Interpretation over a singleton Let I be , and σ ∈ ΣI. 1. I(A)(σ) = I(∀xA)(σ). 2. I(t)(σ) = a. 3. I(Sx1,···,xn t1,···,tn A)(σ) = I(A)(σ). 4. I0(P), σ(P) ∈ {I(n), Ψ(n)} for every n-ary predicate constant (variable), where
Discrete-Time Systems A discrete-time system processes a given input sequence x[] to generates an output sequencey[n] with more desirable properties In most applications, the discrete-time system is a single-input, single-output system:
