Tractable Probabilistic Knowledge Bases with Existence Uncertainty

A central goal of AI is to reason efficiently in domains that are both complex and uncertain. Most attempts toward this end add probability to a tractable subset of first-order logic, but this results in intractable inference. To address this, Domingos and Webb (2012) introduced tractable Markov logic (TML), the first tractable first-order probabilistic representation. Despite its surprising expressiveness, TML has a number of significant limitations. Chief among these is that it does not explicitly handle existence uncertainty, meaning that all possible worlds contain the same objects and relations. This leads to a number of conceptual problems, such as models that must contain meaningless combinations of attributes (e.g., horses with wheels). Here we propose a new formalism, tractable probabilistic knowledge bases (TPKBs), that overcomes this problem. Like TML, TPKBs use probabilistic class and part hierarchies to ensure tractability, but TPKBs have a much cleaner and user-friendly object-oriented syntax and a well-founded semantics for existence uncertainty. TML is greatly complicated by the use of probabilistic theorem proving, an inference procedure that is much more powerful than necessary. In contrast, we introduce an inference procedure specifically designed for TPKBs, which makes them far more transparent and amenable to analysis and implementation. TPKBs subsume TML and therefore essentially all tractable models, including many high-treewidth ones.