Virtual assistants are promoted by the software industry as a radically new species of tools, but a clear definition of their specific way to interact with human users missing. The explicit goal of virtual assistants is to support human users by interacting with them in a fluent way, inspired by natural human communication and collaboration, which are now well understood by human sciences. This paper suggests getting inspiration from human sciences, particularly philosophy of mind and language, to better understand how virtual assistants should interact with human users to provide the expected support. The relevant concepts are summarized into a 5 levels interaction model. This model is intended to be used to architect new developments, to specify human-system interaction, and to classify or benchmark candidate solutions.