Hello Roel,

By configurations, do you refer to truth table configurations or solution terms?

I would normally be tempted to say the same thing, that if some configurations have zero unique coverage this means they are subsets of other, more informative configurations. This points me to the sufficiency analysis, but in this case the coverage is calculated for the solution terms.

Next, and this is one point of (hopefully) a future paper that is now under review, few people realise the coverage of the outcome is a different thing than the coverage of the PI chart.

If a solution term survived the minimization process, and is part of a solution model, it means it covers at least part of the empirical positive configurations, and that makes it valuable regardless of the coverage of the outcome.

Food for thought...

Adrian

Hi Adrian,

Thanks for your reply. I’m much looking forward to seeing your paper published, because I haven’t thought of differences in coverage between the PI chart and the outcome.

I was indeed talking about terms in the solution. So you’re saying that terms in the solution are empirically relevant, regardless of their coverage - because they survived the minimization. Is that correct? If so, I agree that they are empirically relevant. However, are they also logically relevant. Logically, terms in the solution with no unique coverage do not add to the explanation because everything they explain is already explained by another term in the solution. Do you follow me here or are you suggesting something else?

I think the truth table minimization is a logical exercise, not an empirical one. From that perspective, I’m not really concerned about the fact that solution terms with no unique coverage have empirical relevance. But maybe you didn’t think of your answer in terms of a difference between empirical and logical relevance.

As you said, food for thought.

Roel.

Indeed, solution terms not only survived the minimization process, but also cover (some of the) positive outcome configurations. That is, coverage of the PI chart.

It is difficult to think of solution terms explaining cases that no other solution term does, and still have zero coverage. Perhaps I could witness that in a minimal reproducible example.

But even so, since they cover empirical configurations (that no other solution term does), declaring those solution terms not important makes me wonder if the empirical configurations they cover are "relevant".

And that is a universe-question on its own...

In Schneider and Wagemann's T/ESA approach, you can have prime implicants with zero coverage, even zero raw coverage, because configurations entering minimization are not tied to empirics any longer. Whether that makes sense or not is a different question.

Outside of T/ESA, having prime implicants / terms with zero unique coverage in the solution means that they cover no row of the truth table that an alternative PI or a combination of alternative PIs does not also cover in the same model. In other words, they are logically redundant. But if these PIs are logically redundant, they cannot be causally interpreted. These PIs should not be there in the first place. Without any data or meaningful minimal working example, it's difficult to tell what exact problem you have, i.e. whether it's a data or software-related problem etc.