Reorganize ARS and logic notes.

notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json

@@ -220,7 +220,7 @@
     "encoding/index.md": "071cfa6a5152efeda127b684f420d438",
     "c/strings.md": "aba6e449906d05aee98e3e536eb43742",
     "logic/truth-tables.md": "a9fe98af6cabc0e4b087086075e09af5",
-    "logic/short-circuit.md": "a3fb33603a38a6d3b268556dcbdfa797",
+    "logic/short-circuit.md": "3c884bcc88007c5568ea7c047fbecb6f",
     "logic/boolean-algebra.md": "56d2e0be2853d49b5dface7fa2d785a9",
     "_journal/2024-02-13.md": "6242ed4fecabf95df6b45d892fee8eb0",
     "_journal/2024-02/2024-02-12.md": "618c0035a69b48227119379236a02f44",
@@ -558,7 +558,7 @@
     "_journal/2024-06-22.md": "8f566883a70458a20d9c750065ce4025",
     "programming/ars.md": "a62db41d53a0ec5973742a09e0b48f0a",
     "_journal/2024-06-23.md": "72e157bbf19d2d35843873ff9e900927",
-    "_journal/2024-06/2024-06-22.md": "81879cf81ad8f4c1b5622614df648252",
+    "_journal/2024-06/2024-06-22.md": "6b55e35f56e7f7c296c8df6812ba62d3",
     "_journal/2024-06/2024-06-21.md": "12e37e2c57abab09c781b32793fbbe1a",
     "startups/financing.md": "1978def9644211c989564faa3e4a56ea",
     "_journal/2024-06-24.md": "7fc0f4cd231ef7cd6aa2b556d1244cf4",
@@ -571,7 +571,7 @@
     "_journal/2024-06/2024-06-27.md": "237c73268a28f652985a5ef7ca7e188e",
     "_journal/2024-06/2024-06-26.md": "9c5d7e6395496736f2f268e9fdba117f",
     "_journal/2024-06-29.md": "9d43f4f33e03a48aa08e13bb5be365e0",
-    "_journal/2024-06/2024-06-28.md": "3f6a47a6324918b6c3af6b9549663372",
+    "_journal/2024-06/2024-06-28.md": "a72817d49ec7fccf96bac9a44fe055d7",
     "_journal/2024-06-30.md": "97d39a4905e296c6c3fd12e48c4283bd",
     "_journal/2024-06/2024-06-29.md": "9d43f4f33e03a48aa08e13bb5be365e0",
     "_journal/2024-07-02.md": "ca0cc5f69580f5f1896f880b0759e466",
@@ -613,7 +613,11 @@
     "_journal/2024-07/2024-07-16.md": "149222eab7a7f58993b8e4dc8a3fb884",
     "_journal/2024-07-18.md": "a9d26ce938228973f07178a15128a681",
     "_journal/2024-07/2024-07-17.md": "0c816cd6110bdd14d3eac4e5b82510cf",
-    "ontology/dialetheism.md": "4d14b681d6913bd775450c52c2417767"
+    "ontology/dialetheism.md": "175e92654e6bbab8c21afbdc040035a2",
+    "abstract-rewriting-systems/index.md": "b7486b7635cb0d8bafc2a2f095af90fb",
+    "abstract-rewriting-systems/normal-form.md": "2fff9a1d85bca0a2941a54b0084a0309",
+    "_journal/2024-07-19.md": "4b6a8d1fea576f6e88d765cbb85e1331",
+    "_journal/2024-07/2024-07-18.md": "237918b58424435959cbc949d01e7932"
   },
   "fields_dict": {
     "Basic": [

notes/_journal/2024-06/2024-06-22.md

@@ -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".

notes/_journal/2024-06/2024-06-28.md

@@ -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".

notes/_journal/2024-07-19.md

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

notes/abstract-rewriting-systems/normal-form.md

@@ -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

notes/logic/short-circuit.md

@@ -84,9 +84,14 @@ Reference: Gries, David. *The Science of Programming*. Texts and Monographs in
 <!--ID: 1707317708633-->
 END%%
 
-* Associative Laws
+## Laws
-	* $E1 \textbf{ cand } (E2 \textbf{ cand } E3) = (E1 \textbf{ cand } E2) \textbf{ cand } E3$
+
-	* $E1 \textbf{ cor } (E2 \textbf{ cor } E3) = (E1 \textbf{ cor } E2) \textbf{ cor } E3$
+### 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
+### Distributivity
-	* $E1 \textbf{ cand } (E2 \textbf{ cor } E3) = (E1 \textbf{ cand } E2) \textbf{ cor } (E1 \textbf{ cand } E3)$
+
-	* $E1 \textbf{ cor } (E2 \textbf{ cand } E3) = (E1 \textbf{ cor } E2) \textbf{ cand } (E1 \textbf{ cor } E3)$
+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
+### De Morgan's Laws
-	* $\neg (E1 \textbf{ cand } E2) = \neg E1 \textbf{ cor } \neg E2$
+
-	* $\neg (E1 \textbf{ cor } E2) = \neg E1 \textbf{ cand } \neg E2$
+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.

notes/ontology/dialetheism.md

@@ -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).

notes/programming/lean.md

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