Predicate Logic Quantifiers Question
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I'm kinda confused regarding predicate quantifiers.
Firstly, what's the difference between
$forall x .Tourist(x)$ and $forall x in Tourists$
I mean I understand that the first is a predicate form and the second implies that it belongs in the Tourist set but is there a specific case I should be using each one?
Additionally is $forall x.Tourist(x).exists y.Country(y).Likes(x,y)$ the same as:
$forall xexists y.Tourist(x) land Country(y) implies Likes(x,y)$ ??
If not what's the difference?
I'm really struggling to understand these things.
Any help would be much appreciated!
logic predicate-logic quantifiers
asked Dec 6 at 2:47
RottenJunkie555
1
add a comment |
up vote
0
down vote
favorite
I'm kinda confused regarding predicate quantifiers.
Firstly, what's the difference between
$forall x .Tourist(x)$ and $forall x in Tourists$
I mean I understand that the first is a predicate form and the second implies that it belongs in the Tourist set but is there a specific case I should be using each one?
Additionally is $forall x.Tourist(x).exists y.Country(y).Likes(x,y)$ the same as:
$forall xexists y.Tourist(x) land Country(y) implies Likes(x,y)$ ??
If not what's the difference?
I'm really struggling to understand these things.
Any help would be much appreciated!
logic predicate-logic quantifiers
asked Dec 6 at 2:47
RottenJunkie555
1
$∀x ∈ text {Tourists}$ is not predicate logic. In predicate logic we have predicate symbols, like $text {Tourists}(x)$ and quantifiers : $∀$ and $∃$. We quantify variables occurring in formulas with predicate symbols : $∀x text {Tourists}(x)$.
– Mauro ALLEGRANZA
Dec 6 at 7:48
This according to the rules of the syntax. But "intuitively", they mean the same : "every object is a Tourist".
– Mauro ALLEGRANZA
Dec 6 at 7:49
Regarding the formula, the "dot" is used as a parenthesis. Thus, again, the correct expression is the second one, with the $land$.
– Mauro ALLEGRANZA
Dec 6 at 7:51
But in math shorthand, we are used to write something, like $forall n in mathbb N P(n)$. Here we use the set-name $mathbb N$ instead of a predicate symbol : $mathbb N(x)$.
– Mauro ALLEGRANZA
Dec 6 at 7:52
Thus, the "rule" is : "to be consistent and clear". Either : $forall x in A P(x)$ or $forall x (A(x) to P(x))$.
– Mauro ALLEGRANZA
Dec 6 at 7:53
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I'm kinda confused regarding predicate quantifiers.
Firstly, what's the difference between
$forall x .Tourist(x)$ and $forall x in Tourists$
I mean I understand that the first is a predicate form and the second implies that it belongs in the Tourist set but is there a specific case I should be using each one?
Additionally is $forall x.Tourist(x).exists y.Country(y).Likes(x,y)$ the same as:
$forall xexists y.Tourist(x) land Country(y) implies Likes(x,y)$ ??
If not what's the difference?
I'm really struggling to understand these things.
Any help would be much appreciated!
logic predicate-logic quantifiers
asked Dec 6 at 2:47
RottenJunkie555
1
I'm kinda confused regarding predicate quantifiers.
Firstly, what's the difference between
$forall x .Tourist(x)$ and $forall x in Tourists$
I mean I understand that the first is a predicate form and the second implies that it belongs in the Tourist set but is there a specific case I should be using each one?
Additionally is $forall x.Tourist(x).exists y.Country(y).Likes(x,y)$ the same as:
$forall xexists y.Tourist(x) land Country(y) implies Likes(x,y)$ ??
If not what's the difference?
I'm really struggling to understand these things.
Any help would be much appreciated!
logic predicate-logic quantifiers
logic predicate-logic quantifiers
asked Dec 6 at 2:47
RottenJunkie555
1
asked Dec 6 at 2:47
RottenJunkie555
1
asked Dec 6 at 2:47
RottenJunkie555
1
asked Dec 6 at 2:47
RottenJunkie555
1
asked Dec 6 at 2:47
RottenJunkie555
1
1
$∀x ∈ text {Tourists}$ is not predicate logic. In predicate logic we have predicate symbols, like $text {Tourists}(x)$ and quantifiers : $∀$ and $∃$. We quantify variables occurring in formulas with predicate symbols : $∀x text {Tourists}(x)$.
– Mauro ALLEGRANZA
Dec 6 at 7:48
This according to the rules of the syntax. But "intuitively", they mean the same : "every object is a Tourist".
– Mauro ALLEGRANZA
Dec 6 at 7:49
Regarding the formula, the "dot" is used as a parenthesis. Thus, again, the correct expression is the second one, with the $land$.
– Mauro ALLEGRANZA
Dec 6 at 7:51
But in math shorthand, we are used to write something, like $forall n in mathbb N P(n)$. Here we use the set-name $mathbb N$ instead of a predicate symbol : $mathbb N(x)$.
