Logic and Learning

Content

This course introduces advanced concepts at the intersection of logic, knowledge representation, and machine learning. It focuses on the computer-aided creation of logical formulas, a technique with broad applications in artificial intelligence, databases, verification, and knowledge representation and reasoning.

A central theme of the course is example-driven specification, where users provide positive and negative examples and the system reverse-engineers logical formulas that fit these examples. Such formulas can be used for querying data or as explainable classifiers for predicting properties of future data instances.

The course covers a range of logical formalisms, including propositional logic, predicate logic, and modal logic, and explores different learning frameworks, such as supervised learning, PAC (Probably Approximately Correct) learning, exact learning, and neural networks on graphs. Methodologically, it combines the theory of machine learning with model theory and complexity analysis to equip students with a deep understanding of learning logical formulas within various formal frameworks.