The theory of bounded rationality takes into consideration the cognitive limitations of decision makers in accomplishing their goals and emphasizes on satisficing behaviors when searching for solutions. One of the hallmarks of rational behaviors in decision-making process is embodied in how to cope with inconsistency. Building cognitive computing systems for real world applications amounts to developing systems that possess bounded rationality. In this paper, we examine how bounded rationality is exhibited in the human cognitive capabilities in handling inconsistency and propose an initial theory on how to incorporate those capabilities into cognitive computing systems. In particular, we focus our attention on two important phenomena: ratio...