A compact reference for agents compressing natural language into symbolic notation.
| Symbol | Prose/Code Meaning | Example (Prose → Symbolic) |
|---|---|---|
≜ |
"X is defined as Y", "Let X be Y" | "Let x be 5" → x ≜ 5 |
≔ |
"Set X to Y", "X gets Y" | "Set x to 5" → x ≔ 5 |
∧ |
"X and Y" | "A and B" → A ∧ B |
∨ |
"X or Y" | "A or B" → A ∨ B |
¬ |
"not X", "X is false" | "not A" → ¬A |
→ |
"if X then Y", "X implies Y" | "If A then B" → A → B |
↔ |
"X if and only if Y" | "A if and only if B" → A ↔ B |
⇒ |
"X entails Y", "Y follows from X" | "A entails B" → A ⇒ B |
∀ |
"for all X", "every X" | "For all x in S, P(x)" → ∀x∈S:P(x) |
∃ |
"there exists X", "some X" | "There exists x such that P(x)" → ∃x:P(x) |
∃! |
"there is exactly one X" | "Exactly one x satisfies P(x)" → ∃!x:P(x) |
∈ |
"X is in Y", "X belongs to Y" | "x is in S" → x ∈ S |
⊆ |
"X is a subset of Y" | "A is a subset of B" → A ⊆ B |
∪ |
"X or Y", "X union Y" | "A or B" → A ∪ B |
∩ |
"X and Y", "X intersect Y" | "A and B" → A ∩ B |
→ |
"a function from X to Y" | "f maps Int to String" → f: Int → String |
λ |
"a function that takes X and returns Y" | "(x) => x + 1" → λx. x + 1 |
∘ |
"f after g", "compose f and g" | "f after g" → f ∘ g |
≡ |
"X is identical to Y" | "A is identical to B" → A ≡ B |
≢ |
"X is not identical to Y" | "A is not identical to B" → A ≢ B |
𝕍 |
"a validation with success/failure and quality" | "Validation of x with quality ◊⁺" → 𝕍 |
⊑ |
"X is a subtype of Y" (e.g., quality tiers) | "◊⁺⁺ is a subtype of ◊⁺" → ◊⁺⁺ ⊑ ◊⁺ |
Δ⊗λ |
"compatibility between X and Y" | "Can A and B bind?" → Δ⊗λ(A, B) |
⊘ |
"invalid or failed validation" | "Quality tier ⊘" → ⊘ |
∵ |
"Because" | A ∵ B = "A because B" |
∴ |
"Therefore" / "Hence" | B ∴ A = "Thus A holds from B" |
⊢ |
"Proves" (in proof theory) | Γ ⊢ A = "A is provable from Γ" |