3 Mar 2004
CS3243 - Inference
18
Soundness of GMP
lNeed to show that
lp1', …, pn', (p1 Ù … Ù pn Þ q) ╞ qθ
l provided that pi'θ = piθ for all I
l
lLemma: For any sentence p, we have p ╞ pθ by UI
l
1.(p1 Ù … Ù pn Þ q) ╞ (p1 Ù … Ù pn Þ q)θ = (p1θ Ù … Ù pnθ Þ qθ)
2.p1', …, pn' ╞ p1' Ù … Ù pn' ╞ p1'θ Ù … Ù pn'θ
3.From 1 and 2, qθ follows by ordinary Modus Ponens