I've noticed it is often nontrivial to transcribe informal arguments into formal logic, but most introductory texts on formal logic make a show of it. Is this for pedagogical reasons only, or is there more advanced literature on this topic?
The paradoxes of implication, for me so far, have been the largest hidden trap in logic. Perhaps it is because texts strongly associate implication with if-then statements, but now I nearly want to remove implication from any logic that I would want to rely on. Negation, conjunction, and disjunction could be sufficient on their own.
I also worry about other potential hidden traps in logic, as well as the plurality of logical systems. The existence of intentional contexts seems like another hidden trap for someone who isn't aware of it. It also isn't altogether clear into which logical system one should transcribe an argument into. It is hard to see much similarity between a logic that allows "It is possible that I could be making more money than I am" and "It is possible that I'm a paper spoon." It is hard to make use of modal logic when it becomes too difficult to reign these possibilities in. Sometimes I feel lost in possible worlds just trying to articulate a mundane concept.
Is there advanced work on how to deal with these problems and others that I might not be aware of?