Ajò Demonios wrote:It was clearly understood that I could not prove the existence of a strong inference with a single logical chain. To get the demonstration I need at least two steps.

I have no problem with that as long as you keep speaking in first person. We can totally agree that

you need at least two steps, if you say so. Just don't extend that claim to other people who don't share your limits. If you can't do something, it doesn't mean no one can.

The passage between the results of the two inference "or" and the inference "and" is not permitted.

??? I have no idea what you're saying. Perhaps the extra node in both implication chains got you confused. I added it behind the branching part to combine the results, because it was written that way in the AIC. I assure you, they're perfectly valid. It's not my fault if you can't see that. (Btw, if it wasn't clear, the two implication chains are one and the same chain, only demonstrating that the logic works both ways. It doesn't mean that two chains are needed. Both are separately equivalent to the AIC and to each other.)

The results of the two inferences "or" contradict each other. If it is true that r3c3 = 1 is false it can be concluded that it is false that r1c12 = 1 is false and if it is true that r1c12 = 1 is false then it can be concluded that it is false that r3c3 = 1 is false.

Can you say that in an even more complicated way? Please?

If obfuscation is your main argumentation tactic, it's working. I almost didn't even bother to read that, because it's such an utterly horrible way of saying something very simple. Assuming I can follow that at all, you're saying that -1r3c3 -> +1r1c12 and -1r1c12 -> +1r3c3. Not so hard, is it? Or in your language: it is false that it is false that it is true that it is false that it is hard.

In any case, I don't know how you draw such conclusions, but they're neither valid nor have anything to do with my chain. In the solution both 1r3c3 and 1r1c12 are false, so a false value in one (a truth) can't imply a true value in the other (a falsehood), because truths can't lie. Thus such implications are pure nonsense. More importantly, I don't see any relation to my chain. Here's the full logic of my chain written in words:

SpAce wrote:(5)r1c7 = (5,6|5,1)r12c1 - (1)(r12c1 & r3c3) = (1)r9c1|r3c9 ->singles-> (5)r1c7 => +5r1c7; stte

First strong inference: If 5r1c7 is false then either (5,6)r12c1 OR (5,1)r12c1 must be true, and vice versa: if neither (5,6)r12c1 NOR (5,1)r12c1 is true, then 5r1c7 must be true. Thus, at least one side of the strong inference must be true.

The inference is valid.First (and only) weak inference: If either (5,6)r12c1 OR (5,1)r12c1 is true, then both 1r12c1 AND 1r3c3 can't be true (at least one of them must be false), and vice versa: if both 1r12c1 AND 1r3c3 are true, then neither (5,6)r12c1 NOR (5,1)r12c1 can be true. Thus, at least one side of the weak inference must be false.

The inference is valid. (It makes no difference that 1r12c1 AND 1r3c3 can't be true together in reality. AICs don't care about such internal contradictions, as long as the links work. It just means that the chain could be written more shortly as a contradiction chain, as I already demonstrated much earlier.)

Second strong inference: If both 1r12c1 AND 1r3c3 aren't true (at least one is false), then either 1r9c1 OR 1r3c9 must be true, and vice versa: if neither 1r9c1 NOR 1r3c9 is true, then both 1r12c1 AND 1r3c3 must be true. Thus, at least one side of the strong inference must be true.

The inference is valid. (Again, the AIC doesn't care about the obvious contradiction. We could use it, however, to cut the chain and prove directly that either 1r9c1 OR 1r3c9 must be true, but that would defeat the purpose of the exercise. Besides, if you don't like that, the other AIC I wrote doesn't have such a direct contradiction.)

That concludes the relevant part of the chain which proves the derived strong link between 5r1c7 and (1r9c1 OR 1r3c9). In other words, it proves that at least one of the three must be true. If one doesn't like the ORed end-point, it's easy to turn into just one or the other, because (as backdoors) the two are equivalent: 1r9c1 <-singles-> 1r3c9, but that just complicates things unnecessarily. We already have the proof we need to proceed. (And consequently, your claim that it wasn't possible for 5r1c7 is proven false. Sorry. I don't expect you to ever admit it, but that's how it is.)

The ->singles-> implication: If either 1r9c1 OR 1r3c9 is true, then it can be proved in both cases with singles that 5r1c7 is true. Both 1r9c1 and 1r3c9 are backdoors just like 5r1c7, so all three imply each other through singles.

The implication is valid. QED.

That logic is bulletproof, unless I've suddenly turned braindead. I'm sure

you can find holes in it anyway, but it doesn't make them true.

This fact produces the result that the chain is valid only when r3c3 = 1 is false and not when r1c12 = 1 is false. Consequence of this deduction the two inferences "or" are not verified at the same time.

The only valid conclusion here is that, once again, none of what you wrote makes sense. Are you trolling on purpose, or are you serious? I can't tell.

If you're serious, I'm wondering what makes you think you're such an expert in branching AICs? I don't think I've seen a single chain from you that even attempts to use ANDed and ORed nodes, and I highly doubt they'd be correct if you did write them. With a non-existent track record, what gives you such unlimited confidence to claim my chains are incorrect? It's absurd, considering my very existent track record. All evidence indicates that you have no idea what you're talking about, yet you keep lecturing me like there's no tomorrow. It's pretty funny, actually, but it's not a good attitude for learning. For your own sake, I recommend a change of course.

Writing branching logic as correct AICs is a skill that doesn't come without a thorough understanding of Boolean logic and a lot of practice. Most people's intuition produces totally incorrect results, as we can see regularly from those who haven't bothered to learn it. It doesn't really matter as long as the underlying logic is correct and the chain is understandable, but it isn't a matter of opinion whether an AIC is correct or not. The rules are crystal-clear and easily verified, because AICs can always be turned into pure Boolean logic. As such they can be checked with truth tables or Boolean calculators, if need be. There's zero ambiguity at all for those who understand the rules.

My first branched chains were also incorrect, for the exact reason that my intuition failed me like so many others. Fortunately I got good help early on (most notably from eleven and Steve), and unlike you, I didn't spit on it. I respected the fact that they obviously knew more than me, so I listened and learned and practiced instead. That's why my mistakes are extremely rare these days, no matter how complex the logic. (Yeah, I just made one, but it makes no dent in those probabilities. Besides, I eventually found and corrected it myself.)

You'd be better off too if you listened more and talked less until you get the hang of it. You can't improve with your current attitude because you can't even see or at least admit when you're dead wrong. It also makes discussions like this very painful for all parties, even though it might be entertaining for the audience.