In this chapter, we consider the theoretical foundations for representing knowledge in the Internet of Things context. Specifically, we consider (1) the model-theoretic semantics (i.e., extensional semantics), (2) the possible-world semantics (i.e., intensional semantics), (3) the situation semantics, and (4) the cognitive/distributional semantics. Given the peculiarities of the Internet of Things, we pay particular attention to (a) perception (i.e., how to establish a connection to the world), (b) intersubjectivity (i.e., how to align world representations), and (c) the dynamics of world knowledge (i.e., how to model events). We come to the conclusion that each of the semantic theories helps in modeling specific aspects, but does not sufficiently address all three aspects simultaneously.