The F-2 companion robot project introduces a semantic graph-based natural language inference (NLI) system designed to provide cognitive support and rehabilitation for individuals with dementia. The system is designed to enable structured interactions through a cognitive architecture, emphasizing its structured knowledge representation, dynamic context updating, and integrated rational and emotional processing. We propose a method using Principal Component Analysis (PCA) and Truncated Singular Value Decomposition (SVD) to extract latent semantic patterns from lexeme-valence data, enhancing the system’s understanding of word roles and improving semantic disambiguation. The F-2 robot’s NLI capabilities directly target adaptive cognitive training, seeking to deliver personalized and coherent interactions. While as empirical validation remains in progress, this interdisciplinary work offers a theoretical contribution to AI-driven cognitive rehabilitation technologies, that offer human-like cognitive flexibility and empathetic interaction, as well as aiming to significantly enhance the quality of life for an aging global population.