22 (Clues) / 7 (Columns) / Boolean Algebra

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Re: 22 (Clues) / 7 (Columns)

Postby SpAce » Fri Sep 04, 2020 10:15 pm

mith wrote:For the May 17 one, the strong link appears to be valid, it's just not as obvious? I can't really comment on whether the notation is fine or needs something extra, but the logic is sound.

Thank you! As far as I'm concerned, that settles it. I never claimed that my notation was trivial to understand -- just that it was correct.

The other one looks like it will give me a headache right now. :) Care to summarize the dispute?

It's the most complicated case, by far. I'm not sure if I can summarize it any better than what I wrote in my first comment. The dispute was about valid ways to use an embedded chain fragment as a node or a part of a split node. It's different from a normal nested AIC which has well-defined linking properties.

My point was that such a chain fragment has to evaluate to a switchable truth value in order to link with anything, just like any other node. To do that, I suggested adding a strongly-linked FALSE constant '!' to the chain fragment, or ANDing it with the repeated start node. (I had other suggestions too, but I've since dropped them to keep things simple.) On the other hand, eleven argued that his chain was correct without any changes.
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Re: 22 (Clues) / 7 (Columns)

Postby eleven » Fri Sep 04, 2020 10:29 pm

Have you read my post ? Maybe he will think about it, and your thanks go to nirwana.
I am really fed up to discuss things with you, where your only target is "to win". In the other thread you were right, but after your response to my apologize i had no ambition to explain, why.
btw., what's Paolos's opinion? He is not hindered by emotions ;)
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Re: 22 (Clues) / 7 (Columns)

Postby SpAce » Sat Sep 05, 2020 12:17 am

eleven wrote:Have you read my post ? Maybe he will think about it, and your thanks go to nirwana.

I didn't understand your previous post, and I don't understand this comment either. Is the bottom line that you're still claiming that my May 17 strong link was invalid? Have you found some new argument to support that? If so, please present it in an understandable form. (Note that you didn't just deny the validity of the short form but also the longer form I wrote to explain it.)

I am really fed up to discuss things with you, where your only target is "to win".

You're obviously projecting. What I care about is that the truth wins. I can see where the confusion comes from, but is it my fault that the truth happens to be mostly on my side? ;) When it isn't, I really don't want "to win", because that's a loss for everyone, especially myself. Note that I said and meant exactly that during the May 17 discussion too:

SpAce wrote:In particular, how does any of that prove the strong link (3,8)r3c6,r7c9 = (38)b8p26 wrong? Or anything about it at all? This is the fundamental question. At least one of us has the wrong answer to it, and I think it's pretty important to get it right (especially if it's me).

--
eleven wrote:In the other thread you were right

The one about the chain fragments? Really? That's news.

but after your response to my apologize i had no ambition to explain, why.

Sorry if I didn't think your apology seemed very genuine or complete. After having been banned because of your unfair provocations (and seeing that you hadn't been), I wasn't exactly in the mood for anything but a totally unambiguous apology. The same is still true, and it still seems that you don't think you owe one at all. Besides, that statement contradicts what you wrote back then:

eleven wrote:In the moment i am short of time, and it seems, that i would need some time to explain to you, why my AIC now is logically correct.

Does that say you needed time to explain why I was right?

btw., what's Paolos's opinion? He is not hindered by emotions ;)

I don't think this is the time to mock Paolo. We just saw him admit being wrong. I respect that, bot or not.
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Re: 22 (Clues) / 7 (Columns)

Postby eleven » Sat Sep 05, 2020 7:09 am

SpAce wrote:
eleven wrote:Have you read my post ? Maybe he will think about it, and your thanks go to nirwana.

I didn't understand your previous post, and I don't understand this comment either.

Yes, that's the fundamental problem.
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Re: 22 (Clues) / 7 (Columns)

Postby Ajò Dimonios » Sat Sep 05, 2020 8:16 am

Hi Mith

Since no pair 16r4c789 is present in r4c789 is different from 16 are not present in r4c789, do you agree with me that the meaning of the negation of 16r4c789 or 16r4c56 is ambiguous? In the first case the negation options also admit the possibility that 1 xor 6 are present in r4c789, in the second case the only negation option is from the suduku rules that none between 1 and 6 is present in r4c789 because they must be present in r4c56.If this ambiguity does not exist with which terminology it is possible to write the truth that arises from the previous inference (4,5,1,6) r5c3479- (16) r4c789 only the option that both 1 and 6 are not present in r4c789?

