
 IV.6 Satisﬁable and valid
Satisﬁable and valid [Slide 124]
 A ﬁrst order formula f is satisﬁable if and only if there exists a
state σ_{0} such that M⟦f⟧(σ_{0}) = tt.
 A ﬁrst order formula f is valid if and only if for all states σ_{0},
M⟦f⟧(σ_{0}) = tt.
Example 37.
 0 < 1 is a valid formula.
 Formula A < B is satisﬁable because M⟦A < B⟧(σ_{0}) = tt where
state σ_{0} is such that σ_{0}(A) = 0 and σ_{0}(B) = 1.
  