Measuring Algebraic Complexity of Text Understanding Based on Human Concept Learning

This paper advocates for a novel approach to recommend texts at various levels of difficulties based on a proposed method, the algebraic complexity of texts (ACT). Different from traditional complexity measures that mainly focus on surface features like the numbers of syllables per word, characters per word, or words per sentence, ACT draws from the perspective of human concept learning, which can reflect the complex semantic relations inside texts. To cope with the high cost of measuring ACT, the Degree-2 Hypothesis of ACT is proposed to reduce the measurement from unrestricted dimensions to three dimensions. Based on the principle of “mental anchor,” an extension of ACT and its general edition [denoted as extension of text algebraic complexity (EACT) and general extension of text algebraic complexity (GEACT)] are developed, which take keywords' and association rules' complexities into account. Finally, using the scores given by humans as a benchmark, we compare our proposed methods with linguistic models. The experimental results show the order GEACT>EACT>ACT> Linguistic models, which means GEACT performs the best, while linguistic models perform the worst. Additionally, GEACT with lower convex functions has the best ability in measuring the algebraic complexities of text understanding. It may also indicate that the human complexity curve tends to be a curve like lower convex function rather than linear functions.