If you look at the probability book I mentioned it uses an algebraic boolean logic notation and basic set theory to build a formal theory of inference. The first chapter is an condensed introduction to the formal logic and notation used - which is what I was struggling with following some of the more complex equations.

Having read half a book on logic and subsequently learned basic set theory has already helped read the first portion of the probability book. But then I also got really into formal logic, I found it really fascinating as a programmer and I think every person should learn it (with plenty of applications to regular life), so I decided to take a deep dive into it. The venn diagrams visualizations are what helped me the most.

I think one of things that held me back initially was my background as a programmer, it made reading the logic set notation challenging, ie the plus signs meaning disjunctions and primes negation conjunctions.