In Artificial Intelligence, first-order Logic is the most basic form of knowledge representation and the fundamental theory for almost all rule-based inference mechanisms. It is the direct translation if Logic and Boole Algerbra into programming primitives that can be formulated into such a programming language, like Prolog and LISP.In this second lecture, Predicate Calculus is presented with the fundamental entities, functions and inference, including reasoning and resolution. The main difference with Propositional Calculus is that here we have the generalization of working with variables and groups of atoms. Hence, universal and existential descriptors come into play, so are the extra steps required to address these within the resolution process. This is the base of all "real" logic programming with variables and graph search algorithms. Keywords: Machine Learning, Data Analytics, AI, Artificial Intelligence, lectureVideo: https://youtu.be/a8IunNAQ3qU