≔ Logical Symbology ⊧
“The true function of logic… as applied to matters of experience… is analytic rather than constructive; taken a priori, it shows the possibility of hitherto unsuspected alternatives more often than the impossibility of alternatives which seemed prima facie possible. Thus, while it liberates imagination as to what the world may be, it refuses to legislate as to what the world is…”
－ Bertrand Russell
| SYMBOL | Logical CONCEPT |
should be “read as…” |
CATEGORY | Explanation | Examples | Unicode hexadecimal |
HTML decimal |
HTML entity |
LaTeX symbol |
|---|---|---|---|---|---|---|---|---|---|
| ⇒ → ⊃ |
material implication | “implies” if … then |
propositional logic, Heyting algebra |
𝚨 ⇒ 𝚩 is false when 𝚨 is true and 𝚩 is false but true otherwise | 𝚾＝2 ⇒ 𝚾²＝4 is true, but 𝚾²＝4 ⇒ 𝚾＝2 is generally false (since 𝚾 could be -2) |
U+21D2 U+2192 U+2283 |
&﹟8658; &﹟8594; &﹟8835; |
﹠rArr; ﹠rarr; ﹠sup; |
⇒\Rightarrow ⇒\implies →\to ⊃\supset |
| ⇔ ≡ ↔ |
material equivalence | if＆only if iff same meaning |
propositional logic | 𝚨 ⇔ 𝚩 is true only if both 𝚨＆𝚩 are false, or both 𝚨＆𝚩 are true | 𝚾＋5＝𝚼＋2 ⇔ 𝚾＋3＝𝚼 | U+21D4 U+2261 U+2194 |
&﹟8660; &﹟8801; &﹟8596; |
﹠hArr; ﹠equiv; ﹠LeftRightArrow; |
⇔\Leftrightarrow ≡\equiv ↔\iff |
| ¬ ∼ ! |
negation | “not” | propositional logic | ¬𝚨 is true if＆only if 𝚨 is false | ¬(¬𝚨) ⇔ 𝚨 𝚾≠𝚼 ⇔ ¬(𝚾＝𝚼) |
U+00AC U+02DC U+0021 |
&﹟172; &﹟732; &﹟33; |
﹠not; ﹠tilde; ﹠excl; |
¬\not or \neg ~\sim |