– Mauro ALLEGRANZA
Dec 6 at 7:52
Thus, the "rule" is : "to be consistent and clear". Either : $forall x in A P(x)$ or $forall x (A(x) to P(x))$.
– Mauro ALLEGRANZA
Dec 6 at 7:53
add a comment |
$∀x ∈ text {Tourists}$ is not predicate logic. In predicate logic we have predicate symbols, like $text {Tourists}(x)$ and quantifiers : $∀$ and $∃$. We quantify variables occurring in formulas with predicate symbols : $∀x text {Tourists}(x)$.
– Mauro ALLEGRANZA
Dec 6 at 7:48
This according to the rules of the syntax. But "intuitively", they mean the same : "every object is a Tourist".
– Mauro ALLEGRANZA
Dec 6 at 7:49
Regarding the formula, the "dot" is used as a parenthesis. Thus, again, the correct expression is the second one, with the $land$.
– Mauro ALLEGRANZA
Dec 6 at 7:51
But in math shorthand, we are used to write something, like $forall n in mathbb N P(n)$. Here we use the set-name $mathbb N$ instead of a predicate symbol : $mathbb N(x)$.
– Mauro ALLEGRANZA
Dec 6 at 7:52
Thus, the "rule" is : "to be consistent and clear". Either : $forall x in A P(x)$ or $forall x (A(x) to P(x))$.
– Mauro ALLEGRANZA
Dec 6 at 7:53
$∀x ∈ text {Tourists}$ is not predicate logic. In predicate logic we have predicate symbols, like $text {Tourists}(x)$ and quantifiers : $∀$ and $∃$. We quantify variables occurring in formulas with predicate symbols : $∀x text {Tourists}(x)$.
– Mauro ALLEGRANZA
Dec 6 at 7:48
$∀x ∈ text {Tourists}$ is not predicate logic. In predicate logic we have predicate symbols, like $text {Tourists}(x)$ and quantifiers : $∀$ and $∃$. We quantify variables occurring in formulas with predicate symbols : $∀x text {Tourists}(x)$.
– Mauro ALLEGRANZA
Dec 6 at 7:48
This according to the rules of the syntax. But "intuitively", they mean the same : "every object is a Tourist".
– Mauro ALLEGRANZA
Dec 6 at 7:49
This according to the rules of the syntax. But "intuitively", they mean the same : "every object is a Tourist".
– Mauro ALLEGRANZA
Dec 6 at 7:49
Regarding the formula, the "dot" is used as a parenthesis. Thus, again, the correct expression is the second one, with the $land$.
– Mauro ALLEGRANZA
Dec 6 at 7:51
Regarding the formula, the "dot" is used as a parenthesis. Thus, again, the correct expression is the second one, with the $land$.
– Mauro ALLEGRANZA
Dec 6 at 7:51
But in math shorthand, we are used to write something, like $forall n in mathbb N P(n)$. Here we use the set-name $mathbb N$ instead of a predicate symbol : $mathbb N(x)$.
– Mauro ALLEGRANZA
Dec 6 at 7:52
But in math shorthand, we are used to write something, like $forall n in mathbb N P(n)$. Here we use the set-name $mathbb N$ instead of a predicate symbol : $mathbb N(x)$.
– Mauro ALLEGRANZA
Dec 6 at 7:52
Thus, the "rule" is : "to be consistent and clear". Either : $forall x in A P(x)$ or $forall x (A(x) to P(x))$.
– Mauro ALLEGRANZA
Dec 6 at 7:53
Thus, the "rule" is : "to be consistent and clear". Either : $forall x in A P(x)$ or $forall x (A(x) to P(x))$.
– Mauro ALLEGRANZA
Dec 6 at 7:53
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$∀x ∈ text {Tourists}$ is not predicate logic. In predicate logic we have predicate symbols, like $text {Tourists}(x)$ and quantifiers : $∀$ and $∃$. We quantify variables occurring in formulas with predicate symbols : $∀x text {Tourists}(x)$.
– Mauro ALLEGRANZA
Dec 6 at 7:48
This according to the rules of the syntax. But "intuitively", they mean the same : "every object is a Tourist".
– Mauro ALLEGRANZA
Dec 6 at 7:49
Regarding the formula, the "dot" is used as a parenthesis. Thus, again, the correct expression is the second one, with the $land$.
– Mauro ALLEGRANZA
Dec 6 at 7:51
But in math shorthand, we are used to write something, like $forall n in mathbb N P(n)$. Here we use the set-name $mathbb N$ instead of a predicate symbol : $mathbb N(x)$.
– Mauro ALLEGRANZA
Dec 6 at 7:52
Thus, the "rule" is : "to be consistent and clear". Either : $forall x in A P(x)$ or $forall x (A(x) to P(x))$.
– Mauro ALLEGRANZA
Dec 6 at 7:53