| Our everyday language is permeated with causal utterances. In-depth understanding of an event or action is associated with comprehension of the causal mechanisms that led to the event or governed the action. This dissertation gives formal underpinnings to some of the intuitive notions of causation, in the language of structural causal models. This formalism, which is tailored after the structural equation model of engineering and economics, provides a language for specifying the precise meaning of concepts such as influence, causal relevance, counterfactuals, probability of causes and probability of effects. We model actions as local modifications of causal models, that is, the replacement of a set of equations with other equations.;We sharpen our understanding of causality by developing an axiomization for causal relevance in causal models. We examine two versions of conditional causal irrelevance: probabilistic, "If we hold Z constant, changing X cannot change the probability of Y" and deterministic, "If we hold Z constant, changing X cannot alter the value of Y in any circumstance." Comparison of the behavior of these two types of relevance to the behavior of conditional independence reveals some of the fundamental differences between causation and correlation.;Finally, we demonstrate how causal models can be used to calculate quantities of interest. We provide a polynomial-time algorithm that decides, given the graph associated with a causal model, whether the causal effect of one variable on another can be determined from data obtained under controlled conditions. Whenever such a determination is feasible, then the algorithm yields a closed-form expression for the causal effect. |
