論理 — Logic as Luxury
From the general to the specific. If all sapphires are blue, and this gem is a sapphire, then this gem is blue. Deductive reasoning chains universal truths into particular certainties — the crown jewel of logical inference.
∀x(Sapphire(x) → Blue(x)), Sapphire(a) ⊢ Blue(a)
From the specific to the general. Every emerald observed so far has been green. Therefore, probably, the next emerald will be green. Inductive reasoning builds probability from patterns — fashioning likely truths from accumulated evidence.
P(1) ∧ (P(k) → P(k+1)) ⊢ ∀n P(n)
Inference to the best explanation. The ground is wet; rain is the best explanation. Abductive reasoning selects the hypothesis that most elegantly accounts for the evidence — the art of logical intuition, polished to a brilliant shine.
O, (H → O) ⊢ H (best explanation)
The language of truth values. Propositions connected by AND, OR, NOT — the fundamental operators that compose all logical statements. Every complex argument reduces to these atomic connectives, faceted and flawless.
(P ∧ Q) → R ≡ P → (Q → R)
A collection of logical gems