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Candidates in an Alternating Inference Chain are not limited simply to cell values. They can be any true/false premise concerning the state of the Sudoku. I have edited this article to make note of that.

Professor Prune 17:08, 30 March 2008 (EDT)

Candidates & AIC Nodes

Professor Prune, You're adhering very strongly to MJ's seminal article, but it's muddying the waters I feel through the rather backhanded phrasing this leads to.

An AIC node is no more or less than a boolean identity which can be true or false. At its simplest it can consist of a single digit being true or false in a single cell but from there it can get as complicated as one has a stomach for provided it returns either true or false.

For example, for the UR chains I've had to use the notation (8#2)r1c1,r3c4 -[UR]- (5#2)r1c4,r3c1, where #2 is used to signify a count, and which translates to "if there are two 8's on one diagonal, there can't be two 5s on the other".

I feel it's better to drop the concept of candidate premsies altogether and use boolean entities as they're generally better understood. Therefore an AIC node would be defined in those terms, and we can keep to the original definition of candidates.

Dpbobelisk 18:54, 31 March 2008 (CEST)

I'm not happy with the term "candidate premises", either, but I wanted to make sure the Wikipedia reflects the terminology that's used in the greater Sudoku-solving community.

Perhaps in this case the confusion and clumsiness can be solved if we lose the word "candidate" and call the nodes in AICs simply "premises" (i.e., boolean entities that can be true or false). As you say, "candidate" then reverts to its original meaning of "one of the possible values for a cell". For candidates as used in an AIC, a Eureka expression such as (5)r2c2 translates to the premise "r2c2 has the value 5", and (5)r2c2=r2c6 translates to the strong inference "at least one of r2c2 or r2c6 must have the value 5".

I'll make this change when I next get the chance, or feel free to jump in ahead of me if you wish--I may not get the chance several days.

Professor Prune 15:19, 31 March 2008 (EDT)

OK, just updated the Candidate and Alternating Inference Chain articles to use "premise" in place of the confusing "candidate premise". I think this makes things much clearer. Thanks, Dpbobelisk.

Professor Prune 23:34, 31 March 2008 (EDT)