In recent years, event-driven programming languages, in particular those based on Event Condition Action (ECA) rules, have emerged as a promising paradigm for implementing ubiquitous and pervasive systems. These implementations are mostly centralized, where a single server (often in the cloud) collects and processes all the inputs from the environment. In fact, placing the computation on the nodes interacting with the environment requires suitable abstractions for effective communication and coordination of (possibly large) ensembles of these distributed components — abstractions that current ECA languages are still missing. To this end, in this paper we present AbU, a calculus for modeling and reasoning about ECA-based systems with attribute-based communication. The latter is an interaction model recently introduced for the coordination of (possibly large) families of nodes: communication is similar to broadcast but the actual receivers are selected on the spot, by means of predicates over nodes properties. Thus, the programmer can specify interactions between nodes in a declarative way, abstracting from details such as nodes identity, number, or even their existence, without the need for a central server: the computation is moved on the “edge”, thus improving reliability, scalability, privacy and security. After having defined syntax and formal semantics of AbU, we showcase its expressiveness by providing some example applications and the encoding of AbC, the archetypal calculus with attribute-based communication. Then, we focus on two key properties of reactive systems: stabilization (i.e., termination of internal steps) and confluence. For both these properties we provide formal semantic definition, sufficient syntactic conditions on AbU systems, and algorithms to statically check such conditions. Hence, AbU is both a basis for the formal analysis of event-driven architectures with attributed-based interaction, and a reference model for a full-fledged language for IoT and edge computing.