first-order logic

Question

How I can make the following sentences in first order logic as a set of Horn ?.

"The Martians are not informatics appreciate anything more than a computer."

"The Martians informatics appreciate anything more than a slow computer."

"There are fast and slow computers."

I have deduced the following predicates:

or (/ 1) -> multiplicity 1-- be a computer

i (/ 1) -> multiplicity 1 - be an informatic

l (/ 1) -> multiplicity 1 - be slow

m (/ 1) -> multiplicity 1 - be Martian

a (/ 3) -> multiplicity 3 - a (X, Y, Z) --- "X" to appreciate more "Y" to "Z"

Answer 1

HINT

Consider the sentence :

There are fast and slow computers.

We can translate it as :

$∃x(Computer(x)∧Fast(x))∧∃y(Computer(y)∧Slow(y))$.

We have that :

• a basic Horn formula is a disjunction with at most one non-negated atomic formula

• a Horn formula is in prenex form and its matrix is a conjunction of basic horn formulae.

Thus, it is enough to rewrite the above formula in prenex form :

$\exists x \exists y(Computer(x)∧Fast(x)∧Computer(y)∧Slow(y))$.

The matrix is a conjunction of basic Horn formulae, because every conjunct is a disjunction (with a single formula) with at most one non-negated atomic formula.