Natural Language to Formal Propositional Logic, "get neither"

Question

I've been working through a few translations and I found one I am not too sure as to the formatting of.

I believe the first part is right but in the second part where it says he will get neither, I am unsure if the correct format is to negate both symbols, or if there is another way?

The sentence is:

Johnny wants both a train and a bike for Christmas but he will get neither.

This is my current attempt of translation:

Jt = Johnny wants a train

Jb = Johnny wants a bike

$$(Jt\land Jb) \land \lnot(Jt \lor Jb)$$

Thank you

observe that $\lnot (Jt\lor Jb)\iff \lnot Jt\land \lnot Jb$ – Masacroso Jul 27 '17 at 21:52 — Masacroso, Jul 27 '17 at 21:52

Bram28 · Accepted Answer · 2017-07-27T21:14:07.713

3

That doesn't work. Your sentence ends up saying:

Johnny wants both a train and a bike for Christmas but he $\color{red}{wants}$ neither.

You'll need to add some sentence variables that symbolize Johnny getting a train or bike.

So, say you have:

Wt = Johnny wants a train

Wb = Johnny wants a bike

Gt = Johnny gets a train

Gb = Johnny gets a bike

Then you can do:

$(Wt \land Wb) \land \neg (Gt \lor Gb)$

So: your idea was certainly correct ... but you just needed some additional sentences to capture the getting part

edited Jul 27 '17 at 21:14

answered Jul 27 '17 at 21:10

Bram28

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Ahh okay, so by adding lets say two variables Gt and Gb and replacing them for the last two, that should do the trick? – Reggie Snow Jul 27 '17 at 21:13
typed this before you made the edit^ thank you for your response! – Reggie Snow Jul 27 '17 at 21:13
@BenConlon Yup! And like I said, otherwise you totally had the right idea! – Bram28 Jul 27 '17 at 21:15

Natural Language to Formal Propositional Logic, "get neither"

1 Answers1