Exploring the Paradigm Shift from Grounding to Skolemization for Complex Query Answering on Knowledge Graphs
It addresses a fundamental challenge in knowledge graph reasoning for AI applications, representing a paradigm shift rather than an incremental improvement.
This paper tackles the tradeoff between logic fidelity and computational efficiency in complex query answering on incomplete knowledge graphs by proposing a neuro-symbolic framework called LVSA, which theoretically guarantees universality for all EFO1 queries and empirically outperforms state-of-the-art methods while reducing inference costs by orders of magnitude.
Complex Query Answering (CQA) over incomplete Knowledge Graphs (KGs), typically formalized as reasoning with Existential First-Order predicate logic with one free variable (EFO\textsubscript{1}), faces a fundamental tradeoff between logic fidelity and computational efficiency. This work establishes a Grounding-Skolemization dichotomy to systematically analyze this challenge and motivate a paradigm shift in CQA. While Grounding-based methods inherently suffer from combinatorial explosion, most Skolemization-based methods neglect to explicitly model Skolem functions and compromise logical consistency. To address these limitations, we propose the Logic-constrained Vector Symbolic Architecture (LVSA), a neuro-symbolic framework that unifies a differentiable Skolemization module and a neural negator, as well as a logical constraint-driven optimization protocol to harmonize geometric and logical requirements. Theoretically, LVSA guarantees universality for all EFO\textsubscript{1} queries with low computational complexity. Empirically, it outperforms state-of-the-art Skolemization-based methods and reduces inference costs by orders of magnitude compared to Grounding-based baselines.