IV.6 Satisfiable and valid
Satisfiable and valid [Slide 126]
- A first order formula f is satisfiable if and only if there exists a state
σ0 such that M⟦f⟧(σ0) = tt.
- A first order formula f is valid if and only if for all states σ0, M⟦f⟧(σ0) =
tt
.
Example 37.
- 0 < 1 is a valid formula.
- Formula A < B is satisfiable because M⟦A < B⟧(σ0) = tt where state
σ0 is such that σ0(A) = 0 and σ0(B) = 1.