One of the oddest thing in the machine learning and the data science community is the complete discredit of logics. The fact of the matter is that without logics nothing is possible. In fact, logic is the basis of computation. One can derive bayesian statistics from the axiomatization of logics. It is quite shocking that many statisticians never gain the foundational appreciation of logics. In fact, when one looks at decision theory they are back in the world of logics. Statistics is built on three foundational elements of mathematics: Logics, Arithmetic, and Set Theory.
The following books highlight the embedded logics in probability and statistics.
