Nominal concepts represent things as tokens of types. We report six experiments that investigate the nature of the relations we represent between the type of thing something is (e.g. DOG) and its other properties. The experiments provide evidence that we represent principled connections between the type of thing something is (e.g. DOG) and some of its properties (k-properties; e.g. having four legs for dogs), but not other properties (t-properties; e.g. being brown for dogs). Principled connections are different from logical, statistical, and causal connections. Principled connections, (i) license the expectation that tokens of the type will generally possess the k-property, (ii) license explanation of the presence of k-properties in tokens of a type by reference to the type of thing it is, and (iii) license normative expectations concerning the presence of the k-property in tokens of the type. The experiments provide evidence for all three of these aspects of principled connections. The experiments also demonstrate that principled connections must be distinguished from merely strong statistical connections. We suggest that principled connections are one of the fundamental types of relations (in addition to logical, statistical, and causal relations) in terms of which our conceptual knowledge is structured. We argue that principled connections reveal a formal mode of understanding and explanation. This mode of understanding complements other modes of understanding that have been studied within the theory-based approach to conceptual representation. Finally, we suggest that kind representations are distinguished from representations of mere types by the representation of principled connections to k-properties.