Notions of rationality and bounded rationality play important roles in research on the design and implementation of autonomous agents and multi-agent systems, for example in the context of instilling socially intelligent behavior into computing systems. However, the (formal) connection between artificial intelligence research on the design and implementation of boundedly rational and socially intelligent agents on the one hand and formal economic rationality - i.e., choice with clear and consistent preferences - or instrumental rationality - i.e., the maximization of a performance measure given an agent's knowledge - on the other hand is weak. In this paper we address this shortcoming by introducing a formal framework for designing boundedly rational agents that systematically relax instrumental rationality, and we propose a system architecture for implementing such agents.