The advent of Internet of Things (IoT) has boosted the growth in number of devices around us and kindled the possibility of umpteen number of applications. One of the major challenges in the realization of IoT applications is interoperability among various IoT devices and deployments. Thus, the need for a new architecture-comprising smart control and actuation-has been identified by many researchers. In this paper, we propose a Distributed Internet-like Architecture for Things (DIAT), which will overcome most of the obstacles in the process of large-scale expansion of IoT. It specifically addresses heterogeneity of IoT devices, and enables seamless addition of new devices across applications. In addition, we propose an usage control policy model to support security and privacy in a distributed environment. We propose a layered architecture that provides various levels of abstraction to tackle the issues such as scalability, heterogeneity, security, and interoperability. The proposed architecture is coupled with cognitive capabilities that helps in intelligent decision-making and enables automated service creation. Using a comprehensive use-case, comprising elements from multiple-application domains, we illustrate the usability of the proposed architecture.