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The problem of answering logical queries over incomplete knowledge graphs isreceiving significant attention in the machine learning community.Neuro-symbolic models are a promising recent approach, showing good performanceand allowing for good interpretability properties. These models rely on trainedarchitectures to execute atomic queries, combining them with modules thatsimulate the symbolic operators in queries. Unfortunately, most neuro-symbolicquery processors are limited to the so-called tree-like logical queries thatadmit a bottom-up execution, where the leaves are constant values or anchors,and the root is the target variable. Tree-like queries, while expressive, failshort to express properties in knowledge graphs that are important in practice,such as the existence of multiple edges between entities or the presence oftriangles.  We propose a framework for answering arbitrary conjunctive queries overincomplete knowledge graphs. The main idea of our method is to approximate acyclic query by an infinite family of tree-like queries, and then leverageexisting models for the latter. Our approximations achieve strong guarantees:they are complete, i.e. there are no false negatives, and optimal, i.e. theyprovide the best possible approximation using tree-like queries. Our methodrequires the approximations to be tree-like queries where the leaves areanchors or existentially quantified variables. Hence, we also show how some ofthe existing neuro-symbolic models can handle these queries, which is ofindependent interest. Experiments show that our approximation strategy achievescompetitive results, and that including queries with existentially quantifiedvariables tends to improve the general performance of these models, both ontree-like queries and on our approximation strategy.

A neuro-symbolic framework for answering conjunctive queries