5
Fixpoints
•Consider transitive closure, expressed as LFP:
•tc(u,v) = lfpR[E(x,y) Ç 9 z.(E(x,z) Æ R(z,y)](u,v)
•
•Can “unfold” it:
• tc0(x,y) = E(x,y)
• tcn+1(x,y) = 9 z.(E(x,z) Æ 9 x.(x=z Æ tcn(x,y)))
•
•Hence tc(u,v) = Çn ¸ 0 tcn(u,v)  2 Lw1, w