Handling state (especially long-term) is really a struggle for LLMs right now. This issue should become easier to work with as context windows scale up in the next couple years (or months, who knows!).
I'll venture that once truly long range correlations can be managed (at scales 100-1000x what's possible with current GPTs), all the issues about logical reasoning can be answered by training on the right corpus and applying the right kinds of human guided reinforcement.