Can all types of probabilistic independencies be depicted via graphs? I was going through Probabilistic Reasoning In Intelligent Systems by Judea Pearl .In chapter 3 the author tries to motivate the need for qualitative representation of independence relations, that do not require numerical equality check - $P(A,B)$ = $P(A|B)P(B)$. This he proposes because, human beings do not always depend on numerical calculations/probability estimates to reach judgements about independencies. For example, a person can conclude that the chances of a burglary at his/her home tonight is independent of the chances of war in next 10 years, without assigning any probability estimates to the individual events.
My query is, whether this claim - that independence relations are qualitative in nature - is always true. Following is an example where numerical estimates become important.
Let us have a pair of 4-sided dice.
The independence of first die roll from second is quite intuitive; the independence in this case has more to do with the process-wise independence of the two events. However,
$A$ = first die shows 1
$B$ = sum of two dice rolls is 5
Here the independence is purely due to numerical values. Causal diagram of the scenario -

shows that they are dependent. Even though the qualitative nature of the dependence remains (by virtue of the arrow), it’s the numeric values involved that make the two events independent. This independence is of a quantitative nature that’s possible due to the particular numbers involved in this context. How can such independencies be inferred from qualitative aspects alone?
 A: In your example, the independence is not obvious other than by considering the probabilities at play. This shows that humans can not always make correct statements about independence without considering the probabilities numerically. However, the way one arrives at a conclusion does not affect the binary nature of dependence, which is either present or absent and can therefore be considered qualitative.
In many circumstances, human understanding of the world may be mechanistic, which allows us to make many statements about statistical dependencies without having explicitly calculated them (e.g. there is simply no plausible mechanism connecting my daily cereal consumption with the length of the monsoon season in India).
In his subsequent works on causality, Pearl goes to great lengths to show that such mechanistic understanding can be modeled through a causal structure that encodes (conditional) independence relationships qualitatively.
In conclusion, the independencies you mention (ones that  humans can easily reason about, as well as ones that we need to check numerically) are not different in a statistical sense and can therefore be equally represented in graphical models.
