“Except†in predicate logic
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I have a phrase that I am trying to translate into predicate logic. The phrase is as follows:
All lions except old ones roar
So far I have written down that:
$∀x((L(x) land lnot O(x)) to R(x))$
Where $L(x)$ is "$x$ is a lion", $O(x)$ is "$x$ is old", and $R(x)$ is "$x$ roars". I am wondering if this is correct notation. I am mostly confused about the "except" in the phrase because as I have translated states that all lions who are not old roar.
Does any one have any thoughts about the notation for this phrase?
discrete-mathematics logic first-order-logic predicate-logic logic-translation
edited Sep 22 at 18:12
Andrés E. Caicedo
63.6k7156238
asked Sep 22 at 0:25
user3471031
254
 |Â
show 2 more comments
up vote
3
down vote
favorite
I have a phrase that I am trying to translate into predicate logic. The phrase is as follows:
All lions except old ones roar
So far I have written down that:
$∀x((L(x) land lnot O(x)) to R(x))$
Where $L(x)$ is "$x$ is a lion", $O(x)$ is "$x$ is old", and $R(x)$ is "$x$ roars". I am wondering if this is correct notation. I am mostly confused about the "except" in the phrase because as I have translated states that all lions who are not old roar.
Does any one have any thoughts about the notation for this phrase?
discrete-mathematics logic first-order-logic predicate-logic logic-translation
edited Sep 22 at 18:12
Andrés E. Caicedo
63.6k7156238
asked Sep 22 at 0:25
user3471031
254
2
Do you think your sentence states that old lions don't roar, or does it simply say that young and middle-aged lions do roar (as you correctly interpret it)?
– Fabio Somenzi
Sep 22 at 0:28
1
This is predicate logic, not propositional logic.
– Henning Makholm
Sep 22 at 0:29
@FabioSomenzi I think my sentence says that lions who are not old roar, which can also be lions who are young and middle aged roar
– user3471031
Sep 22 at 0:32
3
Yes, I was being (perhaps unsuccessfully) mildly facetious. There are two issues to be resolved. One is whether "except" implies that old lions are not guaranteed to roar, or whether they are guaranteed not to roar. Natural language is often ambiguous, but I'd vote for the latter interpretation. The other issue, raised by Henning Makholm, is that yours is a sentence of predicate logic. You don't have quantification in propositional logic.
– Fabio Somenzi
Sep 22 at 0:38
1
@user3471031: your rendering says nothing about whether old lions roar, which is the first version in Fabio Somenzi's comment. He then says he votes for the second version where old lions are guaranteed not to roar. I would agree with the first and your rendering. I think the important thing is to understand the difference.
– Ross Millikan
Sep 22 at 1:17
 |Â
show 2 more comments
up vote
3
down vote
favorite
up vote
3
down vote
favorite
I have a phrase that I am trying to translate into predicate logic. The phrase is as follows:
All lions except old ones roar
So far I have written down that:
$∀x((L(x) land lnot O(x)) to R(x))$
Where $L(x)$ is "$x$ is a lion", $O(x)$ is "$x$ is old", and $R(x)$ is "$x$ roars". I am wondering if this is correct notation. I am mostly confused about the "except" in the phrase because as I have translated states that all lions who are not old roar.
Does any one have any thoughts about the notation for this phrase?
discrete-mathematics logic first-order-logic predicate-logic logic-translation
edited Sep 22 at 18:12
Andrés E. Caicedo
63.6k7156238
asked Sep 22 at 0:25
user3471031
254
I have a phrase that I am trying to translate into predicate logic. The phrase is as follows:
All lions except old ones roar
So far I have written down that:
$∀x((L(x) land lnot O(x)) to R(x))$
Where $L(x)$ is "$x$ is a lion", $O(x)$ is "$x$ is old", and $R(x)$ is "$x$ roars". I am wondering if this is correct notation. I am mostly confused about the "except" in the phrase because as I have translated states that all lions who are not old roar.
