
 II.7 Satisﬁable and valid
Satisﬁable and valid [Slide 40]
 A propositional formula f is satisﬁable if and only if there exists
a state σ_{0} such that M⟦f⟧(σ_{0}) = tt.
 A propositional formula f is valid if and only if for all states σ_{0},
M⟦f⟧(σ_{0}) = tt.
Example 6.
 true is a valid formula.
 Proposition P ∧ Q is satisﬁable because M⟦P ∧ Q⟧(σ_{0}) = tt
where state σ_{0} is such that σ_{0}(P) = tt and σ_{0}(Q) = tt.
  