II.7 Satisfiable and valid
Satisfiable and valid [Slide 40]
- A propositional formula f is satisfiable if and only if there exists a state
σ0 such that M⟦f⟧(σ0) = tt.
- A propositional formula f is valid if and only if for all states σ0,
M⟦
f
⟧
(σ0) = tt.
Example 6.
- true is a valid formula.
- Proposition P ∧ Q is satisfiable because M⟦P ∧ Q⟧(σ0) = tt where state
σ0 is such that σ0(P) = tt and σ0(Q) = tt.