Translating plurals in first-order logic

64 Views Asked by At

Using the dictionary P: ...wakes up earlier than...

I am asked to translate the sentence:

"The earliest riser wakes up earlier than the latest riser"

which I have translated successfully - but I am then also asked to translate:

"The earliest risers wake up earlier than the latest risers"

which seems like there is no alternative way to translate. Is there?

1

There are 1 best solutions below

0
On

I'd say this.

$\forall x \lnot\exists y(Qx \land Qy \land\lnot x=y\land Pyx) \land \forall w \lnot\exists z(Qw \land Qz \land\lnot w=z\land Pwz) \land Pxw$

But I'm waiting a feedback from you because it seems all too easy and - as usual with natural language translations - some semantic aspects are not satisfying. Interesting exercise btw.

Actually I found a specific article here from which you seem to be totally right: some plurals from NL to FOL are a big problem that apparently requires the introduction of specific "plural" variables and a specific relation "x is one of".