Effects of restricting generality
| Al heard everything | ⊨ | Al heard every dog | ⊨ | Al heard every large dog |
| ∀x Hax | ⊨ | (∀x: Dx) Hax | ⊨ | (∀x: Dx ∧ Lx) Hax |
| ∀x Hax | ⊨ | ∀x (Dx → Hax) | ⊨ | ∀x ((Dx ∧ Lx) → Hax) |
| more general (less specific) ⟵ | ⟶ more specific (less general) | |||
| Al heard something | ⫤ | Al heard a dog | ⫤ | Al heard a large dog |
| ∃x Hax | ⫤ | (∃x: Dx) Hax | ⫤ | (∃x: Dx ∧ Lx) Hax |
| ∃x Hax | ⫤ | ∃x (Dx ∧ Hax) | ⫤ | ∃x ((Dx ∧ Lx) ∧ Hax) |