Extending Complex Logical Queries on Uncertain Knowledge Graphs

TL;DR

This work extends complex logical query answering to uncertain knowledge graphs by introducing Soft Queries on Uncertain KGs (SQUK). It presents a neural-symbolic framework called SRC that combines forward inference over uncertain knowledge graph embeddings with backward calibration to mitigate prediction errors, supported by theoretical error bounds. The authors construct the SQUK dataset and show through experiments that SRC and its calibration variants outperform baseline query embeddings and symbolic methods, while LLMs struggle with uncertain soft constraints. The approach promises improved reasoning under uncertainty with practical implications for applications requiring nuanced, confidence-aware decision making over large KGs.

Abstract

The study of machine learning-based logical query answering enables reasoning with large-scale and incomplete knowledge graphs. This paper advances this area of research by addressing the uncertainty inherent in knowledge. While the uncertain nature of knowledge is widely recognized in the real world, it does not align seamlessly with the first-order logic that underpins existing studies. To bridge this gap, we explore the soft queries on uncertain knowledge, inspired by the framework of soft constraint programming. We propose a neural symbolic approach that incorporates both forward inference and backward calibration to answer soft queries on large-scale, incomplete, and uncertain knowledge graphs. Theoretical discussions demonstrate that our method avoids catastrophic cascading errors in the forward inference while maintaining the same complexity as state-of-the-art symbolic methods for complex logical queries. Empirical results validate the superior performance of our backward calibration compared to extended query embedding methods and neural symbolic approaches.

Figures (4)

• Figure 1: (a) Examples of two soft queries in the candidate search procedure. The soft queries introduced in this paper are jointly defined by first-order logic and soft requirements. In particular, soft requirements (necessity and importance) are introduced to characterize fine-grained decision-making preferences, distinguishing them from first-order queries. (b) Incomplete uncertain KG for to what extent a candidate possesses a skill. Solid lines indicate the observed knowledge, while dashed lines indicate the unobserved data. Values indicate confidence level, where the higher value indicates the fact is more likely to be true.
• Figure 2: A toy model illustrating the process of the SRC. Each variable node is assigned a state vector, which is updated through the algorithm as edges are removed. The final state vector of the free variable is the desired.
• Figure 3: A toy model to present the process of SRC algorithm.
• Figure 4: Query structures of query types. The white, yellow, and red circles represent constant, existential, and free nodes, respectively. The negative atomic formulas are represented by red edges, while atomic formulas are represented by black edges. Like the previous naming convention ren_beta_2020yin2024rethinking, we use "P" for projection, "I" for intersection, "N" for negation, "M" for multi-edge, and "L" for existential leaf.

Theorems & Definitions (30)

• Definition 1: Uncertain knowledge graph
• Definition 2
• Definition 3: Syntax of soft queries
• Definition 4: Substitution
• Definition 5: Semantic of soft queries
• Definition 6: Utility vector
• Definition 7: Soft query graph
• Lemma 1
• Lemma 2
• Definition 8