To "decompile" the formula x ( y F(x, y) y z (M(x, y) M(y, z))), let us break it down into its significant subformulas:
Evidently, this is the sentence we sought to express.
- The subformula y F(x, y) means
that 'x is a father'.
- The subformula
y z (M(x, y) M(y, z)) means that
'x is a maternal grandmother'; for it says that x is a mother of some y who in
turn is a mother of some z.
- The entire formula therefore says 'For all x, if x is a father,
then x is not a maternal grandmother'.
- We can express this sentence more elegantly as 'Anyone who is a father is not a maternal grandmother'.
Back to Question.