OR, AND, IMPLIES.

AW wrote:Allowing that the general pattern for chaining is (where Q is to be taken generally as "some conclusion") :

((A implies Q) and (~A implies Q))

That is a fine start point, and using it as a start point will naturally lead one to want to write how to get there using similar language. The start point for an AIC is:

Assuming we want to prove Q cannot exist

Q -- {puzzle conditions}.

To my way of thinking, a good language choice should naturally mirror:

{puzzle conditions}. What language choice is a better mirror?

Clearly, since all language choices can be replaced with equivalent language choices, the choice of mirror is in the eye of the beholder. I merely see the language choice of strong and weak as mirroring the rules of the game:

Each large container can have no more than one of each candidate. - This is a weak link.

Each large container must have at least one of each candidate. - This is a strong link.

The unwritten rules:

Each cell must have at least one candidate. - A strong link.

Each cell can have no more than one candidate. - A weak link.

Certainly, one can write equivalent mirrors, using AND or using IMPLICATION - either exclusively using those operators, or using some combination of them.

Language choices for examining a problem are important, not because we cannot express the idea with other representations, but rather because the choice of language, if done carefully, serves to illuminate rather than obfuscate. All language choices have a price - they will always make some ideas harder to express, other ideas easier to express. For me, language choice comes down to:

What is more concise?

What is more clear?

What allows me to get done what I want to get done?

Perhaps the choice I prefer is best illustrated with an example:

Mirror image, using AIC, for a naked double, a hidden double, and an X wing:

1) Recognize on the puzzle grid the following:

a)A==B

b)C==D

c)B--C

d)D--A

2)write:

A==B -- C==D -- A.

3)Conclusions:

A==D

B==C

4) Conclusions are transparent, and all one needs to justify all three patterns. IMHO, this is fairly simple, and awfully elegant. Of course, those are arbitrary evaluations. As noted previously, 1c and 1d above are puzzle independent, and if we are analyzing a standard nxn sudoku, need not be listed.

Using implications, can one write down all the information considered, and reach alll the possible conclusions, as efficiently? more efficiently?

If so, then it is as good a language choice, or perhaps better.