As computational power has continued to increase, and sensors have become more accurate, the corresponding advent of systems that are at once cognitive and immersive has arrived. These \textit{cognitive and immersive systems} (CAISs) fall squarely into the intersection of AI with HCI/HRI: such systems interact with and assist the human agents that enter them, in no small part because such systems are infused with AI able to understand and reason about these humans and their knowledge, beliefs, goals, communications, plans, etc. We herein explain our approach to engineering CAISs. We emphasize the capacity of a CAIS to develop and reason over a `theory of the mind' of its human partners. This capacity entails that the AI in question has a sophisticated model of the beliefs, knowledge, goals, desires, emotions, etc.\ of these humans. To accomplish this engineering, a formal framework of very high expressivity is needed. In our case, this framework is a \textit{cognitive event calculus}, a particular kind of quantified multi-operator modal logic, and a matching high-expressivity automated reasoner and planner. To explain, advance, and to a degree validate our approach, we show that a calculus of this type satisfies a set of formal requirements, and can enable a CAIS to understand a psychologically tricky scenario couched in what we call the \textit{cognitive polysolid framework} (CPF). We also formally show that a room that satisfies these requirements can have a useful property we term \emph{expectation of usefulness}. CPF, a sub-class of \textit{cognitive microworlds}, includes machinery able to represent and plan over not merely blocks and actions (such as seen in the primitive `blocks worlds' of old), but also over agents and their mental attitudes about both other agents and inanimate objects.

We briefly introduce herein a new form of distributed, multi-agent artificial intelligence, which we refer to as "tentacular." Tentacular AI is distinguished by six attributes, which among other things entail a capacity for reasoning and planning based in highly expressive calculi (logics), and which enlists subsidiary agents across distances circumscribed only by the reach of one or more given networks.