logic translation

Question

Quantified Logic Translation

Using the given the symbolization key, translate the following sentences.

UD:	people
Bx:	x is a baker.
Jx:	x is a judge.
Px:	x can make pâte à choux.
Ux:	x lives under the sea.
Sxy:	x is suspicious of y.
m:	Mel
n:	Nadiya
p:	Paul

Question: There is someone who is suspicious of anyone who is suspicious of everyone

Example: If a person is suspicious of themself, then everyone is suspicious of them. Answer: Ax(Sxx->AySyx)

The Question is really tricky and im struggling understanding it.

Answer 1

Here's a way to get started on this one. For any translation in quantified predicate logic, you'll first want to identify which predicates from your symbolization key are relevant. In this case, it seems like the two-place predicate 'Sxy' is the only one that you'll need, just like in your example translation.

The next thing to think about is which quantifiers will be needed. The sentence at hand begins with 'There is', which is a good indication that the translated sentence will begin with an existential quantifier (which is usually represented with a backwards 'E'). Looking through the rest of the sentence, we also see the words 'anyone' and 'everyone'. This is a good indication that the translated sentence will contain two universal quantifiers (usually represented with an upside-down 'A').

From here, there are some remaining challenges: (1) to figure out where the quantifiers should be placed in relation to one another, (2) to figure out which variables to use, and (3) to figure out which (if any) additional logical symbols will be needed. If you're still working on this problem, I would be happy to help you work through these steps!