Semantics

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Reply Tue 17 Nov, 2009 11:05 pm
1. If #= [Fx->[[upsidedownAxFx->Fx]->Fx]] and a='x' and b=y, then #[a/b] equals...


So what I think is being asked here is all free occurences of "a" need to be replaced by the variable "b."

So there are 5 "x's" and this problem will be solved by a recognition of that the scope of upsidedown Ax is...

I agree that the first "x" is clearly outside of its scope, and that the third "x" is clearly inside it's scope, but even though the 4th and 5th "x's" are not under its scope to the same degree, they still seem to be under it.

So where do I go from here... What's it going to look like?


5. Find a sentence ! of L such that ! contains each of the logical signs in L at least once....


As for this one, would it be correct, do you think, to assume that we are referring to the major logical signs (and, or, if/then, if and only if, not...). A sentence in this context would be a formula that contains no free occurence of a variable.
 
Emil
 
Reply Tue 17 Nov, 2009 11:15 pm
@Horace phil,
Horace;104218 wrote:
1. If #= [Fx->[[upsidedownAxFx->Fx]->Fx]] and a='x' and b=y, then #[a/b] equals...


So what I think is being asked here is all free occurences of "a" need to be replaced by the variable "b."

So there are 5 "x's" and this problem will be solved by a recognition of that the scope of upsidedown Ax is...

I agree that the first "x" is clearly outside of its scope, and that the third "x" is clearly inside it's scope, but even though the 4th and 5th "x's" are not under its scope to the same degree, they still seem to be under it.

So where do I go from here... What's it going to look like?


5. Find a sentence ! of L such that ! contains each of the logical signs in L at least once....


As for this one, would it be correct, do you think, to assume that we are referring to the major logical signs (and, or, if/then, if and only if, not...). A sentence in this context would be a formula that contains no free occurence of a variable.


What does the symbols mean? You may use these symbols for convenience. I will translate your (1) into my preferred symbols:
[INDENT]1. If # = (Fx→((∀xFx)→Fx)→Fx)∧a=x∧b=y, then #(a/b) =...
[/INDENT]
 
Horace phil
 
Reply Wed 18 Nov, 2009 09:26 am
@Horace phil,
Yes, that's my understanding of them.
Unforuntaly I don't always know how to properly produce the universal qua... or the if/then on my computer...
 
Emil
 
Reply Wed 18 Nov, 2009 09:35 am
@Horace phil,
Horace;104301 wrote:
Yes, that's my understanding of them.
Unforuntaly I don't always know how to properly produce the universal qua... or the if/then on my computer...


Universal quantifier. Neither "→" or "⇒" means "if, then". They mean material conditional and logical implication respectively. (Some use other symbols.) Logical implication and material conditions correspond somewhat to if, then statements in english, but not completely. There is a difference. Don't take my word for it, read up on relevance logics etc.

I linked you to a page with the symbols. One solution is to copy/paste them when you need them. Another idea is to download the program that I had made. It makes it a lot easier to use non-standard symbols.
 
 

 
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