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Re: 22 (Clues) / 7 (Columns)

Postby SpAce » Sat Sep 05, 2020 11:02 am

eleven wrote:
SpAce wrote:I didn't understand your previous post, and I don't understand this comment either.

Yes, that's the fundamental problem.

Of course. If you write texts that I don't understand, I'm the problem. If I write chains that you don't understand, I'm the problem. I think everyone's getting the picture.

Once again, you're proving my point all by yourself.
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Re: 22 (Clues) / 7 (Columns)

Postby eleven » Sat Sep 05, 2020 12:43 pm

SpAce, what should i do with someone, who writes such a logical nonsense here.
It is so wrong, that i knew, that pointing it out would lead to another stupid discussion.
Fixing that would be a lot of work. And obviously no one else here is interested anyway ...
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Re: 22 (Clues) / 7 (Columns)

Postby mith » Sat Sep 05, 2020 1:23 pm

Ajò Dimonios wrote:Hi Mith

Since no pair 16r4c789 is present in r4c789 is different from 16 are not present in r4c789, do you agree with me that the meaning of the negation of 16r4c789 or 16r4c56 is ambiguous? In the first case the negation options also admit the possibility that 1 xor 6 are present in r4c789, in the second case the only negation option is from the suduku rules that none between 1 and 6 is present in r4c789 because they must be present in r4c56.If this ambiguity does not exist with which terminology it is possible to write the truth that arises from the previous inference (4,5,1,6) r5c3479- (16) r4c789 only the option that both 1 and 6 are not present in r4c789?

Paolo


There is nothing ambiguous about the negation of a (16)r4c789. There is nothing ambiguous about the negation of (1|6)r4c789. We can define them precisely.

If you stick to logical notation, everything will be clear. What you wrote above is not clear.

The negation of (16)r4c789 is NOT(1r4c789) OR NOT(1r4c789).
The negation of (1|6)r4c789 is NOT(1r4c789) AND NOT(1r4c789).

The latter allows us to conclude (16)r4c56. The former, on its own, does not. That's all there is to it.

I'm not sure why you are still discussing this. You have agreed that (16)r4c789 is not strongly linked to (16)r4c56, and thus cannot be used as a strong link in an AIC. You need a strong link or the conclusion of the AIC (that at least one end is true) is not valid. There is nothing more complicated here.
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Re: 22 (Clues) / 7 (Columns)

Postby mith » Sat Sep 05, 2020 1:35 pm

eleven wrote:SpAce, what should i do with someone, who writes such a logical nonsense here.
It is so wrong, that i knew, that pointing it out would lead to another stupid discussion.
Fixing that would be a lot of work. And obviously no one else here is interested anyway ...


SpAce, for this link, there may well be some logical truth somewhere in what you said, but NOR is not associative; you can certainly chain NOR gates together, but it's not clear from your chain of statements what the inputs are.

(The ORs, ANDs, NOTs chain is just another way of writing an AIC; no problem there.)
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Re: 22 (Clues) / 7 (Columns) / Boolean Algebra

Postby Ajò Dimonios » Sat Sep 05, 2020 1:51 pm

Since there is no ambiguity, can you answer the second question I asked?

If this ambiguity does not exist with which terminology it is possible to write the truth that arises from the previous inference (4,5,1,6) r5c3479- (16) r4c789 only the option that both 1 and 6 are not present in r4c789?


Since it is not the same as the negation of (16) r4c789.

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Re: 22 (Clues) / 7 (Columns)

Postby SpAce » Sat Sep 05, 2020 1:55 pm

mith wrote:SpAce, for this link, there may well be some logical truth somewhere in what you said, but NOR is not associative; you can certainly chain NOR gates together, but it's not clear from your chain of statements what the inputs are.

Truth be told, I took that NOR-chain directly from some online Boolean algebra calculator (*) that transformed the same input into several minimal forms. I didn't bother to work it out manually, so I don't really know if it works or not. I was genuinely surprised that it seemed so simple, so I decided to post it just for fun. If it has problems, I'm all ears.

That said, I find it pretty funny that eleven digs up such a totally irrelevant example to show how wrong I am :D


(*) Added. It was probably WolframAlpha. It assumes NOR and NAND to be n-ary operators. That would explain the associativity problem. (I don’t have time to investigate further right now. Typing this on my phone, which I hate anyway.)
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Re: 22 (Clues) / 7 (Columns)

Postby SpAce » Sat Sep 05, 2020 11:19 pm

eleven wrote:SpAce, what should i do with someone, who writes such a logical nonsense here.
It is so wrong, that i knew, that pointing it out would lead to another stupid discussion.
Fixing that would be a lot of work. And obviously no one else here is interested anyway ...

