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Hi,

I was confused by this statement :"Weak inference is caused by any type of link, strong or weak"

Strong inference does not always implies weak inference.

There are cases where we may have strong inference but no weak inference

See this thread : http://www.sudoku.com/forums/viewtopic.php?t=3865

Myth Jellies distinguish this third case as "Inverse Link, Converse Link, Strong-Only Link"

r.e.s. calls it "semi-strong"

Such inference may be found in Empty Rectangle for example.

regards, Jean-Christophe

ER, Almost Fish, ALS and UR can cause strong (grouped) inference without weak inference. However, a strong link causes both weak and strong inference. The explanation on this page should also mention the strong-only inference, with the aliases. If there are no takers, I will add it next weekend.

Ruud 23:23, 14 May 2007 (CEST)

Ruud said "However, a strong link causes both weak and strong inference"

This subtle distinction between link & inference is inconsistent with the definition of a strong link which is OK for me : http://www.sudopedia.org/wiki/Strong_link

The way these inference terms have been described here is plain wrong.

• A strong inference A=B strictly means that A and B can't both be false. Sometimes they can both be true
• A weak inference A-B strictly means that A and B can't both be true. OFTEN they can both be false

Only when all the candidates involved in a strong inference are bilocals in a house or bivalues in a cell will that inference automatically satisfy both these definitions. In these cases it can be freely used as either a strong or a weak inference, but not in other cases.

Take this example of a potential UR

• (123)a . (12-)b
• - - - - - - - - - -
• (12-)c . (124)d

There is a strong inference (3)a=(4)d as if they are both false we have two solutions. However, there is no automatic weak inference between them as both could be true.

With cells A and D in different boxes, there is no direct link between the two of them but there is a direct inference.

I also have reservations about whether these "converse links" are eligible in bidirectional inference chains, where we should be able to follow the logic left to right or right to left. If this can't be done then a one-sided assumption has been introduced.

Dpbobelisk 01:11, 17 May 2007 (CEST)

I agree with Dpbobelisk. These definitions are just plain wrong.

An inference is any statement or assertion concerning the state of the Sudoku that must be either true or false.

"Strong" or "weak" are attributes of the association between two premises:

Two premises are strongly linked if they cannot both be false. Or stated another way, at least one of them must be true. It may be possible that both of them are true.

Two premises are weakly linked if they cannot both be true. Or stated another way, at least one of them must be false. It may be possible that neither of them is true.

"Link" and "inference" are really the same thing.

It is not true, as the article text currently states, that chains or loops must alternate between strong and weak inferences. It is possible in some cases to make deductions where the inferences do not alternate. What is true is that where one has an inference chain alternating between strong and weak links, and the link from the starting inference and to the ending inference are both strong, this amounts to a direct strong link between the starting and ending inference, and any eliminations that would be allowed by this strong link can be performed (see Alternating Inference Chain).

Professor Prune 00:07, 26 March 2008 (EDT)

I have cleaned up the terminology usage here. I also have made it clear that while many types of strong link/inference also amount to a weak link/inference, that is not universally the case, and added Dpobelisk's UR example.

Professor Prune 15:55, 30 March 2008 (EDT)