Tracking objects and estimating objects’ sizes from their interactions are challenging state estimation problems in artificial intelligence and robotics. Robotics applications, with their physical needs, demand algorithms that provide good results in limited periods of time.

This paper presents an efficient inference algorithm that uses a probabilistic relational representation of possible worlds to limit the computational cost of estimating the likelihood of a query being true. This approach is faster, and therefore more promising for real-time applications, than existing approaches, such as magic sets.

The method is based on distributional clauses, which are used to generate conditional probabilities and to estimate the likelihood of queries in a static world. This is extended to enable inference in a dynamic world where the model for state estimation is given. This last restriction is removed by adapting machine learning techniques to discern the model parameters. Experiments in virtual and physical worlds answer questions about the accuracy, efficiency, and practical applicability of the approach.

The concepts presented make for fairly challenging reading. However, a helpful appendix presents key concepts, including logic programming, distributional clauses, and a comparison with Murphy’s filtering algorithm for dynamic Bayesian networks. Throughout the paper, plentiful examples support the more theoretical definitions and theorems.

In all, this paper is likely to prove rewarding for anyone with an interest in machine learning, probabilistic reasoning, or intelligent robotics.