf{ cand } (E2 \textbf{ cand } E3) = (E1 \textbf{ cand } E2) \textbf{ cand } E3$
* $E1 \textbf{ cor } (E2 \textbf{ cor } E3) = (E1 \textbf{ cor } E2) \textbf{ cor } E3$
## Laws
### Associativity
Given propositions $E1$, $E2$, and $E3$,
* $E1 \textbf{ cand } (E2 \textbf{ cand } E3) = (E1 \textbf{ cand } E2) \textbf{ cand } E3$
* $E1 \textbf{ cor } (E2 \textbf{ cor } E3) = (E1 \textbf{ cor } E2) \textbf{ cor } E3$
%%ANKI
Basic
@ -104,9 +109,12 @@ Reference: Gries, David. *The Science of Programming*. Texts and Monographs in
<!--ID: 1707317708636-->
END%%
* Distributive Laws
* $E1 \textbf{ cand } (E2 \textbf{ cor } E3) = (E1 \textbf{ cand } E2) \textbf{ cor } (E1 \textbf{ cand } E3)$
* $E1 \textbf{ cor } (E2 \textbf{ cand } E3) = (E1 \textbf{ cor } E2) \textbf{ cand } (E1 \textbf{ cor } E3)$
### Distributivity
Given propositions $E1$, $E2$, and $E3$,
* $E1 \textbf{ cand } (E2 \textbf{ cor } E3) = (E1 \textbf{ cand } E2) \textbf{ cor } (E1 \textbf{ cand } E3)$
* $E1 \textbf{ cor } (E2 \textbf{ cand } E3) = (E1 \textbf{ cor } E2) \textbf{ cand } (E1 \textbf{ cor } E3)$
%%ANKI
Basic
@ -116,9 +124,12 @@ Reference: Gries, David. *The Science of Programming*. Texts and Monographs in
<!--ID: 1707317708638-->
END%%
* De Morgan's Laws
* $\neg (E1 \textbf{ cand } E2) = \neg E1 \textbf{ cor } \neg E2$
* $\neg (E1 \textbf{ cor } E2) = \neg E1 \textbf{ cand } \neg E2$
### De Morgan's Laws
Given propositions $E1$ and $E2$,
* $\neg (E1 \textbf{ cand } E2) = \neg E1 \textbf{ cor } \neg E2$
* $\neg (E1 \textbf{ cor } E2) = \neg E1 \textbf{ cand } \neg E2$
%%ANKI
Basic
@ -136,8 +147,6 @@ Reference: Gries, David. *The Science of Programming*. Texts and Monographs in
<!--ID: 1707317708642-->
END%%
Gries lists other "Laws" but they don't seem as important to note here. What's worth noting is that the other [[equiv-trans#Equivalence Schemas|equivalence schemas]] still apply if we can limit operands to just $T$ and $F$.
## Bibliography
* Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.

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@ -25,7 +25,32 @@ Reference: Graham Priest, Francesco Berto, and Zach Weber, “Dialetheism,” in
<!--ID: 1721354092775-->
END%%
%%ANKI
Basic
What is used to refer to the so-called "standard logic" of mathematics?
Back: Classical logic.
Reference: Graham Priest, Koji Tanaka, and Zach Weber, “Paraconsistent Logic,” in _The Stanford Encyclopedia of Philosophy_, ed. Edward N. Zalta, Spring 2022 (Metaphysics Research Lab, Stanford University, 2022), [https://plato.stanford.edu/archives/spr2022/entries/logic-paraconsistent/](https://plato.stanford.edu/archives/spr2022/entries/logic-paraconsistent/).
<!--ID: 1721380604985-->
END%%
%%ANKI
Basic
What classical principle is excluded in paraconsistent logics?
Back: The principle of explosion.
Reference: Graham Priest, Koji Tanaka, and Zach Weber, “Paraconsistent Logic,” in _The Stanford Encyclopedia of Philosophy_, ed. Edward N. Zalta, Spring 2022 (Metaphysics Research Lab, Stanford University, 2022), [https://plato.stanford.edu/archives/spr2022/entries/logic-paraconsistent/](https://plato.stanford.edu/archives/spr2022/entries/logic-paraconsistent/).
<!--ID: 1721380604997-->
END%%
%%ANKI
Basic
Dialetheism is intimately connected to what type of logical systems?
Back: Paraconsistent logical systems.
Reference: Graham Priest, Koji Tanaka, and Zach Weber, “Paraconsistent Logic,” in _The Stanford Encyclopedia of Philosophy_, ed. Edward N. Zalta, Spring 2022 (Metaphysics Research Lab, Stanford University, 2022), [https://plato.stanford.edu/archives/spr2022/entries/logic-paraconsistent/](https://plato.stanford.edu/archives/spr2022/entries/logic-paraconsistent/).
<!--ID: 1721380605000-->
END%%
## Bibliography
* Graham Priest, Francesco Berto, and Zach Weber, “Dialetheism,” in _The Stanford Encyclopedia of Philosophy_, ed. Edward N. Zalta and Uri Nodelman, Summer 2024 (Metaphysics Research Lab, Stanford University, 2024), [https://plato.stanford.edu/archives/sum2024/entries/dialetheism/](https://plato.stanford.edu/archives/sum2024/entries/dialetheism/).
* Graham Priest, Koji Tanaka, and Zach Weber, “Paraconsistent Logic,” in _The Stanford Encyclopedia of Philosophy_, ed. Edward N. Zalta, Spring 2022 (Metaphysics Research Lab, Stanford University, 2022), [https://plato.stanford.edu/archives/spr2022/entries/logic-paraconsistent/](https://plato.stanford.edu/archives/spr2022/entries/logic-paraconsistent/).
* Nikk Effingham, _An Introduction to Ontology_ (Cambridge: Polity Press, 2013).

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@ -1,9 +0,0 @@
---
title: Lean
TARGET DECK: Obsidian::STEM
FILE TAGS: lean
tags:
- lean
---
## Overview