The inverse conjunction fallacy

If people believe that some property is true of all members of a class such as sofas, then they should also believe that the same property is true of all members of a conjunctively defined subset of that class such as uncomfortable handmade sofas. A series of experiments demonstrated a failure to observe this constraint, leading to what is termed the inverse conjunction fallacy. Not only did people often express a belief in the more general statement but not in the more specific, but also when they accepted both beliefs, they were inclined to give greater confidence to the more general. It is argued that this effect underlies a number of other demonstrations of fallacious reasoning, particularly in category-based induction. Alternative accounts of the phenomenon are evaluated, and it is concluded that the effect is best interpreted in terms of intensional reasoning [Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychological Review, 90, 293–315.]

Conjunctions of social categories considered from different points of view

Conjunctions of divergent social categories may elicit emergent attributes to render the composite concept more coherent. Following Kunda, Miller & Clare, (1990) participants listed and rated attributes for people who belong to unexpected conjunctions of social categories. In order to explore the flexibility in such constructions, they were also asked to adopt the point of view of a person in one of the two categories. Experiment 1 found that when adopting the point of view of one constituent category, people tended to combine the concepts antagonistically, meaning that they attributed to members of the conjunction the more negative aspects of the opposing category. Experiment 2 showed that this polarizing effect was reduced when the point of view category was itself unusual. Strong gender stereotype differences were also found in the degree to which combinations were antagonistic. Female stereotypes as points of view generated a greater degree of integration in the conceptual combination

A Description Logic of Typicality for Conceptual Combination

We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of combining prototypical concepts, an open problem in the fields of AI and cognitive modelling. Our logic extends the logic of typicality ALC + TR, based on the notion of rational closure, by inclusions p :: T(C) v D (“we have probability p that typical Cs are Ds”), coming from the distributed semantics of probabilistic Description Logics. Additionally, it embeds a set of cognitive heuristics for concept combination. We show that the complexity of reasoning in our logic is EXPTIME-complete as in ALC

Interaction of point sources and vortices for incompressible planar fluids

We consider a new system of differential equations which is at the same time gradient and locally Hamiltonian. It is obtained by just replacing a factor in the equations of interaction for N point vortices, and it is interpreted as an interaction of N point sources. Because of the local Hamiltonian structure and the symmetries it obeys, it does possess some of the first integrals that appear in the N vortex problem. We will show that binary collisions are easily blown up in this case since the equations of motion are of first order. This method may be easily generalized to the blow up of higher order collisions. We then generalize the model further to interactions of sources and vortices.Comment: 9 page

Experimental Evidence for Quantum Structure in Cognition

We proof a theorem that shows that a collection of experimental data of membership weights of items with respect to a pair of concepts and its conjunction cannot be modeled within a classical measure theoretic weight structure in case the experimental data contain the effect called overextension. Since the effect of overextension, analogue to the well-known guppy effect for concept combinations, is abundant in all experiments testing weights of items with respect to pairs of concepts and their conjunctions, our theorem constitutes a no-go theorem for classical measure structure for common data of membership weights of items with respect to concepts and their combinations. We put forward a simple geometric criterion that reveals the non classicality of the membership weight structure and use experimentally measured membership weights estimated by subjects in experiments to illustrate our geometrical criterion. The violation of the classical weight structure is similar to the violation of the well-known Bell inequalities studied in quantum mechanics, and hence suggests that the quantum formalism and hence the modeling by quantum membership weights can accomplish what classical membership weights cannot do.Comment: 12 pages, 3 figure

Using an artificial neural network to classify multicomponent emission lines with integral field spectroscopy from SAMI and S7

