Logic in the Talmud

Is it publicly available?
If not, why not?

Definitely available. Buy on Amazon

Why was the series (mostly) written in English?

Sorry, my mistake.

Thank you. I would love to understand more.
The structure of the Gemara seems to be built on arguments and conclusions, but many times it seems to contradict logical necessity. Sometimes it seems unnecessary, sometimes it is only possible, and sometimes it even seems the exact opposite, etc. How can I understand the Gemara with my tools? In addition, how do you use modern logical tools? It did not exist in their time, at least the awareness of them?
Thank you.

This does not contradict logic, but arguments in everyday contexts are not necessarily logical arguments. Some of them are analogies and generalizations, etc. I cannot answer such general questions. The laws of logic are conceptualizations of ways of thinking that existed before, even before someone grasped them and turned them into a logical law (even before Aristotle, everyone knew that if all chairs are made of wood and this is a chair, then it is made of wood). Modern tools continue to conceptualize ways of thinking that existed before and used them even if unconsciously.