Does any one have any thoughts about the notation for this phrase?
discrete-mathematics logic first-order-logic predicate-logic logic-translation
discrete-mathematics logic first-order-logic predicate-logic logic-translation
edited Sep 22 at 18:12
Andrés E. Caicedo
63.6k7156238
asked Sep 22 at 0:25
user3471031
254
edited Sep 22 at 18:12
Andrés E. Caicedo
63.6k7156238
asked Sep 22 at 0:25
user3471031
254
edited Sep 22 at 18:12
Andrés E. Caicedo
63.6k7156238
edited Sep 22 at 18:12
Andrés E. Caicedo
63.6k7156238
edited Sep 22 at 18:12
Andrés E. Caicedo
63.6k7156238
63.6k7156238
asked Sep 22 at 0:25
user3471031
254
asked Sep 22 at 0:25
user3471031
254
asked Sep 22 at 0:25
user3471031
254
254
2
Do you think your sentence states that old lions don't roar, or does it simply say that young and middle-aged lions do roar (as you correctly interpret it)?
– Fabio Somenzi
Sep 22 at 0:28
1
This is predicate logic, not propositional logic.
– Henning Makholm
Sep 22 at 0:29
@FabioSomenzi I think my sentence says that lions who are not old roar, which can also be lions who are young and middle aged roar
– user3471031
Sep 22 at 0:32
3
Yes, I was being (perhaps unsuccessfully) mildly facetious. There are two issues to be resolved. One is whether "except" implies that old lions are not guaranteed to roar, or whether they are guaranteed not to roar. Natural language is often ambiguous, but I'd vote for the latter interpretation. The other issue, raised by Henning Makholm, is that yours is a sentence of predicate logic. You don't have quantification in propositional logic.
– Fabio Somenzi
Sep 22 at 0:38
1
@user3471031: your rendering says nothing about whether old lions roar, which is the first version in Fabio Somenzi's comment. He then says he votes for the second version where old lions are guaranteed not to roar. I would agree with the first and your rendering. I think the important thing is to understand the difference.
– Ross Millikan
Sep 22 at 1:17
 |Â
show 2 more comments
2
Do you think your sentence states that old lions don't roar, or does it simply say that young and middle-aged lions do roar (as you correctly interpret it)?
– Fabio Somenzi
Sep 22 at 0:28
1
This is predicate logic, not propositional logic.
– Henning Makholm
Sep 22 at 0:29
@FabioSomenzi I think my sentence says that lions who are not old roar, which can also be lions who are young and middle aged roar
– user3471031
Sep 22 at 0:32
3
Yes, I was being (perhaps unsuccessfully) mildly facetious. There are two issues to be resolved. One is whether "except" implies that old lions are not guaranteed to roar, or whether they are guaranteed not to roar. Natural language is often ambiguous, but I'd vote for the latter interpretation. The other issue, raised by Henning Makholm, is that yours is a sentence of predicate logic. You don't have quantification in propositional logic.
– Fabio Somenzi
Sep 22 at 0:38
1
@user3471031: your rendering says nothing about whether old lions roar, which is the first version in Fabio Somenzi's comment. He then says he votes for the second version where old lions are guaranteed not to roar. I would agree with the first and your rendering. I think the important thing is to understand the difference.
– Ross Millikan
Sep 22 at 1:17
2
2
Do you think your sentence states that old lions don't roar, or does it simply say that young and middle-aged lions do roar (as you correctly interpret it)?
– Fabio Somenzi
Sep 22 at 0:28
Do you think your sentence states that old lions don't roar, or does it simply say that young and middle-aged lions do roar (as you correctly interpret it)?
– Fabio Somenzi
Sep 22 at 0:28
1
1
This is predicate logic, not propositional logic.
– Henning Makholm
Sep 22 at 0:29
This is predicate logic, not propositional logic.
– Henning Makholm
Sep 22 at 0:29
@FabioSomenzi I think my sentence says that lions who are not old roar, which can also be lions who are young and middle aged roar
– user3471031
Sep 22 at 0:32
@FabioSomenzi I think my sentence says that lions who are not old roar, which can also be lions who are young and middle aged roar
– user3471031
Sep 22 at 0:32
3
3
Yes, I was being (perhaps unsuccessfully) mildly facetious. There are two issues to be resolved. One is whether "except" implies that old lions are not guaranteed to roar, or whether they are guaranteed not to roar. Natural language is often ambiguous, but I'd vote for the latter interpretation. The other issue, raised by Henning Makholm, is that yours is a sentence of predicate logic. You don't have quantification in propositional logic.
