Global schemes encode symbols in overlapping fashion over all units. One possible global scheme is to view the activation states of the units, with each unit generating a real value between −1 and 1, as propositions:  State p entails state q (equivalently, p is at least as specific as q) if the activation qi of each unit i in state q satisfies pi ≤ qi ≤ 0, or qi = 0, or 0 ≤ qi ≤ pi depending on whether the activation pi of that unit in state p is negative, zero, or positive respectively. Propositional symbols can then be interpreted in terms of such states, and truth functions in terms of simple max-min operations and sign inversions performed on network states. (See Blutner, 2004; however, Blutner ultimately focuses on a localist scheme in which units represent atomic propositions and connections represent biconditionals.) Holographic neural network schemes (e.g., Manger et al. 1994; Plate 2003) can also be viewed as global; in the simplest cases these use one “giant neuron” that multiplies an input vector whose components are complex numbers by a complex-valued matrix; a component of the resultant complex-valued output vector, written in polar coordinates as reiθ, supplies a classification through the value of θ and a confidence level through the value of r. A distinctive characteristic of such networks is their ability to classify or reconstruct patterns from partial or noisy inputs.