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tlanglet
Joined: 17 Oct 2007 Posts: 2462 Location: Northern California Foothills

Posted: Thu Jul 01, 2010 7:51 pm Post subject: Questionable Logic 


Here is the code after basics for Danny's puzzle 10/07/01: VH.
Code:  ++++
 3 4 1  26 5 8  7 9 26 
 8 26 7  246 1 9  246 5 3 
 9 26 5  7 3 46  18 246 18 
++++
 46 7 2  1 46 3  5 8 9 
 46 1 3  8 9 5  246 246 7 
 5 89 89  46 2 7  3 1 46 
++++
 1 589 4689  3 468 46  24689 7 24568 
 7 58 468  9 468 2  1468 3 14568 
 2 3 4689  5 7 1  4689 46 468 
++++

Play this puzzle online at the Daily Sudoku site
Note the two AURs: AUR 89 in r67c23 & AUR 18 in r38c79
Both of these two AURs create a pseudocell (456)
Looking at the AUR 18 we make the following observations:
1. The pseudocell in r8c79 can be viewed as (46=5)
2. The contents of r9c9 can be viewed as (8=46)
3, Thus a short chain may be formed: (8=46)r9c9  (46=5)r8c79  (5=8)r8c2; r8c79,r9c3<>8
A similr step is possible for AUR 89.
Question: Is my logic valid?
Ted 

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ronk
Joined: 07 May 2006 Posts: 397

Posted: Thu Jul 01, 2010 9:46 pm Post subject: Re: Questionable Logic 


tlanglet wrote:  Looking at the AUR 18 we make the following observations:
1. The pseudocell in r8c79 can be viewed as (46=5)
2. The contents of r9c9 can be viewed as (8=46)
... 
In order to have a pair of candidates on one or both sides of a strong inference, there has to be a pair of cells. R9c9 is a single cell, so it obviously doesn't qualify. The r8c79 pseudocell is a pair of cells that behaves like a single cell, so it doesn't qualify either. 

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daj95376
Joined: 23 Aug 2008 Posts: 3855

Posted: Thu Jul 01, 2010 10:28 pm Post subject: 


ronk wrote:  In order to have a pair of candidates on one or both sides of a strong inference, there has to be a pair of cells.

Good point!
Ted: you need an ALS relationship.
(8=46)r9c89  UR(46=5)r8c79  (5=8)r8c2; r8c79,r9c3<>8 

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ronk
Joined: 07 May 2006 Posts: 397

Posted: Fri Jul 02, 2010 10:17 am Post subject: 


daj95376 wrote:  ronk wrote:  In order to have a pair of candidates on one or both sides of a strong inference, there has to be a pair of cells.

Ted: you need an ALS relationship.
(8=46)r9c89  UR(46=5)r8c79  (5=8)r8c2; r8c79,r9c3<>8 
I didn't think this exeption would surface so quickly. For the pseudocell r8c79, we have the valid strong inference (46=5) r8c79 with a pair of candidates on one side of the inference. A pseudocell behaves like a single cell, so how is this possible?
A pseudocell with three candidates is effectively an AALS, and an AALS may be doublylinked to an ALS. In this context "doublylinked" means there are two "restricted commons." As written, there is an implied logical 'and' (&) between the candidates ...
(8=4&6)r9c89  UR(4&6=5)r8c79
... at least when read lefttoright. Written below in the opposite direction, there is an implied logical 'or' () between the candidates ...
(5=46)r8c79  (46=8)r9c89 

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tlanglet
Joined: 17 Oct 2007 Posts: 2462 Location: Northern California Foothills

Posted: Fri Jul 02, 2010 11:58 am Post subject: 


Ron & Danny,
Thanks for the feedback. I need to chew on the info some more to (hopefully?) understand it since my fundamentals are still weak.
In fact, when I first saw the two patterns, I formed as ALS using the bivalue (46) in r7c6 and r9c8 respectively. However while preparing to post that solution, I got thinking about the alternate and decided to post it instead.
Thanks again..........
Ted 

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daj95376
Joined: 23 Aug 2008 Posts: 3855

