Paul,

PIsaacson wrote:the point is that the combination of the cells described in example 1 contains many potential eliminations beyond what can be discovered by just examining the end-point ALSs. Decomposition into sub-chains really squeezes the most mileage possible out of ALS chains.

Looking at the above logic diagram, I thought it might be useful to say something about the eliminations and assignments that show up, and maybe some that do not. One question might be, why do some diagrams not show the assignment of a candidate in a bi-value cell that has an elimination. The answer is based on the idea of logic scope.

Scope of Base / Cover Set Logic and EliminationsFor any base cover set logic:

The scope of the logic includes only the base and cover sets that are a part of logic, i.e., what you see.

The scope of constrained candidates is the group of all candidates in all strong (base) sets in the logic. This group of candidates is constrained by both the base and cover sets, which in turn determines eliminations and assignments.

The scope of possible eliminations and assignments caused by the constrained candidates includes all candidates in both the cover sets and base sets.

For example, if the logic causes the elimination of a candidate, and that candidate is a bi-value cell

not in the scope of logic , then the elimination does not result in the assignment of the other candidate in the bi-value set.

The scope rules can also lead to the following

subtle situation. Candidates that are in cover sets but not in bases can sometimes see each other. When they do, they could affect the logic of the constrained candidates in a way that causes an elimination somewhere else. This elimination is not a consequence of the primary constrained candidates, and is not counted.

When scope is defined this way, the logic will apply to any puzzle that has the same logic. Without the scope definition, this may not be true.

This definition of scope does allow the elimination or assignment of candidates in the base sets, but such eliminations or assignments are not necessarily cannibalistic.

..