The design of automated systems for the recognition of specific human activities is among the most promising research activities in Ambient Intelligence. The literature suggests the adoption of wearable devices, relying on acceleration information to model the activities of interest and distance metrics for the comparison of such models with the run-time data. Most current solutions do not explicitly model the uncertainty associated with the recognition, but rely on crisp thresholds and comparisons which introduce brittleness and inaccuracy in the system. We propose a framework for the recognition of simple activities in which recognition uncertainty is modelled using possibility distributions. We show that reasoning about this explicitly modelled uncertainty leads to a system with enhanced recognition accuracy and precision.