This paper proposes three new formal models of autonomic proximity-based federation among smart objects with wireless network connectivity and services available on the Internet. Each smart object is modeled as a set of ports, each of which represents an I/O interface for a function of this smart object to interoperate with some function of another smart object. This paper first proposes our first-level formal modeling of smart objects and their federation, giving also the semantics of federation defined in a Prolog-like language. Then it proposes the second-level formal modeling using graph rewriting rules for developing application frameworks using a dynamically changing single federation, and finally, proposes the third-level formal modeling based on collectively autocatalytic sets for the development of complex application scenarios in which many smart objects are involved in mutually related more than one federation.
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