First, causality is nothing more than a mental fact.
From a logical point of view, causality is moreover an expectation, a feature from reason, understanding, than a physical fact. If you speak at the door, at the same time somebody is opening it, it is impossible to say that the cause the door was opened was the vibrations emitted by your voice. In the universe, everything is the cause of everything. Judea Pearl (although a bit complex, you might take a look to his book about causality) noticed that, and established formal ways to define that one fact is the cause of a second. But that is based on conventions (which allows us to state formally and legally when a vaccine is the cause of the creation of inner defenses). It is impossible to state that the flap of a butterfly's wings in France will not cause a storm in Brazil in six months. According to Hume, causality is nothing more than a constant conjunction between a sequence of events which gives the impression of a necessary connection.
Second, causality provides a partial view of nature.
From a systemic point of view, an open system has multiple inputs and multiple outputs. For example, a coffee machine will produce a coffee (consequence) when you introduce a coin (apparent cause). But the fact is that the coffee is not made of the metal of the coin. The coffee is the result of several inputs (coffee, water, sugar, electricity, a plastic cup, a button signal) and it is not the only result (the machine will also waste some water, sugar, a lot of heat, and money for the seller. From the mental point of view of an individual, a button push in the web site of Amazon (cause) will produce a book on his mailbox after some days (consequence).
Reason uses such simple mechanism in order to survive: focusing on a single input of a system, and expecting a single output. That is usually enough to take decisions and survive (e.g. the dog barks --cause--, then I get far from it or it might bite me --consequence--, without considering the whole situation; that is enough to survive). Such point of view is called reductionism. The systems discipline is precisely the one that focus its discourse in the fact that systems should always be observed as a whole, and not only with a reductionist view. It should be remarked that reductionism might be considered a pejorative perspective by some writers, which is not necessarily correct. A baby just needs to cry (cause) to get some food (consequence), without need to consider the whole.
A "boolean-causality connection" would just be a mental idea of a necessary connection between two logical facts.