Jeff wrote:Can you give an example of a link that can only have a strong inference? Reason for my asking is that it seems to me that a link with a strong inference will always have a weak inference.

One example from uniqueness:

vidarino wrote:Consider this grid, with a type 5 UR in R14C12.

- Code: Select all
`13* 135* 8 | 15 27 67 | 9 46 246`

12 6 4 | 18 3 9 | 5 7 28

9 57 27 | 568 268 4 | 1 3 268

----------------------+-----------------------+----------------------

135* 13* 9 | 68 68 2 | 7 45 34

567 8 67 | 4 1 3 | 2 56 9

4 2 36 | 7 9 5 | 8 1 36

----------------------+-----------------------+----------------------

3678 37 1367 | 9 67 18 | 4 2 5

28 4 12 | 3 5 18 | 6 9 7

67 9 5 | 2 4 67 | 3 8 1

Now, since one of the 5s in the UR must be true, they can be considered as forming a strong link between their respective corners.

According to current definitions, there exists the Strong Inference "if r4c2<>5 then r1c2=5" and v.v., but there is no Strong Link since "if r4c2=5 then r1c2<>5" is not also true.

One example from almost-locked-sets:

bennys wrote:

- Code: Select all
`+-------------+-------------+-------------+`

| 24 7 8 | 24 6 5 | 1 9 3 |

| 9 3 24 | 248 1 48 | 56 7 56 |

| 5 1 6 | 7 3 9 | 8 4 2 |

+-------------+-------------+-------------+

| 28 9 23 | 458 7 6 |#35 1 #45 |

|*17 6 5 | 3 9 14 | 2 8 #47 |

| 178 4 *13 | 58 2 18 | 357 6 9 |

+-------------+-------------+-------------+

| 6 5 7 | 1 4 2 | 9 3 8 |

| 14 2 14 | 9 8 3 | 67 5 67 |

| 3 8 9 | 6 5 7 | 4 2 1 |

+-------------+-------------+-------------+

A={R5C1,R6C3}

B={R4C7,R4C9,R5C9}

x=7

z=3

I'm reasonably sure you would treat both ALS sets A and B as strong nodes, but I think the option to treat them as links should also exist. Under current definitions, we have Strong Inferences "if r5c1<>7 then r6c3=3" and "if r4c7<>3 then r5c9=7" and v.v., but neither is a Strong Link.

However, if Strong Link implied only Strong Inference, there would be less confusion IMO, at least in the long run.

Jeff wrote:If we could define unanimously 'Weak Link' as a link with only a 'Weak Inference' and Strong Link' as a link with only a 'Strong Inference', the terms 'Strong Inference' and 'Weak Inference' wouldn't need to be introduced in the first place.

Maybe, but I think the inference definitions would still be useful because the (proposed) Conjugate Link term can then be defined in terms of both inferences.

Ron

P.S. If appropriate, I plan to address the balance of your post separately.