Logic Embeddings for Complex Query Answering
This addresses the challenge of efficient and accurate query answering in incomplete knowledge graphs, particularly for negation queries, but is incremental as it builds on existing query embedding methods.
The paper tackles the problem of answering complex logical queries over incomplete knowledge bases by proposing Logic Embeddings, which use Skolemisation to eliminate existential variables for efficient querying, resulting in competitive speed and accuracy, outperforming on negation queries with improved uncertainty modeling as shown by a superior correlation between answer set size and embedding entropy.
Answering logical queries over incomplete knowledge bases is challenging because: 1) it calls for implicit link prediction, and 2) brute force answering of existential first-order logic queries is exponential in the number of existential variables. Recent work of query embeddings provides fast querying, but most approaches model set logic with closed regions, so lack negation. Query embeddings that do support negation use densities that suffer drawbacks: 1) only improvise logic, 2) use expensive distributions, and 3) poorly model answer uncertainty. In this paper, we propose Logic Embeddings, a new approach to embedding complex queries that uses Skolemisation to eliminate existential variables for efficient querying. It supports negation, but improves on density approaches: 1) integrates well-studied t-norm logic and directly evaluates satisfiability, 2) simplifies modeling with truth values, and 3) models uncertainty with truth bounds. Logic Embeddings are competitively fast and accurate in query answering over large, incomplete knowledge graphs, outperform on negation queries, and in particular, provide improved modeling of answer uncertainty as evidenced by a superior correlation between answer set size and embedding entropy.