– Fabio Somenzi
Sep 22 at 0:38
Yes, I was being (perhaps unsuccessfully) mildly facetious. There are two issues to be resolved. One is whether "except" implies that old lions are not guaranteed to roar, or whether they are guaranteed not to roar. Natural language is often ambiguous, but I'd vote for the latter interpretation. The other issue, raised by Henning Makholm, is that yours is a sentence of predicate logic. You don't have quantification in propositional logic.
– Fabio Somenzi
Sep 22 at 0:38
1
1
@user3471031: your rendering says nothing about whether old lions roar, which is the first version in Fabio Somenzi's comment. He then says he votes for the second version where old lions are guaranteed not to roar. I would agree with the first and your rendering. I think the important thing is to understand the difference.
– Ross Millikan
Sep 22 at 1:17
@user3471031: your rendering says nothing about whether old lions roar, which is the first version in Fabio Somenzi's comment. He then says he votes for the second version where old lions are guaranteed not to roar. I would agree with the first and your rendering. I think the important thing is to understand the difference.
– Ross Millikan
Sep 22 at 1:17
 |Â
show 2 more comments
2 Answers
2
active
oldest
votes
up vote
5
down vote
accepted
∀x(L(x)∧¬O(x)→R(x))
says all lions that are not old roar.
To render the except requires more:
∀x(L(x)∧¬O(x)→R(x)) ∧ ∀x(L(x)∧O(x)→¬R(x))
answered Sep 22 at 2:10
William Elliot
5,7152517
add a comment |Â
up vote
3
down vote
I think this also works (assuming that except means that old lions do not roar):
$$forall x,Big[L(x)rightarrowbig(neg O(x)leftrightarrow R(x)big)Big],.$$
answered Sep 22 at 2:49
Batominovski
27k22881
Are not the two answers equivalent statements?
– William Elliot
Sep 22 at 3:11
I was offering a more compact version (i.e., only one quantifier is needed).
– Batominovski
Sep 22 at 3:13
+1 Yes. Suppose $x$ is a lion. If $x$ is not old then $x$ roars. If $x$ is old then x does not roar.
– Dan Christensen
Sep 22 at 4:27
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
5
down vote
accepted
∀x(L(x)∧¬O(x)→R(x))
says all lions that are not old roar.
To render the except requires more:
∀x(L(x)∧¬O(x)→R(x)) ∧ ∀x(L(x)∧O(x)→¬R(x))
answered Sep 22 at 2:10
William Elliot
5,7152517
add a comment |Â
up vote
5
down vote
accepted
∀x(L(x)∧¬O(x)→R(x))
says all lions that are not old roar.
To render the except requires more:
∀x(L(x)∧¬O(x)→R(x)) ∧ ∀x(L(x)∧O(x)→¬R(x))
answered Sep 22 at 2:10
William Elliot
5,7152517
add a comment |Â
up vote
5
down vote
accepted
up vote
5
down vote
accepted
∀x(L(x)∧¬O(x)→R(x))
says all lions that are not old roar.
To render the except requires more:
∀x(L(x)∧¬O(x)→R(x)) ∧ ∀x(L(x)∧O(x)→¬R(x))
answered Sep 22 at 2:10
William Elliot
5,7152517
∀x(L(x)∧¬O(x)→R(x))
says all lions that are not old roar.
To render the except requires more:
∀x(L(x)∧¬O(x)→R(x)) ∧ ∀x(L(x)∧O(x)→¬R(x))
answered Sep 22 at 2:10
William Elliot
5,7152517
edited Sep 22 at 2:39
answered Sep 22 at 2:10
William Elliot
5,7152517
answered Sep 22 at 2:10
William Elliot
5,7152517
answered Sep 22 at 2:10
William Elliot
5,7152517
5,7152517
add a comment |Â
add a comment |Â
up vote
3
down vote
I think this also works (assuming that except means that old lions do not roar):
$$forall x,Big[L(x)rightarrowbig(neg O(x)leftrightarrow R(x)big)Big],.$$
answered Sep 22 at 2:49
Batominovski
27k22881
Are not the two answers equivalent statements?
– William Elliot
Sep 22 at 3:11
I was offering a more compact version (i.e., only one quantifier is needed).
