As with another answer, I am also skeptical of the distinctions made in the DIKW pyramid.
Nonetheless, a very popular machine learning approach for answering 'Why?' questions is the application of Bayesian reasoning: given a causal data model, reverse inference can be used to find the probability distribution of events which lead to a given outcome.
It could be argued that defining 'cause' in terms of distributions rather than specific concrete mechanisms is a rather limited notion of 'Why?'.
However, it may be that there are some forms of causality that we don't know how to represent, specifically 'first-hand experience'. Indeed, common usage of the term 'wisdom' generally refers to first-hand experience, rather than information gained from some other source.
The idea is that knowledge can be expressed declaratively, whereas wisdom must be derived from experience.
For an AI represented as a computer program, the distinction between declarative and first-hand experience might appear irrelevant, since in principle any experience can be encoded and made available without the program having to 'experience' it first-hand.
However, the following humorous definition of `wisdom' might perhaps shed some light on a distinction that's pertinent to AI research:
Knowledge is knowing that a tomato is a fruit.
Wisdom is knowing that you shouldn't eat it with custard.
This notion of 'Wisdom' could be said to require qualia. It is the subject of much debate whether qualia exist and/or are necessary for consciousness - see for example the thought experiment of 'The Black and White Room'.
So the notion is that there is a distinction between having a Bayesian network representation of wisdom that says: "It is 99.7% likely that putting a tomato in custard is undesirable" and the first-hand experience to the effect that it tastes odd with custard.
