Collective Grounding: Applying Database Techniques to Grounding Templated Models

Abstract

The process of instantiating, or "grounding", a first-order model is a fundamental component of reasoning in logic. It has been widely studied in the context of theorem proving, database theory, and artificial intelligence. Within the relational learning community, the concept of grounding has been expanded to apply to models that use more general templates in the place of first-order logical formulae. In order to perform inference, grounding of these templates is required for instantiating a distribution over possible worlds. However, because of the complex data dependencies stemming from instantiating generalized templates with interconnected data, grounding is often the key computational bottleneck to relational learning. While we motivate our work in the context of relational learning, similar issues arise in probabilistic databases, particularly those that do not make strong tuple independence assumptions. In this paper, we investigate how key techniques from relational database theory can be utilized to improve the computational efficiency of the grounding process. We introduce the notion of collective grounding which treats logical programs not as a collection of independent rules, but instead as a joint set of interdependent workloads that can be shared. We introduce the theoretical concept of collective grounding, the components necessary in a collective grounding system, implementations of these components, and show how to use database theory to speed up these components. We demonstrate collective groundings effectiveness on seven popular datasets, and show up to a 70% reduction in runtime using collective grounding. Our results are fully reproducible and all code, data, and experimental scripts are included.