Here,weproposea spatio-translational embeddingmodel,called BoxE,that simultaneously addresses all these limitations.

Knowledge base completion (KBC) aims to automatically infer missing facts by exploiting information already present in a knowledge base (KB). A promising approach for KBC is to embed knowledge into latent spaces and make predictions from learned embeddings. However, existing embedding models are subject to at least one of the following limitations: (1) theoretical inexpressivity, (2) lack of support for prominent inference patterns (e.g., hierarchies), (3) lack of support for KBC over higher-arity relations, and (4) lack of support for incorporating logical rules. Here, we propose a spatio-translational embedding model, called BoxE, that simultaneously addresses all these limitations. BoxE embeds entities as points, and relations as a set of hyper-rectangles (or boxes), which spatially characterize basic logical properties. This seemingly simple abstraction yields a fully expressive model offering a natural encoding for many desired logical properties. BoxE can both capture and inject rules from rich classes of rule languages, going well beyond individual inference patterns. By design, BoxE naturally applies to higher-arity KBs. We conduct a detailed experimental analysis, and show that BoxE achieves state-of-the-art performance, both on benchmark knowledge graphs and on more general KBs, and we empirically show the power of integrating logical rules.

Quanshi Zhang is the corresponding author.

KBs are, however, highly incomplete, which makes their downstream use more challenging.

This paper evaluates the capabilities of 28 large language models (LLMs) to reason with 20 defeasible reasoning patterns involving generic generalizations (e.g., 'Birds fly', 'Ravens are black') central to non-monotonic logic. Generics are of special interest to linguists, philosophers, logicians, and cognitive scientists because of their complex exception-permitting behaviour and their centrality to default reasoning, cognition, and concept acquisition. We find that while several frontier models handle many default reasoning problems well, performance varies widely across models and prompting styles. Few-shot prompting modestly improves performance for some models, but chain-of-thought (CoT) prompting often leads to serious performance degradation (mean accuracy drop -11.14%, SD 15.74% in models performing above 75% accuracy in zero-shot condition, temperature 0). Most models either struggle to distinguish between defeasible and deductive inference or misinterpret generics as universal statements. These findings underscore both the promise and limits of current LLMs for default reasoning.