Extending the role of causality in probabilistic modeling
Joost Vennekens, Marc Denecker, Maurice Bruynooghe · Lirias · 2006
Causality plays an important role in probabilistic modeling. Often, a probability distribution can be naturally described as the outcome of a causal process, in which different random variables interact through a series of non-deterministic events. However, formal tools such as Bayesian networks do not directly represent such events, but focus instead on derivate concepts such as probabilistic independencies and conditional probabilities. In this paper, we present a logic, designed from fundamental causal principles, which has a representation of such non-deterministic, probabilistic events as its basic construct. We show that Bayesian networks can be described in this language and illustrate some of its interesting properties. We then relate this logic to a certain class of probabilistic logic programming languages. We show that our logic induces a semantics for disjunctive logic programs, in which these represent non-deterministic processes. We show that logic programs under the well-founded semantics can be seen as a language of deterministic causality, which we relate to McCain & Turner’s causal theories.