Originally Posted by FullWings
But do their "decision problems under uncertainty" include a very limited amount of time for assessment and action?
Yes.
Originally Posted by FullWings
There are finite probabilities that normal actions taken on board aircraft may have diverse undesired catastrophic results, through system failure/design/build or just plain bad luck. These probabilities are low enough for the failure modes to be discarded by the operator as unlikely and confusing and are not included in SOPs for this reason.
This is blue-sky hypothesising. As far as I can tell, none of these "low enough" "finite probabilities" have ever been estimated; neither is it clear that one could do so.
Originally Posted by FullWings
Yes, there may be a small chance that the software has failed to provide an adequate solution to a complicated multi-body problem - but what do I do about that,
If you wish to make it compulsory, you devise a provably-correct algorithm, prove it correct, and put the proof in the public domain for peer review.
And if you can't do that, you let it be advisory and let people choose what to do. And respect them for making a choice which, while different from yours, is still rational.
Originally Posted by FullWings
especially as I know that incorrect action (or inaction) will lead to a "sub-optimal safety scenario" 99.99% of the time?
You don't "know" that; in particular, you don't know about that 99.99%. By the way, that is far too often for the typical TLS's required to be assured in similar cases.
PBL