# Exploring the Paradigm Shift from Grounding to Skolemization for Complex Query Answering on Knowledge Graphs

arXiv: https://arxiv.org/abs/2509.10837 · HTML: https://mlsanity.com/paper/2509.10837/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 13 Sep 2025.

## Abstract (arXiv)

Complex Query Answering (CQA) over incomplete Knowledge Graphs (KGs), typically formalized as reasoning with Existential First-Order predicate logic with one free variable (EFOtextsubscript1), 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 EFOtextsubscript1 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.