How to express this sentence by using quantifiers and logical operators

Question

Here is the sentence:

There is a shortest person, but there is no tallest person.

I'm voting to close this question as off-topic because it pertains to logic and mathematics but not programming. — Smandoli, Sep 21 '15 at 14:14
@Smandoli In zodiac's defense, there is a valid tag with open questions and followers on the subjects (excluding quantifiers). — Patrick87, Sep 21 '15 at 14:27

ergonaut · Answer 1 · 2015-09-21T14:50:41.793

0

There exists person where person < i, for all persons i, i != person.

There doesn't exists a person where person > i, for all persons i, i != person.

∃p : T(i,p) ∀i, i!=p, i in (x, y, z)

~(∃p : T(p,i) ∀i, i!=p), i in (x y, z)

edited Sep 21 '15 at 14:50

answered Sep 21 '15 at 14:20

ergonaut

Thank you. But i have to say sorry, i forgot to say. It is given variable x, y, z and T(x, y) for "x is taller than y". And all variable have to quantified by yourself. – zodiac Sep 21 '15 at 14:41

score 0 · Answer 2 · answered Sep 21 '15 at 14:21

0

Something like:

(EXISTS x in People | FORALL y in People \ {x} y TALLER_THAN x)
AND
NOT (EXISTS w in People | FORALL z in People \ {w} w TALLER_THAN z)

Some notes:

"BUT" can usually be translated as "AND NOT", unless the first sentence is a negative, in which case it actually means "AND".
"THERE IS" can usually be translated as "EXISTS"
Any superlative (e.g., "MOST" or "BEST" or ending in "-EST") usually means "EXISTS x SUCH THAT FORALL Y =/= x | X MORE ? THAN Y".

answered Sep 21 '15 at 14:21

Patrick87

Thank you. But i have to say sorry, i forgot to say. It is given variable x, y, z and T(x, y) for "x is taller than y". And all variable have to quantified by yourself. – zodiac Sep 21 '15 at 14:40
The choice of variables is unimportant. In fact, you only need two variables, `x` and `y`, the `x` and `y` at the beginning will be scoped by the quantifiers they are associated with (they are "bound"), and you can safely reuse them in the second part. For T(x, y)... just replace `a TALLER_THAN b` with `T(a, b)`. – Patrick87 Sep 21 '15 at 14:47
@zodiac Did you see my comment? – Patrick87 Sep 21 '15 at 18:04

score -1 · Answer 3 · answered Sep 21 '15 at 14:14

-1

shortest && !(tallest)

Is this you are expecting

answered Sep 21 '15 at 14:14

Arvind Chavhan

Thank you. But i have to say sorry, i forgot to say. It is given variable x, y, z and T(x, y) for "x is taller than y". And all variable have to quantified by yourself. – zodiac Sep 21 '15 at 14:41

3 Answers3