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Hi guys,
I am confused with a logic inference.
According to a book, if A, then not B, can be notated like A-->/B or A(-|-)B. However, in 7sage, it is maybe notated like A(---)/B.
Here's the question.
According to the question key, the inference is,
G(--s--)/E
F-->H
H(--s--)/E
But, if we use E-->/F to replace the part of E(-|-)F (because according to the very beginning of the post,A-->/B AND A(-|-)B are actually the same thing ), we get,
then the inference are,
E-->G-->H (this is very difference with the original above, which is not inference can be made like this)
E-->H (Which according to the original above, there is not such inference can be made like this)
/F-->H (which is different from the above original inference which is F-->H)
However, if we replace the original part of E(-|-)F with E(---)/F, interestingly, the inference different with above two.
Here we have:
E(---)/F--> G -->H
and the inference we have are
except we can make the exactly same inference with the 2 ones, we also can infer that,
G(--s--)/F
G(--s--)E
E(--s--)H
these inferences are totally different with the original ones.
the trick thing is according to the book, E(-|-)F is the same with E-->/F, and according to 7sage, actually E(-|-)F is E(---)/F, which leading to the hypothesis that if we replace the E(-|-)F to whatever these two different versions, the inferences made should be the same. Who can please clarify me?
Thank you!
Cynthia
0
3 comments
No, it's not a Bi-conditional. If A then not B is a not both rule: A ---> B, for it's not clear if it's required for A to even show up. "If...then..." is a conditional itself. The meaning of this statement does not equate a bi-conditional.
Sami gave you a much more detailed breakdown of the inferences and possible errors made due to the confusion on the concept. It does a much better job of explaining the nuances on the logic.
my question is whether E(-|-)F, E(---)/F, and E--->/F are the same thing?
in other words, should the" if A, then not B" be biconditional notated?
@cynthiawu82687 said:
Hi guys,
I am confused with a logic inference.
According to a book, if A, then not B, can be notated like A-->/B or A(-|-)B. However, in 7sage, it is maybe notated like A(---)/B.
Here's the question.
E(-|-)F--> G -->H (the original one)
According to the question key, the inference is,
G(--s--)/E
F-->H
H(--s--)/E
But, if we use E-->/F to replace the part of E(-|-)F (because according to the very beginning of the post,A-->/B AND A(-|-)B are actually the same thing ), we get,
E-->/F--> G -->H (the replaced first )
then the inference are,
E-->G-->H (this is very difference with the original above, which is not inference can be made like this)
I think over here you are making the mistake of equating F--->G
and linking it in this chain with /F--->G
In the first chain All things F are G
In the second sentence you have linked up all things "not F" are G.
They mean two different things.
If you write it according to the first sentence:
F-->G-->H
and if you link it up with E--->/F you will get:
F--->G----->H and F--->/E (contrapositive of the above sentence helps me to see the inference better)
if all of F is G and all of F is /E, then we know there is at lease a some intersection between G and E. (G (-s-)/E)
and if all of F is H and all of F is /E, the again there is a some intersection between H and /E. (H (-s-) /E)
*These statements are equivalent to the inferences you derived in your first example.
I hope this helps.