Interpretation over a singleton Let i be s lap ,10>,anda∈∑ 1.T(A()=(xA)() 2.T(+)()=a 3.(Snn)(0)=(4)() 4. Io(P),a (P)E(T(n, un) for every n-an predicate constant(variable), where ( n(,,an)=t and u(n) n)=f Ifh a then v occurs in a Ifh a. then a occurs in a Logic in Computer Science -p 3/19Interpretation over a singleton Let I be < {a}, I0 >, 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 I(n)(a1, · · · , an) = T and Ψ(n)(a1, · · · , an) = F If ` A, then ∨ occurs in A. If ` A, then ∼ occurs in A. Logic in Computer Science – p.3/19