SINNet proposes a paradigm shift for rendering conversational systems and social robotics a more acceptable and trustworthy technology even when using deep learning approaches. It will focus on the verbal component of the interaction, will target the agent-user social relationship, and model the behaviors indexing the state of the social relationship between agent and user, going thus beyond the analysis of the user’s positive and negative sentiments. It implies developing easy-to-adapt and easy-to-explain neural models able to analyze the user’s behavior contributing to user- agent co-construction processes such as the ones characterizing the rapport with the agent, or the trust and affiliation in the agent, as well as to generate the agent’s answer fostering the user-agent social relationship. This SINNet project will establish interdisciplinarity as a core challenge by providing a shared formalism between complex (e.g., psychological or socio- linguistic) theories of social interactions and the underlying formalism in deep learning and language models.