Posted: Fri Jul 02, 2010 3:36 pm Post subject: 


ronk wrote:  I didn't think this exeption would surface so quickly. For the pseudocell r8c79, we have the valid strong inference (46=5) r8c79 with a pair of candidates on one side of the inference. A pseudocell behaves like a single cell, so how is this possible?
A pseudocell with three candidates is effectively an AALS, and an AALS may be doublylinked to an ALS. In this context "doublylinked" means there are two "restricted commons." As written, there is an implied logical 'and' (&) between the candidates ...
(8=4&6)r9c89  UR(4&6=5)r8c79
... at least when read lefttoright. Written below in the opposite direction, there is an implied logical 'or' () between the candidates ...
(5=46)r8c79  (46=8)r9c89 
Yes, what a mess we end up with when compact expressions are used in notation. Let's write this thing out and reduce some of the clutter.
First: UR(456)r8c79 is my interpretation  nonexclusive "or"
Second: als is really (8)r9c9 = (46)r9c89  thus the need for two cells
Leaving a lefttoright of:
(8)r9c9 = (46)r9c89  UR(46=5)r8c79
Leaving a rightto=left of:
UR(5=46)r8c79  (46)r9c89 = (8)r9c9
I give others credit for understanding the compact notation on the als, and I give them credit for understanding what is meant when I drop the () designator in the UR:
(8=46)r9c89  UR(46=5)r8c79
I don't want to think of how many &'s and 's you'd need to explain the lefttoright and righttoleft interpretations of Luke's last als term here. I still get nightmares from when Myth Jellies insisted on including the logical operators in his expressions! _ 

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ronk
Joined: 07 May 2006 Posts: 397

Posted: Fri Jul 02, 2010 5:24 pm Post subject: 


daj95376 wrote:  I give others credit for understanding the compact notation on the als, and I give them credit for understanding what is meant when I drop the () designator in the UR:
(8=46)r9c89  UR(46=5)r8c79
I don't want to think of how many &'s and 's you'd need to explain the lefttoright and righttoleft interpretations of ... 
My detailing the logic of doublylinking an AALS to an ALS is certainly not the same as suggesting logical '&' and '' symbols be used in most AICs. Did I say that? Do I otherwise post AICs using the symbols? Did I not use twice use the word "implied"?
Besides, beyond producing clutter, over half the people using the symbols would just get it wrong, like you did when ...
you wrote:  Leaving a lefttoright of:
(8)r9c9 = (46)r9c89  UR(46=5)r8c79 


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daj95376
Joined: 23 Aug 2008 Posts: 3855

Posted: Fri Jul 02, 2010 6:03 pm Post subject: 


ronk wrote:  Besides, beyond producing clutter, over half the people using the symbols would just get it wrong, like you did when ...
you wrote:  Leaving a lefttoright of:
(8)r9c9 = (46)r9c89  UR(46=5)r8c79 

Hmmmmm!!! When I was taking logic, they taught us that:
not( A or B) ==>> not(A) and not(B)
Now, if I take my expression " UR(46=5)r8c79" and spread the not operator across the operand containing the or operator, then I get the following logical expression:
If r8c79 does not contain <4> and r8c79 does not contain <6>, then r8c9 must contain <5>.
Regards, Danny
[Edit: replaced r8c79=5 with r8c9=5, and removed unnecessary comment.]
Last edited by daj95376 on Fri Jul 02, 2010 9:54 pm; edited 1 time in total 

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ronk
Joined: 07 May 2006 Posts: 397

Posted: Fri Jul 02, 2010 7:46 pm Post subject: 


daj95376 wrote:  ronk wrote:  Besides, beyond producing clutter, over half the people using the symbols would just get it wrong, like you did when ...
you wrote:  Leaving a lefttoright of:
(8)r9c9 = (46)r9c89  UR(46=5)r8c79 

Hmmmmm!!! When I was taking logic, they taught us that:
not( A or B) ==>> not(A) and not(B) 
Believe it or not, I do understand Boolean logic and I understand your POV. Maybe we should change the AIC notation name to AIBE (Alternating Inference Boolean Expression). I tend to look at chain notation as an inference stream, not a Boolean expression. That's probably also why I still prefer niceloop notation for chains, where the above would look like ...
8 r9c89 46 UR:r8c79 5
Then it's '4&6' reading lefttoright and '46' reading righttoleft, without question. IOW r9c89 holds 4 and 6 reading L2R, r8c79 holds 4 or 6 reading R2L.
BTW there's no need to yell. 

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daj95376
Joined: 23 Aug 2008 Posts: 3855

Posted: Fri Jul 02, 2010 11:59 pm Post subject: 


ronk wrote:  daj95376 wrote:  not( A or B) ==>> not(A) and not(B) 
BTW there's no need to yell. 
I'm sorry if it seemed like yelling. I'm accustomed to seeing mathematical expressions in bold. 

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