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Explore the intersection of logic, probabilistic reasoning, and machine learning through this comprehensive lecture series by Professor Adnan Darwiche from UCLA. Delve into the theoretical foundations and practical applications of automated reasoning, with a unifying focus on tractable Boolean and arithmetic circuits through knowledge compilation techniques. Master fundamental concepts in Boolean logic semantics, quantified Boolean logic, and resolution methods before advancing to modern SAT solvers and DPLL algorithms. Learn about exhaustive DPLL, local search methods, and MAXSAT problems, then progress to beyond-NP complexity classes and tractable circuit representations. Study various circuit types including DNNF circuits with decomposability properties, d-DNNF circuits incorporating determinism and smoothness, OBDD binary decision diagrams, and SDD sentential decision diagrams. Examine both top-down and bottom-up knowledge compilation approaches, probabilistic extensions through PSDD circuits, and their applications in model-based diagnosis and decision explanation. Discover how to compile Bayesian network classifiers, neural networks, and random forest classifiers into tractable representations. Understand the reduction of probabilistic reasoning problems like MPE to weighted MAX-SAT and MAR to weighted model counting, while exploring arithmetic circuits for tractable reasoning. Conclude with advanced topics including query-oriented arithmetic circuits, tensor graphs, constrained SDDs, width parameters, auxiliary variables, and extended resolution techniques.
