A Distribution Semantics for Probabilistic Term Rewriting

Probabilistic programming is becoming increasingly popular thanks to its ability to specify problems with a certain degree of uncertainty. In this work, we focus on term rewriting, a well-known computational formalism. In particular, we consider systems that combine traditional rewriting rules with probabilities. Then, we define a distribution semantics for such systems that can be used to model the probability of reducing a term to some value. We also show how to compute a set of "explanations" for a given reduction, which can be used to compute its probability. Finally, we illustrate our approach with several examples and outline a couple of extensions that may prove useful to improve the expressive power of probabilistic rewrite systems.

Explaining Explanations in Probabilistic Logic Programming

The emergence of tools based on artificial intelligence has also led to the need of producing explanations which are understandable by a human being. In some approaches, the system is not transparent (often referred to as a "black box"), making it difficult to generate appropriate explanations. In this work, though, we consider probabilistic logic programming, a combination of logic programming (for knowledge representation) and probability (to model uncertainty). In this setting, one can say that models are interpretable, which eases its understanding. However, given a particular query, the usual notion of "explanation" is associated with a set of choices, one for each random variable of the model. Unfortunately, this set does not have a causal structure and, in fact, some of the choices are actually irrelevant to the considered query. In order to overcome these shortcomings, we present an approach to explaining explanations which is based on the definition of a query-driven inference mechanism for probabilistic logic programs.

Explanations as Programs in Probabilistic Logic Programming

The generation of comprehensible explanations is an essential feature of modern artificial intelligence systems. In this work, we consider probabilistic logic programming, an extension of logic programming which can be useful to model domains with relational structure and uncertainty. Essentially, a program specifies a probability distribution over possible worlds (i.e., sets of facts). The notion of explanation is typically associated with that of a world, so that one often looks for the most probable world as well as for the worlds where the query is true. Unfortunately, such explanations exhibit no causal structure. In particular, the chain of inferences required for a specific prediction (represented by a query) is not shown. In this paper, we propose a novel approach where explanations are represented as programs that are generated from a given query by a number of unfolding-like transformations. Here, the chain of inferences that proves a given query is made explicit. Furthermore, the generated explanations are minimal (i.e., contain no irrelevant information) and can be parameterized w.r.t. a specification of visible predicates, so that the user may hide uninteresting details from explanations.