Mixing
“Except†in prepositional logic
Clash Royale CLAN TAG#URR8PPP
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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 20 mins ago
Taroccoesbrocco
3,97861535
asked 5 hours ago
user3471031
233
 |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 20 mins ago
Taroccoesbrocco
3,97861535
asked 5 hours ago
user3471031
233
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
5 hours ago
1
This is predicate logic, not propositional logic.
– Henning Makholm
5 hours ago
@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
5 hours ago
2
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
5 hours ago
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
4 hours ago
 |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 20 mins ago
Taroccoesbrocco
3,97861535
asked 5 hours ago
user3471031
233
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 20 mins ago
Taroccoesbrocco
3,97861535
asked 5 hours ago
user3471031
233
edited 20 mins ago
Taroccoesbrocco
3,97861535
asked 5 hours ago
user3471031
233
edited 20 mins ago
Taroccoesbrocco
3,97861535
edited 20 mins ago
Taroccoesbrocco
3,97861535
edited 20 mins ago
Taroccoesbrocco
3,97861535
3,97861535
asked 5 hours ago
user3471031
233
asked 5 hours ago
user3471031
233
asked 5 hours ago
user3471031
233
233
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
5 hours ago
1
This is predicate logic, not propositional logic.
– Henning Makholm
5 hours ago
@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
5 hours ago
2
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
5 hours ago
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
4 hours ago
 |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
5 hours ago
1
This is predicate logic, not propositional logic.
– Henning Makholm
5 hours ago
@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
5 hours ago
2
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
5 hours ago
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
4 hours ago
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
5 hours ago
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
5 hours ago
1
1
This is predicate logic, not propositional logic.
– Henning Makholm
5 hours ago
This is predicate logic, not propositional logic.
– Henning Makholm
5 hours ago
@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
5 hours ago
@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
5 hours ago
2
2
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
5 hours ago
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
5 hours ago
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
4 hours ago
@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
4 hours ago
 |Â
show 2 more comments
2 Answers
2
active
oldest
votes
up vote
4
down vote
∀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 4 hours ago
William Elliot
5,3962517
add a comment |Â
up vote
2
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 3 hours ago
Batominovski
26.4k22881
Are not the two answers equivalent statements?
– William Elliot
3 hours ago
I was offering a more compact version (i.e., only one quantifier is needed).
– Batominovski
2 hours ago
+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
1 hour ago
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
4
down vote
∀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 4 hours ago
William Elliot
5,3962517
add a comment |Â
up vote
4
down vote
∀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 4 hours ago
William Elliot
5,3962517
add a comment |Â
up vote
4
down vote
up vote
4
down vote
∀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 4 hours ago
William Elliot
5,3962517
∀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 4 hours ago
William Elliot
5,3962517
edited 3 hours ago
answered 4 hours ago
William Elliot
5,3962517
answered 4 hours ago
William Elliot
5,3962517
answered 4 hours ago
William Elliot
5,3962517
5,3962517
add a comment |Â
add a comment |Â
up vote
2
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 3 hours ago
Batominovski
26.4k22881
Are not the two answers equivalent statements?
– William Elliot
3 hours ago
I was offering a more compact version (i.e., only one quantifier is needed).
– Batominovski
2 hours ago
+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
1 hour ago
add a comment |Â
up vote
2
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 3 hours ago
Batominovski
26.4k22881
Are not the two answers equivalent statements?
– William Elliot
3 hours ago
I was offering a more compact version (i.e., only one quantifier is needed).
– Batominovski
2 hours ago
+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
1 hour ago
add a comment |Â
up vote
2
down vote
up vote
2
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 3 hours ago
Batominovski
26.4k22881
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 3 hours ago
Batominovski
26.4k22881
answered 3 hours ago
Batominovski
26.4k22881
answered 3 hours ago
Batominovski
26.4k22881
answered 3 hours ago
Batominovski
26.4k22881
26.4k22881
Are not the two answers equivalent statements?
– William Elliot
3 hours ago
I was offering a more compact version (i.e., only one quantifier is needed).
– Batominovski
2 hours ago
+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
1 hour ago
add a comment |Â
Are not the two answers equivalent statements?
– William Elliot
3 hours ago
I was offering a more compact version (i.e., only one quantifier is needed).
– Batominovski
2 hours ago
+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
1 hour ago
Are not the two answers equivalent statements?
– William Elliot
3 hours ago
Are not the two answers equivalent statements?
– William Elliot
3 hours ago
I was offering a more compact version (i.e., only one quantifier is needed).
– Batominovski
2 hours ago
I was offering a more compact version (i.e., only one quantifier is needed).
– Batominovski
2 hours ago
+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
1 hour ago
+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
1 hour ago
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
5 hours ago
1
This is predicate logic, not propositional logic.
– Henning Makholm
5 hours ago
@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
5 hours ago
2
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
5 hours ago
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
4 hours ago