Raven’s Progressive Matrices (RPM) are a family of psychological intelligence tests widely used for the assessment of abstract visual reasoning. From a cognitive psychology perspective, abstract reasoning in RPM tests involves constructing high-level representations from images and deriving potential relations from these representations. Therefore, rich and flexible internal representations, along with systematic relation representations in human cognition, are essential for solving RPM tests. Inspired by Vector Symbolic Architecture (VSA), a form of high-dimensional (HD) distributed representations with algebraic operations, we introduce various types of VSA-based atomic HD vectors with distinct semantic representations, including numeric values, periodic values, and logical values. Meanwhile, we propose numerical and logical relation functions as relation representations that take multiple HD attribute representations as inputs and define relations among them with strong rule expressiveness. Further, we present a Systematic Abductive Reasoning model with diverse relation representations (Rel-SAR) for solving RPMs, inspired by the original Neuro-VSA model. In our approach, visual attribute extraction and rule inference are integrated within a fully unified computational framework that leverages above various types of HD semantic representations and relation functions. Experimental results demonstrate that our model enhances task interpretability and improves the capacity for systematic abductive reasoning.