Uncover the reasons for performance differences between measurement functions (Provably)

Recently, an exciting experimental conclusion in Li et al. (Knowl Inf Syst 62(2):611-637, 1) about measures of uncertainty for knowledge bases has attracted great research interest for many scholars. However, these efforts lack solid theoretical interpretations for the experimental conclusion. The main limitation of their research is that the final experimental conclusions are only derived from experiments on three datasets, which makes it still unknown whether the conclusion is universal. In our work, we first review the mathematical theories, definitions, and tools for measuring the uncertainty of knowledge bases. Then, we provide a series of rigorous theoretical proofs to reveal the reasons for the superiority of using the knowledge amount of knowledge structure to measure the uncertainty of the knowledge bases. Combining with experiment results, we verify that knowledge amount has much better performance for measuring uncertainty of knowledge bases. Hence, we prove an empirical conclusion established through experiments from a mathematical point of view. In addition, we find that for some knowledge bases that cannot be classified by entity attributes, such as ProBase (a probabilistic taxonomy), our conclusion is still applicable. Therefore, our conclusions have a certain degree of universality and interpretability and provide a theoretical basis for measuring the uncertainty of many different types of knowledge bases, and the findings of this study have a number of important implications for future practice.