. Stochastic logic programs (SLPs) are logic programs with labelled clauses which dene a log-linear distribution over refutations of goals. The loglinear distribution provides, by marginalisation, a distribution over variable bindings, allowing SLPs to compactly represent quite complex distributions. We analyse the fundamental statistical properties of SLPs addressing issues concerning innite derivations, `unnormalised' SLPs and impure SLPs. After detailing existing approaches to parameter estimation for log-linear models and their application to SLPs, we present a new algorithm called failure-adjusted maximisation (FAM). FAM is an instance of the EM algorithm that applies specically to normalised SLPs and provides a closed-form for computing parameter updates within an iterative maximisation approach. We empirically show that FAM works on some small examples and discuss methods for applying it to bigger problems. c 2000 Kluwer Academic Publishers. Printed in the Netherlands. ...

We examine the relation between constructive processes and the concept of causality. We observe that causality has an inherent dynamic aspect, i.e., that, in essence, causal information concerns the evolution of a domain over time. Motivated by this observation, we construct a new representation language for causal knowledge, whose semantics is defined explicitly in terms of constructive processes. This is done in a probabilistic context, where the basic steps that make up the process are allowed to have non-deterministic effects. We then show that a theory in this language defines a unique probability distribution over the possible outcomes of such a process. This result offers an appealing explanation for the usefulness of causal information and links our explicitly dynamic approach to more static causal probabilistic modeling languages, such as Bayesian networks. We also show that this language, which we have constructed to be a natural formalization of a certain kind of causal statements, is closely related to logic programming. This result demonstrates that, under an appropriate formal semantics, a rule of a normal, a disjunctive or a certain kind of probabilistic logic program can be interpreted as a description of a causal event.

Learning probabilistic models has been an important direction of research in the machine learning community, as has been learning first-order logic models. Ideally, we would like to be able to combine the two, i.e., to learn first-order probabilistic models. Because of their ability to handle uncertainty and compactly model complex domains, these models are the object of growing research interest. This research comprises three main directions: knowledge-based model construction (KBMC), stochastic logic programs (SLPs), and probabilistic relational models (PRMs). This paper surveys these approaches, and suggests opportunities for further research and improvement, particularly with regard to modifying them so they may scale to handle large amounts of training data.