Knowledge representation based approaches to AI involve encoding knowledge in a logical language and performing logical inference to derive conclusions. Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. The authors explore one possible approach to combining these two kinds of representations. They present a model theory/semantics for first order logic based on vectors of reals. They describe the model theory, discuss some interesting properties of such a system and present a simple approach to query answering.