/sci/ - Science & Math » Thread #13535925

167KiB, 5204x1308, about_logic_implications.png

View Same Google iqdb SauceNAO

Math, Boolean algebra, Transitivity

What if the sequence of logic implications becomes a line? Thu 19 Aug 12:59:34 2021 No.13535925 View Reply Original Report

Quoted By: >>13535974 >>13536183

Chain (for example in sudoku) is a sequence of connected implications:
x1 -> x2 -> x3 ... -> xn
Set of solutions:
1. false -> false -> ... -> false -> true -> true -> ... -> true
2. all variables equal

All other stuff you can found on a picture.

If anyone of you already seen things like that please recommend me books or links to that.

Also you can contribute to this idea, to make it more rigorous or general.

Anonymous

View Same Google iqdb SauceNAO t12.png, 25KiB, 1521x614

Anonymous Thu 19 Aug 2021 13:28:25 No.13535974 Report

Quoted By:

>>13535925
Wouldn't the ultimate argument intersect with all other arguments at the apex intersection.
Not sure how you would map logical statements to a two dimensional space.
I have been working on a similar enough idea, but it is really for systematic thinking and not for some rigorous logic/syntax space.
A binary tree could map to all integers. If there is some way to interleave two different trees into a coordinate system. Logically speaking, there is no reason to believe any argument follows a line unless you choose some strange network to make it in. It will be some curve that is likely to terminate. I would probably start by by thinking about how to construct a generalized logic tree.
A fractal of such a tree could allow for rationals but I really don't see how you could make any typical algebraic operations meaningful. Suppose you have an argument at point (1,3) and it interacts with some argument which is either defined as (+0, /2) or (+0, -1.5) to yield a point (1,1.5) . There is absolutely no reason to believe the (+0, /2) would apply the same way to any other argument. It is also very questionable whether argument mapping could ever have some kind of reducible equivalency. A +1 argument, whatever that may be, repeated n times does not make it a +n argument. This should be pretty clear by the relationships between any two adjacent logical quasi-points.

What if the sequence of logic implications becomes a line?

View Same Google iqdb SauceNAO how to map logical implications.png, 12KiB, 384x420

What if the sequence of logic implications becomes a line? Thu 19 Aug 2021 14:59:19 No.13536183 Report

Quoted By:

>>13535925 (OP)
>Not sure how you would map logical statements to a two dimensional space.
Just follow steps:
1. Make chain
a -> b -> c -> d
2. Place points M(a), M(b), M(c), M(d) on 2d plane
3. Connect with lines M(a) to M(b), M(b) to M(c), etc.
4. Limit (maximum distance between pairs of points) to 0

What if the sequence of logic implications becomes a line?

View Same Google iqdb SauceNAO boundary of tree.png, 13KiB, 789x292

What if the sequence of logic implications becomes a line? Thu 19 Aug 2021 15:54:21 No.13536349 Report

Quoted By:

>A fractal of such a tree could allow for rationals but I really don't see how you could make any typical algebraic operations meaningful.
Maybe algebraic operations is too complex for this?

About binary tree:
We can map set of implications S like:
root -> r_1 -> r_1_1
-> r_2 -> r_2_1 -> r_2_1_1
-> r_3 -> r_3_1
-> r_3_2

to a tree. (See on picture)

We can define operation on trees (or on lists of implcations):
For example:
boudary_of(S) =
Set {r_1_1, r_2_1_1, r_3_1, r_3_2}

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches