In pervasive and ubiquitous computing systems, human activity recognition has immense potential in a large number of application domains. Current activity recognition techniques (i) do not handle variations in sequence, concurrency and interleaving of complex activities; (ii) do not incorporate context; and (iii) require large amounts of training data. There is a lack of a unifying theoretical framework which exploits both domain knowledge and data-driven observations to infer complex activities. In this article, we propose, develop and validate a novel Context-Driven Activity Theory (CDAT) for recognizing complex activities. We develop a mechanism using probabilistic and Markov chain analysis to discover complex activity signatures and generate complex activity definitions. We also develop a Complex Activity Recognition (CAR) algorithm. It achieves an overall accuracy of 95.73% using extensive experimentation with real-life test data. CDAT utilizes context and links complex activities to situations, which reduces inference time by 32.5% and also reduces training data by 66%.