Loglinear models for first-order probabilistic reasoning
This provides a framework for probabilistic reasoning in first-order logic, which is incremental as it builds on existing loglinear model techniques.
The paper tackles the problem of first-order probabilistic reasoning by applying loglinear models from probabilistic constraint logic programming, showing how Inductive Logic Programming can be used to induce model features from data while maintaining a conservative extension of first-order reasoning.
Recent work on loglinear models in probabilistic constraint logic programming is applied to first-order probabilistic reasoning. Probabilities are defined directly on the proofs of atomic formulae, and by marginalisation on the atomic formulae themselves. We use Stochastic Logic Programs (SLPs) composed of labelled and unlabelled definite clauses to define the proof probabilities. We have a conservative extension of first-order reasoning, so that, for example, there is a one-one mapping between logical and random variables. We show how, in this framework, Inductive Logic Programming (ILP) can be used to induce the features of a loglinear model from data. We also compare the presented framework with other approaches to first-order probabilistic reasoning.