Was that your best shot?

I finally found time to work out the NOR-chain. It was just like I suspected. It works if the outer NORs are interpreted as a single n-ary operator (i.e. a multiple-input NOR-gate) instead of multiple binary operators. Thus my mistake was not reading (and writing) the small print when I copied that chain from WolframAlpha. Would you agree with that, mith?

I probably would have been more careful had I thought the whole thing was anything but a curiosity. Of course I should have known that anything at all can be turned against me, when there's someone out there whose mission is to find something -- anything -- to try to embarrass me. Sorry to say, eleven, but I don't really feel embarrassed at all. (That said, I'm glad you brought it up, so I found out about the problem.)

--
My turn. Can I now get unambiguous answers about the two threads I asked about? The way I see the current situation:

May 17:

-mith has declared my strong link valid
-eleven has said something else, though I don't really understand what, and he's refused to clarify

My question: mith, did you understand what eleven said? Did it change your mind, as he implied it should?

Another one Trick SE 9.0 Puzzle:

-mith has said nothing
-eleven has said I was right???

My question: eleven, did that mean you finally accepted that neither your original nor the "corrected" version were valid AICs, but mine were? If so, then that's settled. If it didn't mean that, then I'd like to hear mith's opinion.
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Re: 22 (Clues) / 7 (Columns) / Boolean Algebra

Postby mith » Sun Sep 06, 2020 1:41 am

Ok, interpreted that way, yes, the logic is fine. I'm not a fan of the non-binary operators, though I shudder to think what monstrosity that would be without.
(Just because you *can* write any boolean expression using only NOR gates doesn't mean you *should*.)

As I said, the logic of the May 17 link is clearly sound. I got the impression eleven was quibbling about the notation / lack of detail on why that link is strong, since it is not immediately obvious just from the cells involved? But I'm not entirely clear even on which puzzle he was talking about you being right, so.

I can do logic all day, but if you're looking for an arbiter of AIC notation, you're in trouble. :)
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Re: 22 (Clues) / 7 (Columns) / Boolean Algebra

Postby mith » Sun Sep 06, 2020 1:44 am

Ajò Dimonios wrote:Since there is no ambiguity, can you answer the second question I asked?

If this ambiguity does not exist with which terminology it is possible to write the truth that arises from the previous inference (4,5,1,6) r5c3479- (16) r4c789 only the option that both 1 and 6 are not present in r4c789?


Since it is not the same as the negation of (16) r4c789.

Paolo


(4,5,1,6)r5c3479 - (1|6)r4c789 is correct. The negation of 1 OR 6 is NOT(1) AND NOT(6) (that is, both 1 and 6 are not present). If the left side is true, (1|6)r4c789 is false.
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Re: 22 (Clues) / 7 (Columns) / Boolean Algebra

Postby eleven » Sun Sep 06, 2020 10:24 am

Is it really that hard to understand ??

The point is not, if the link is true, but if it is proved.
Any elimination chain, AIC, implication, what else, must prove, that the elimination is valid.
But SpAce's link is not proved. Depending on, what (additional) links are used, negating one side, you can follow, that the other side is false or true.

Otherwise in the current puzzle
Code: Select all
+-------------------------+-------------------------+-------------------------+
| 23467   1467    2347    | 2358    12568   123568  | 1245    12578   9       |
| 234     14      8       | 7       1259    12359   | 6       125     1245    |
| 267     9       5       | 28      4       1268    | 12      1278    3       |
+-------------------------+-------------------------+-------------------------+
| 4578    2       47      | 458     3       568     | 145     9       14568   |
| 34589   458     6       | 1       2589    2589    | 7       2358    2458    |
| 1       458     349     | 24589   25689   7       | 2345    23568   24568   |
+-------------------------+-------------------------+-------------------------+
| 256789  5678    279     | 23589   125789  4       | 12359   123567  12567   |
| 24579   457     1       | 6       2579    2359    | 8       2357    257     |
| 256789  3       279     | 2589    125789  12589   | 1259    4       12567   |
+-------------------------+-------------------------+-------------------------+

i can write
(3r1c3=3r5c1) => -3r6c3, stte,
because (looking at the solution) the link is true.
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