Computational learning theory is a branch of computer science that studies the mathematical and algorithmic underpinnings of machine learning. It provides the concepts and methods to classify the computational feasibility of different learning problems. This project lies at the intersection of computational learning theory and logic, and it builds on recently identified new connections between learning theory and universal algebra. Its high-level goals are (i) to improve our understanding of learnability for fragments of first-order logic, motivated by applications in data management and knowledge representation, and (ii) to further develop and exploit the recently identified connections with universal algebra (as well as combinatorial graph theory, finite model theory, and fixed point logics), to developing a rich technical framework for proving new results. More concretely, we will study aspects of computational learning theory for fragments of first order logic under constraints (that is, in the presence of a background theory), with applications in data management and knowledge representation.
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