– Batominovski
Sep 22 at 3:13
+1 Yes. Suppose $x$ is a lion. If $x$ is not old then $x$ roars. If $x$ is old then x does not roar.
– Dan Christensen
Sep 22 at 4:27
add a comment |Â
up vote
3
down vote
I think this also works (assuming that except means that old lions do not roar):
$$forall x,Big[L(x)rightarrowbig(neg O(x)leftrightarrow R(x)big)Big],.$$
answered Sep 22 at 2:49
Batominovski
27k22881
Are not the two answers equivalent statements?
– William Elliot
Sep 22 at 3:11
I was offering a more compact version (i.e., only one quantifier is needed).
– Batominovski
Sep 22 at 3:13
+1 Yes. Suppose $x$ is a lion. If $x$ is not old then $x$ roars. If $x$ is old then x does not roar.
– Dan Christensen
Sep 22 at 4:27
add a comment |Â
up vote
3
down vote
up vote
3
down vote
I think this also works (assuming that except means that old lions do not roar):
$$forall x,Big[L(x)rightarrowbig(neg O(x)leftrightarrow R(x)big)Big],.$$
answered Sep 22 at 2:49
Batominovski
27k22881
I think this also works (assuming that except means that old lions do not roar):
$$forall x,Big[L(x)rightarrowbig(neg O(x)leftrightarrow R(x)big)Big],.$$
answered Sep 22 at 2:49
Batominovski
27k22881
answered Sep 22 at 2:49
Batominovski
27k22881
answered Sep 22 at 2:49
Batominovski
27k22881
answered Sep 22 at 2:49
Batominovski
27k22881
27k22881
Are not the two answers equivalent statements?
– William Elliot
Sep 22 at 3:11
I was offering a more compact version (i.e., only one quantifier is needed).
– Batominovski
Sep 22 at 3:13
+1 Yes. Suppose $x$ is a lion. If $x$ is not old then $x$ roars. If $x$ is old then x does not roar.
– Dan Christensen
Sep 22 at 4:27
add a comment |Â
Are not the two answers equivalent statements?
– William Elliot
Sep 22 at 3:11
I was offering a more compact version (i.e., only one quantifier is needed).
– Batominovski
Sep 22 at 3:13
+1 Yes. Suppose $x$ is a lion. If $x$ is not old then $x$ roars. If $x$ is old then x does not roar.
– Dan Christensen
Sep 22 at 4:27
Are not the two answers equivalent statements?
– William Elliot
Sep 22 at 3:11
Are not the two answers equivalent statements?
– William Elliot
Sep 22 at 3:11
I was offering a more compact version (i.e., only one quantifier is needed).
– Batominovski
Sep 22 at 3:13
I was offering a more compact version (i.e., only one quantifier is needed).
– Batominovski
Sep 22 at 3:13
+1 Yes. Suppose $x$ is a lion. If $x$ is not old then $x$ roars. If $x$ is old then x does not roar.
– Dan Christensen
Sep 22 at 4:27
+1 Yes. Suppose $x$ is a lion. If $x$ is not old then $x$ roars. If $x$ is old then x does not roar.
– Dan Christensen
Sep 22 at 4:27
add a comment |Â
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2
Do you think your sentence states that old lions don't roar, or does it simply say that young and middle-aged lions do roar (as you correctly interpret it)?
– Fabio Somenzi
Sep 22 at 0:28
1
This is predicate logic, not propositional logic.
– Henning Makholm
Sep 22 at 0:29
@FabioSomenzi I think my sentence says that lions who are not old roar, which can also be lions who are young and middle aged roar
– user3471031
Sep 22 at 0:32
3
Yes, I was being (perhaps unsuccessfully) mildly facetious. There are two issues to be resolved. One is whether "except" implies that old lions are not guaranteed to roar, or whether they are guaranteed not to roar. Natural language is often ambiguous, but I'd vote for the latter interpretation. The other issue, raised by Henning Makholm, is that yours is a sentence of predicate logic. You don't have quantification in propositional logic.
– Fabio Somenzi
Sep 22 at 0:38
1
@user3471031: your rendering says nothing about whether old lions roar, which is the first version in Fabio Somenzi's comment. He then says he votes for the second version where old lions are guaranteed not to roar. I would agree with the first and your rendering. I think the important thing is to understand the difference.
– Ross Millikan
Sep 22 at 1:17