The hippocampus and entorhinal cortex encode spaces by spatially local and hexagonal grid activity patterns (place cells and grid cells), respectively. In addition, the same brain regions also implicate neural representations for nonspatial, semantic concepts (concept cells). These observations suggest that neurocomputational mechanisms for spatial knowledge and semantic concepts are related in the brain. However, the exact relationship remains to be understood. Here, we show a mathematical correspondence between a value function for goal-directed spatial navigation and an information measure for word embedding models in natural language processing. Based on this relationship, we integrate spatial and semantic computations into a neural representation model called "disentangled successor information" (DSI). DSI generates biologically plausible neural representations: spatial representations like place cells and grid cells, and concept-specific word representations which resemble concept cells. Furthermore, with DSI representations, we can perform inferences of spatial contexts and words by a common computational framework based on simple arithmetic operations. This computation can be biologically interpreted by partial modulations of cell assemblies of nongrid cells and concept cells. Our model offers a theoretical connection of spatial and semantic computations and suggests possible computational roles of hippocampal and entorhinal neural representations.