Spaced Out in Cyberspace? Evaluations of Computer‐Based Information1

This study draws on cognitive elaboration theory to examine when and why people evaluate computer‐based information more favorably than information from a less automated source. Half of participants received information from a computer, while half received the identical information from a less automated source. Moreover, participants were induced to be more vs. less involved in the information‐acquisition process. As predicted, participants in the low‐involvement condition evaluated the information more favorably when it came from a computer than from a less automated source. This difference was eliminated in the high‐involvement condition. Further supporting our reasoning, the interaction effect between information source and level of involvement was more pronounced for participants low, rather than high, in need for cognition.     

A Predictive Approach to Nonparametric Inference for Adaptive Sequential Sampling of Psychophysical Experiments

We present a predictive account on adaptive sequential sampling of stimulus-response relations in psychophysical experiments. Our discussion applies to experimental situations with ordinal stimuli when there is only weak structural knowledge available such that parametric modeling is no option. By introducing a certain form of partial exchangeability, we successively develop a hierarchical Bayesian model based on a mixture of Pólya urn processes. Suitable utility measures permit us to optimize the overall experimental sampling process. We provide several measures that are either based on simple count statistics or more elaborate information theoretic quantities. The actual computation of information theoretic utilities often turns out to be infeasible. This is not the case with our sampling method, which relies on an efficient algorithm to compute exact solutions of our posterior predictions and utility measures. Finally, we demonstrate the advantages of our framework on a hypothetical sampling problem.     

Bohrification of operator algebras and quantum logic

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to be families of projections indexed by a partially ordered set ${\mathcal{C}(A)}$ of appropriate commutative subalgebras of A. In fact, to achieve both maximal generality and ease of use within topos theory, we assume that A is a so-called Rickart C*-algebra and that ${\mathcal{C}(A)}$ consists of all unital commutative Rickart C*-subalgebras of A. Such families of projections form a Heyting algebra in a natural way, so that the associated propositional logic is intuitionistic: distributivity is recovered at the expense of the law of the excluded middle. Subsequently, generalizing an earlier computation for n × n matrices, we prove that the Heyting algebra thus associated to A arises as a basis for the internal Gelfand spectrum (in the sense of Banaschewski?CMulvey) of the ??Bohrification?? ${\underline A}$ of A, which is a commutative Rickart C*-algebra in the topos of functors from ${\mathcal{C}A}$ to the category of sets. We explain the relationship of this construction to partial Boolean algebras and Bruns?CLakser completions. Finally, we establish a connection between probability measures on the lattice of projections on a Hilbert space H and probability valuations on the internal Gelfand spectrum of ${\underline A}$ for A?=?B(H).