Integral field spectroscopy (IFS) surveys are changing how we study galaxies and are creating vastly more spectroscopic data available than before. The large number of resulting spectra makes visual inspection of emission line fits an infeasible option. Here, we present a demonstration of an artificial neural network (ANN) that determines the number of Gaussian components needed to describe the complex emission line velocity structures observed in galaxies after being fit with LZIFU. We apply our ANN to IFS data for the S7 survey, conducted using the Wide Field Spectrograph on the ANU 2.3 m Telescope, and the SAMI Galaxy Survey, conducted using the SAMI instrument on the 4 m Anglo-Australian Telescope. We use the spectral fitting code LZIFU (Ho et al. 2016a) to fit the emission line spectra of individual spaxels from S7 and SAMI data cubes with 1-, 2- and 3-Gaussian components. We demonstrate that using an ANN is comparable to astronomers performing the same visual inspection task of determining the best number of Gaussian components to describe the physical processes in galaxies. The advantage of our ANN is that it is capable of processing the spectra for thousands of galaxies in minutes, as compared to the years this task would take individual astronomers to complete by visual inspection

Effects of classification context on categorization in natural categories

The patterns of classification of borderline instances of eight common taxonomic categories were examined under three different instructional conditions to test two predictions: first, that lack of a specified context contributes to vagueness in categorization, and second, that altering the purpose of classification can lead to greater or lesser dependence on similarity in classification. The instructional conditions contrasted purely pragmatic with more technical/quasi-legal contexts as purposes for classification, and these were compared with a no-context control. The measures of category vagueness were between-subjects disagreement and within-subjects consistency, and the measures of similarity based categorization were category breadth and the correlation of instance categorization probability with mean rated typicality, independently measured in a neutral context. Contrary to predictions, none of the measures of vagueness, reliability, category breadth, or correlation with typicality were generally affected by the instructional setting as a function of pragmatic versus technical purposes. Only one subcondition, in which a situational context was implied in addition to a purposive context, produced a significant change in categorization. Further experiments demonstrated that the effect of context was not increased when participants talked their way through the task, and that a technical context did not elicit more all-or-none categorization than did a pragmatic context. These findings place an important boundary condition on the effects of instructional context on conceptual categorization

An effect of semantic memory on immediate memory in the visual domain

The present study extends the findings of Hemmer and Steyvers (2009a) by investigating the influence of semantic memory on short-term visual memory. In an experiment we tested how prior knowledge moderates serial position effects, using familiar (vegetables) and non-familiar stimuli (random shapes). Participants (Ps) saw lists of six images; each list held images of vegetables or random shapes. Immediately after list presentation, one of the items was presented again, in a new, randomly determined size. Ps were asked to resize the image so that it was as close as possible to the size of the just presented item. Results showed that, for the familiar items (vegetables), memory for the item’s size was supported by prior knowledge of the normal size of the objects; this was not the case for the random shapes. Moreover, there was a stronger serial position effect for random shapes than vegetables suggesting that for the serial positions where memory is typically lowest, the serial position effect was moderated through the support from long-term knowledge

Modeling Concept Combinations in a Quantum-theoretic Framework

We present modeling for conceptual combinations which uses the mathematical formalism of quantum theory. Our model faithfully describes a large amount of experimental data collected by different scholars on concept conjunctions and disjunctions. Furthermore, our approach sheds a new light on long standing drawbacks connected with vagueness, or fuzziness, of concepts, and puts forward a completely novel possible solution to the 'combination problem' in concept theory. Additionally, we introduce an explanation for the occurrence of quantum structures in the mechanisms and dynamics of concepts and, more generally, in cognitive and decision processes, according to which human thought is a well structured superposition of a 'logical thought' and a 'conceptual thought', and the latter usually prevails over the former, at variance with some widespread beliefsComment: 5 pages. arXiv admin note: substantial text overlap with arXiv:1311.605

Symmetry, bifurcation and stacking of the central configurations of the planar 1+4 body problem

In this work we are interested in the central configurations of the planar 1+4 body problem where the satellites have different infinitesimal masses and two of them are diametrically opposite in a circle. We can think this problem as a stacked central configuration too. We show that the configuration are necessarily symmetric and the other sattelites has the same mass. Moreover we proved that the number of central configuration in this case is in general one, two or three and in the special case where the satellites diametrically opposite have the same mass we proved that the number of central configuration is one or two saying the exact value of the ratio of the masses that provides this bifurcation.Comment: 9 pages, 2 figures. arXiv admin note: text overlap with arXiv:1103.627