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I'm trying to represent the following statement in first order logic:

Bill Gates funds all those who Stevie Jobs does not fund.

Not 100% sure about the correctness of the logic that I'm using here:

all x (Funds(Bill Gates,x) & -Funds(Stevie Jobs,x)).
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  • $\begingroup$ The statement gives the sense that if Steve jobs does not fund someone then Bill Gates would fund him. Hence the correct for 'might be', ($\forall x$) $\sim$(Steve jobs funds x) $\rightarrow$ (Bill gates funds $x$) $\endgroup$ Commented Jun 1, 2022 at 2:04

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Bill Gates funds all those who Stevie Jobs does not fund.

all x (Funds(Bill Gates,x) & -Funds(Stevie Jobs,x)).

Your proposed translation says that nobody is funded by Stevie; on the other hand, the given statement does not preclude somebody from being funded by both Bill and Stevie.

Your proposed translation also says that everybody is funded by Bill; on the other hand, the given statement clearly allows for Bill not funding somebody that Stevie funds.

Rewriting the given statement: "All those who Stevie Jobs doesn't fund, Bill Gates funds."

This is a conditional—not a conjunction—statement, and the correct translation is $$\forall x \Big(\lnot S(x)\to B(x)\Big).$$

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  • $\begingroup$ If we build a truth table, the case where S(x) = T and B(x) = T will cause the formula you suggested to return true, when it should return false, right? In this case we are saying Stevie Jobs funds, Bill Gates funds, and the formula is true. $\endgroup$ Commented Jun 1, 2022 at 23:05
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    $\begingroup$ As explained above, the given statement does allow for the case where Mary is funded by both Bill and Stevie. The answer that I gave can be read, "Each person that Stevie doesn't fund, Bill funds." A truth table is incapable of dealing with quantified sentences like the above. $\endgroup$ Commented Jun 2, 2022 at 0:19

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