Example: Ex -interpretations

• If a universe U is defined using Ex , then an interpretation I of U is an Ex -Interpretation if and only if:

• • A ⊑ B if an only if I(A) ⊂ I(B) (for all A-s and B-s)
  • A ≣ B if an only if I(A) = I(B) (for all A-s and B-s)
  • a:B if an only if I(a) ∊ I(B)

• The interpretation formalizes the intuition of individuals belonging to a classes

• Interpretations may be different! For example: I1(A) = I1(B) and I2(A) ≠ I2(B)

• • both are valid Ex-Interpretations, though they map to different sets