If I understand the diagrams in the article correctly (I haven't had a careful read) the correct terminology is that reasoning with new observations can be non-

If I understand the diagrams in the article correctly (I haven't had a careful read) the correct terminology is that reasoning with new observations can be non-monotonic, not that it is unsound. Non-monotonic reasoning means that the set of true consequences of a theory can both increase and decrease in cardinality, as new observations are made. A "theory" here is a set of axioms (which are assumed to be true, without further proof), and the theorems that can be derived from the axioms, under some set of rules of inference. If the rules of inference themselves are sound, then any decrease or increase of the set of true consequences of the theory is also sound. Non-monotonic reasoning is claimed to be a better match for the way humans reason under uncertainty in the real world, than classical logic (which is monotonic) because it means a reasoning agent can "change its mind" when new information comes in, and so the agent does not have to be stuck with faulty initial assumptions. This new information is in the form of "observations", which the article labels together with axioms. Technically speaking, observations are logical atoms, i.e. "facts", while axioms of a theory can be both facts and "rules" (where rules are more complex formulae composed of atoms). We normally don't directly observe new rules of the world but are left having to infer them using induction (which is not sound). New facts about the world can also be inferred: by abduction, like the thing that Sherlock Holmes does (and which is also unsound, and maps to probabilistic inference). In any case observations are not axioms, because they tend to come from a different source than axioms, which are basically made up by humans. e.g. "two parallel lines never meet" is an axiom while "things fall towards the ground" is an observation. On the other hand, it makes sense to lump observations together with axioms because they both make up the basis from which conclusions are drawn. So the author of the article is fudging it a bit but is not entirely off. tl;dr, under a non-monotonic inference framework the results of inference can change when new observations are made, and that creates no contradiction with the fact that inference steps are not taken in error. But note that all this is basically logic talk and has nothing to do with business. I was drawn to the article because of its title, but I find it has nothing to do with logical reasoning (which interests me) but is instead about thinking about business (which doesn't). I'm not sure if the framework of soundness (and completeness) and monotonicity can be directly applied to a business context.