"Would life be more interesting if I were in AI?" Answering Counterfactuals based on Probabilistic Inductive Logic Programming

Probabilistic logic programs are logic programs where some facts hold with a specified probability. Here, we investigate these programs with a causal framework that allows counterfactual queries. Learning the program structure from observational data is usually done through heuristic search relying on statistical tests. However, these statistical tests lack information about the causal mechanism generating the data, which makes it unfeasible to use the resulting programs for counterfactual reasoning. To address this, we propose a language fragment that allows reconstructing a program from its induced distribution. This further enables us to learn programs supporting counterfactual queries.

On the Independencies Hidden in the Structure of a Probabilistic Logic Program

Pearl and Verma developed d-separation as a widely used graphical criterion to reason about the conditional independencies that are implied by the causal structure of a Bayesian network. As acyclic ground probabilistic logic programs correspond to Bayesian networks on their dependency graph, we can compute conditional independencies from d-separation in the latter. In the present paper, we generalize the reasoning above to the non-ground case. First, we abstract the notion of a probabilistic logic program away from external databases and probabilities to obtain so-called program structures. We then present a correct meta-interpreter that decides whether a certain conditional independence statement is implied by a program structure on a given external database. Finally, we give a fragment of program structures for which we obtain a completeness statement of our conditional independence oracle. We close with an experimental evaluation of our approach revealing that our meta-interpreter performs significantly faster than checking the definition of independence using exact inference in ProbLog 2.

"What if?" in Probabilistic Logic Programming

A ProbLog program is a logic program with facts that only hold with a specified probability. In this contribution we extend this ProbLog language by the ability to answer "What if" queries. Intuitively, a ProbLog program defines a distribution by solving a system of equations in terms of mutually independent predefined Boolean random variables. In the theory of causality, Judea Pearl proposes a counterfactual reasoning for such systems of equations. Based on Pearl's calculus, we provide a procedure for processing these counterfactual queries on ProbLog programs, together with a proof of correctness and a full implementation. Using the latter, we provide insights into the influence of different parameters on the scalability of inference. Finally, we also show that our approach is consistent with CP-logic, i.e. with the causal semantics for logic programs with annotated with disjunctions.