This paper defines logical functional models in the category of finite dimensional vector spaces over the field of real numbers. The functional models are given by functors from the free compact closed lexical category associated to a pregroup grammar. Any functional model is completely compositional and includes first order predicate logic. Each functional model is mapped to a vector space model in the sense of Kartsaklis, Sadrzadeh, et al. via a 'canonical' probability of the functional model. The logical connectives of the functional model are transferred to the vector space model where they become algebraic operators. The algebraic logical operators subsume the quantum logical operators of van Rijsbergen. The transfer provides an insight into how logical operators and other function words interpreted in abstract semantics change when implemented in vector space semantics.