Axiomatic Quantum Theory

The basis of a rigorous formal axiomatization of quantum mechanics is constructed, built upon Dirac's bra–ket notation. The system is three-sorted, with separate variables for scalars, vectors and operators. First-order quantification over all three types of variable is permitted. Economy in the axioms is effected by, e.g., assigning a single logical function * to transform (i) a scalar into its complex conjugate, (ii) a ket vector into a bra and a bra into a ket, (iii) an operator into its adjoint. The system is accompanied by a formal semantics. Further papers will deal with vector subspaces and projection operators, operators with continuous spectra, tensor products, observables, and quantum mechanical probabilities.     

Carding for the Purchase of Alcohol: I'm Tougher Than Other Clerks Are1

The present research examined whether clerks believed themselves to be more likely to card customers than “other” clerks. Store clerks (N= 121) from 23 stores of a major grocery chain rated 4 person‐product profiles of hypothetical shoppers each representing distinctive lifestyle groups. Embedded within a series of items were key questions that asked how likely it was that they and other clerks would ask for identification from the shopper for the purchase of alcohol. Across all conditions, data revealed a significant positivity bias suggesting that the clerks felt that they were much better than other clerks at determining who should be asked for identification. The data are discussed in terms of their motivational implications for the false uniqueness bias.