Probabilistic Inductive Constraint Logic

Probabilistic logic models are used ever more often to deal with the uncertain relations that are typical of the real world. However, these models usually require expensive inference and learning procedures. Very recently the problem of identifying tractable languages has come to the fore. In this paper we consider the models used by the Inductive Constraint Logic (ICL) system, namely sets of integrity constraints, and propose a probabilistic version of them. A semantics in the style of the distribution semantics is adopted, where each integrity constraint is annotated with a probability. These probabilistic constraint logic models assign a probability of being positive to interpretations. This probability can be computed in linear time in the number of ground instantiations of the constraints. Parameter learning can be performed using an L-BFGS procedure. We also propose the system PASCAL for “ProbAbiliStic inductive ConstrAint Logic” that learns both the structure and the parameters of these models. PASCAL has been tested on a process mining dataset giving promising results.