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References: Reasoning over Knowledge Graphs

  1. Knowledge Graph - Wikipedia - Covers the structure, history, and major applications of knowledge graphs, including Freebase, Wikidata, and commercial deployments. Provides essential background on the triple-store data model underpinning all KG reasoning methods.

  2. Ontology (information science) - Wikipedia - Explains formal ontologies and description logics, which form the theoretical basis for logical query languages over knowledge graphs. Connects box-embedding geometric semantics to classical AI knowledge representation.

  3. Belief propagation - Wikipedia - Describes message-passing inference on graphical models, the algorithmic ancestor of path-based KG reasoning methods such as NBFNet. Understanding sum-product message passing clarifies why Bellman-Ford-style graph propagation is a natural fit for multi-hop inference.

  4. Knowledge Graphs: Fundamentals, Techniques, and Applications - Mayank Kejriwal, Craig A. Knoblock, Pedro Szekely - MIT Press - Comprehensive graduate-level treatment of knowledge graph construction, embedding, and reasoning. Chapter 9 covers multi-hop query answering and situates Query2Box and BetaE within the broader ontological reasoning literature.

  5. Introduction to Statistical Relational Learning - Lise Getoor, Ben Taskar (eds.) - MIT Press - Foundational collection on probabilistic logic and relational learning, directly motivating differentiable rule-learning approaches (DRUM, Neural LP) covered in the path-based reasoning section. Essential context for understanding how neural KG methods relate to classical statistical relational AI.

  6. Query2Box: Reasoning over Knowledge Graphs in Vector Space Using Box Embeddings - arXiv - Introduces axis-aligned box embeddings to represent answer sets of conjunctive queries, with a learnable intersection operator. The geometric AND-as-intersection intuition is the conceptual anchor for the entire chapter's treatment of logical query answering.

  7. Beta Embeddings for Multi-Hop Logical Reasoning in Knowledge Graphs - arXiv - Extends the query-embedding paradigm to handle negation by representing entity sets as Beta distributions. Demonstrates that complement distributions naturally encode NOT, enabling full first-order existential positive query answering.

  8. Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction - arXiv - Proposes NBFNet, which initializes per-query node representations and propagates them via learnable Bellman-Ford iterations. Achieves state-of-the-art link prediction on FB15k-237 and WN18RR while remaining interpretable through path score extraction.

  9. KG-Reasoning Papers With Code - Papers With Code - Tracks reproducible benchmarks for KG completion and multi-hop reasoning, including Query2Box, BetaE, CQD, and NBFNet results on FB15k-237, WN18RR, and the EPFO query benchmark. Useful for comparing methods on standardized leaderboards with linked code.

  10. Stanford CS224W: Machine Learning with Graphs — Knowledge Graph Reasoning (Lecture 10) - Stanford University - Lecture slides and notes covering multi-hop path queries, the GQE-to-Query2Box progression, and BetaE, with visual walkthroughs of box intersection and Beta distribution complement operations. Directly complements the derivations in this chapter.