Judea Pearl, at the University of California, Los Angeles, publishes in 1988 "Probabilistic Reasoning in Intelligent Systems", a work establishing Bayesian networks as a rigorous mathematical framework for representing and computing probability and uncertainty relationships among multiple interconnected variables. Until then, artificial intelligence systems based on rigid logical rules — such as the expert systems of Feigenbaum's generation — handled poorly the uncertainty inherent to reasoning about the real world, where evidence is incomplete and causal relationships are probabilistic, not deterministic. Pearl represents these relationships as a directed graph in which each node is a variable and each connection indicates a direct probabilistic dependency, allowing efficient calculation of how evidence observed in some variables updates the probability of other related variables, even in systems with hundreds of interconnected variables. Pearl later extends this framework, in the 1990s and 2000s, into a formal, rigorous theory of causality — mathematically distinguishing correlation from causation via his "do-calculus" — providing tools that allow artificial intelligence systems to reason not only about which events tend to occur together but about what effects would result from actively intervening on a variable, a distinction fundamental for medical, economic, and data-driven public-policy applications.