This advanced course is designed to focus on the intersection between formal logic and machine learning, from both a theoretical and practical point of view. Our objective is to explore basic and advanced concepts in formal logic intended as tools to express machine learning concepts.
In the first part, we shall start with introductory material in logic ‘as a tool’, from propositional to first-order logic, concepts such as satisfiability, validity, entailment and minimization of formulas. Then we shall move to non-classical logic, and, in particular, to modal, temporal and spatial logics, extending the previous ideas to this more general context. Then, we shall introduce the concept of many-valued, classical and non-classical logic, as a further extension and generalization.
In the second part of the course, we shall move to symbolic machine learning models, and we shall focus on two key aspects: how these models can be used to learn from both tabular and non-tabular data, and how they can be seen as logical tools. Then, we shall move to the idea of logical explanations of machine learning models, with standard and advanced techniques.
The course will be organized into five classes of three hours each. Each class will be then paired with a practice, hands-on lecture, of one hour, for a total of 4 hours per day, 5 days (Monday to Friday). All practice will be guided and will be focused on solving practical problems.
Ideally, by the end of the course, the attendees will be able to design, solve, and explain an advanced machine learning problem using logical tools. Examples will include modern published results.
This school is presented by the Applied Computational Logic and Artificial Intelligence Lab at the University of Ferrara and the schools of Mathematics, Computer Science, and Applied Mathematics at the University of Witwatersrand.