Question

Formalize the following sentences into FOL using the key and domain.

Domain: U(x, y, z): B(x,y): L(x,y): S(x, y): Wix,y): P(x): R(x): Everything x understands y at least as well as z x bores y x listens to y x is a student of y x wastes y's time x is a professor x is unpopular

Please formalize this sentence: "If something is understood equally well by all of a student's professors, then that student doesn't understand it as well as their professors."

Answer 1

Let
T
be a student, something to understand. For (professors) we have that they understand equally well if $U(p,y,q)\wedge U(q,y,p)$ , that is, if each one of understands as well as the other.

We write "something is understood equally well by all of a student's professors" as

$\forall p \forall q (S(x,p)\wedge S(x,q) \to U(p,t,q)\wedge U(q,y,p))$

and "that student doesn't understand it as well as their professors" as

$\forall p ( S(x,p)\to \neg U(x,y,p))$

The whole sentence is then

$\forall p \forall q [S(x,p)\wedge S(x,q) \to U(p,t,q)\wedge U(q,y,p)] \to \forall p [S(x,p)\to \neg U(x,y,p)]$.