Human behavior recognition is one of the significant components of Ambient Assisted Living (AAL) systems and personal assistive robots allowing to improve the quality of their lives in terms of safety, autonomy, and well-being. A critical aspect of preventing dangerous situations for users, especially elderlies, is to recognize abnormal human behavior. In spite of the extensive exploration of abnormality recognition in various fields, there remain some challenges in developing effective approaches for recognizing abnormal human behaviors in AAL systems due to the limitations of data-driven and knowledge-driven approaches. In this paper, a context-aware framework combining data-driven and knowledge-driven approaches is proposed to better characterize human behaviors and recognize abnormal behaviors using commonsense reasoning while considering human behavior context. The proposed framework comprises five main modules, which leverage Long Short-Term Memory (LSTM) models and Probabilistic Answer Set Programming (PASP)-based commonsense reasoning to recognize human activities and represent abnormal human behaviors, as well as reason about those behaviors. The proposed framework is evaluated using two datasets, namely Orange4Home and UCI HAR. The obtained results indicate the capability of the proposed framework to characterize human behaviors and recognize abnormal human behaviors with high performance.