Formal logic to describe causation?

Question

I'm looking for any formal work that has been done on describing causation the way people understand it. I am not looking for logical implication, more a way to talk about "Why?" questions. Basically, does formal logic have any way to describe what it means to explain why something happened?

eg. "Why is this book open? I was reading it earlier"

I am looking for a strictly-defined operator X to describe the relationship between these two statements such that,

"I was reading it earlier." X "This book is open."

is true, and

"Macron leads France." X "This book is open"

is false.

Also, there should be wiggle-room for multiple different explanations of an event, ie., double-implication isn't going to work.

Answer 1

Relevance logicians claim that what is unsettling about these so-called paradoxes is that in each of them the antecedent seems irrelevant to the consequent.

In addition, relevance logicians have had qualms about certain inferences that classical logic makes valid. For example, consider the classically valid inference

The moon is made of green cheese. Therefore, either it is raining in Ecuador now or it is not.

Again here there seems to be a failure of relevance. The conclusion seems to have nothing to do with the premise. Relevance logicians have attempted to construct logics that reject theses and arguments that commit “fallacies of relevance”.

Relevant logicians point out that what is wrong with some of the paradoxes (and fallacies) is that is that the antecedents and consequents (or premises and conclusions) are on completely different topics.

https://plato.stanford.edu/entries/logic-relevance/