The ability to infer intentions, emotions, and other unobservable psychological states from people's behavior is a hallmark of human social cognition, and an essential capability for future Artificial Intelligence systems. The commonsense theories of psychology and sociology necessary for such inferences have been a focus of logic-based knowledge representation research, but have been difficult to employ in robust automated reasoning architectures. In this paper we model behavior interpretation as a process of logical abduction, where the reasoning task is to identify the most probable set of assumptions that logically entail the observable behavior of others, given commonsense theories of psychology and sociology. We evaluate our approach using Triangle-COPA, a benchmark suite of 100 challenge problems based on an early social psychology experiment by Fritz Heider and Marianne Simmel. Commonsense knowledge of actions, social relationships, intentions, and emotions are encoded as defeasible axioms in first-order logic. We identify sets of assumptions that logically entail observed behaviors by backchaining with these axioms to a given depth, and order these sets by their joint probability assuming conditional independence. Our approach solves almost all (91) of the 100 questions in Triangle-COPA, and demonstrates a promising approach to robust behavior interpretation that integrates both logical and probabilistic reasoning.