The logics of orthoalgebras

The notion of unsharp orthoalgebra is introduced and it is proved that the category of unsharp orthoalgebras is isomorphic to the category of D-posets. A completeness theorem for some partial logics based on unsharp orthoalgebras, orthoalgebras and orthomodular posets is proved.     

Memory impairment and source misattribution in postevent misinformation experiments with short retention intervals

The four experiments reported here provide evidence that (1) misleading postevent suggestions can impair memory for details in a witnessed event and (2) subjects sometimes remember sug-gested details as things seen in the event itself. All four experiments used recall tests in which subjects were warned of the possibility that the postevent information included misleading sug-gestions and were instructed to report both what they witnessed in the event and what was men-tioned in the postevent narrative. Recall of event details was poorer on misled items than on control items, and subjects sometimes misidentified the sources of their recollections. Our re-sults suggest that these findings are not due to guessing or response biases, but rather reflect genuine memory impairment and source monitoring confusions.     

Women,men, and aggression in an egalitarian society

Vanatinai, a small island society off New Guinea, is egalitarian, with no indigenous formal systems of rank or authority. Assertiveness and autonomy are highly valued as personal qualities and equivalent for males and females. Overt aggression is condemned and violence is rare. Women were the aggressors in four out of five incidents over ten years. Sexual jealousy was the dominant motif in all five cases. This article considers, in historical contexts, indigenous concepts of the gendered person and their relations to anger, violence, and the supernatural aggression of sorcery and witchcraft. The Vanatinai case is evidence that the rarity of intragroup violence, especially of attacks by men on women, is a characteristic of egalitarian societies.An earlier version of this paper was read at the Session on Female Aggression at the American Anthropological Association Annual Meeting, Chicago, in November 1991. I would like to thank session participants, Douglas Fry, Victoria Burbank, Robert Lepowsky, Florence Lepowsky, and the anonymous reviewers forSex Roles for their helpful comments at various points. The fieldwork in Papua New Guinea on which this paper is based was carried out over a total of eighteen months in 1977–1979, 1981, and 1987. I gratefully acknowledge the financial support of the National Science Foundation, Chancellor's Patent Fund and Department of Anthropology of the University of California, Berkeley, the Papua New Guinea Institute of Applied Social and Economic Research, the National Institute of Child Health and Human Development of the National Institutes of Health, the Wenner-Gren Foundation, and the Graduate School of the University of Wisconsin, Madison.     

A simplification of a result by zellini on the maximal rank of symmetric three-way arrays

Zellini (1979, Theorem 3.1) has shown how to decompose an arbitrary symmetric matrix of ordern ×n as a linear combination of 1/2n(n+1) fixed rank one matrices, thus constructing an explicit tensor basis for the set of symmetricn ×n matrices. Zellini's decomposition is based on properties of persymmetric matrices. In the present paper, a simplified tensor basis is given, by showing that a symmetric matrix can also be decomposed in terms of 1/2n(n+1) fixed binary matrices of rank one. The decomposition implies that ann ×n ×p array consisting ofp symmetricn ×n slabs has maximal rank 1/2n(n+1). Likewise, an unconstrained INDSCAL (symmetric CANDECOMP/PARAFAC) decomposition of such an array will yield a perfect fit in 1/2n(n+1) dimensions. When the fitting only pertains to the off-diagonal elements of the symmetric matrices, as is the case in a version of PARAFAC where communalities are involved, the maximal number of dimensions can be further reduced to 1/2n(n–1). However, when the saliences in INDSCAL are constrained to be nonnegative, the tensor basis result does not apply. In fact, it is shown that in this case the number of dimensions needed can be as large asp, the number of matrices analyzed.     

Spatial compatibility of signal-response position in pointing

Two experiments are reported in which, by means of a pointing task, we studied the stimulus-position effect, i.e. the inverted U-shape form of the reaction-time function in relation to stimulus position in tasks in which stimuli and/or responses are arranged in a horizontal array. The response consisted of aiming the index finger from a central starting point at a target area on a screen. Reaction time was the main dependent variable. The spatial relation between the position of the imperative signal and the position of the response was manipulated by varying the spatial S-R compatibility and physical distance that separated the positions of stimulus and response. The stimulus-position effect was shown to depend on the compatibility of the S-R relation (Exp. 1). In Exp. 2 it was found that the modulation of the stimulus-position effect by spatial compatibility disappeared completely when the distance between the positions of stimulus and response was reduced. None of the experiments revealed that the stimulus position effect depended on signal discriminability, which renders an interpretation of this effect in terms of perceptual processes unlikely. We argue that the attentional model of spatial coding provides the most reasonable explanation of the obtained reaction-time patterns.     

Learning capacities during sleep: A preliminary study in a group of schizophrenic inpatients

The relationship between sleep and learning processes is analysed in a sample of schizophrenic patients, starting from more recent hypotheses about the function of REM sleep in learning and memory processes. This is done by means of two experiments: in the first AA. evaluate the possibility to elicit a simple motor conditional reflex acquired during daytime in different sleep stages. With the second experiment daytime learning performances are evaluated with and without a reinforcement administered during REM sleep. Results for the first experiment underline a qualitative difference between REM and nREM sleep in a reflexological perspective. In nREM sleep the conditional response is better maintained than in REM sleep. The second experiment confirms the possibility to improve daytime learning performances after an additional presentation of learning material in REM. The joint study of sleep abnormalities and learning and cognitive impairment in schizophrenic patients is finally suggested.     

A generalization of Kristof's theorem on the trace of certain matrix products

Kristof has derived a theorem on the maximum and minimum of the trace of matrix products of the form \(X_1 \hat \Gamma _1 X_2 \hat \Gamma _2 \cdots X_n \hat \Gamma _n\) where the matrices \(\hat \Gamma _i\) are diagonal and fixed and theX _i vary unrestrictedly and independently over the set of orthonormal matrices. The theorem is a useful tool in deriving maxima and minima of matrix trace functions subject to orthogonality constraints. The present paper contains a generalization of Kristof's theorem to the case where theX _i are merely required to be submatrices of orthonormal matrices and to have a specified maximum rank. The generalized theorem contains the Schwarz inequality as a special case. Various examples from the psychometric literature, illustrating the practical use of the generalized theorem, are discussed.     

Some clarifications of the CANDECOMP algorithm applied to INDSCAL

Carroll and Chang have claimed that CANDECOMP applied to symmetric matrices yields equivalent coordinate matrices, as needed for INDSCAL. Although this claim has appeared to be valid for all practical purposes, it has gone without a rigorous mathematical footing. The purpose of the present paper is to clarify CANDECOMP in this respect. It is shown that equivalent coordinate matrices are not granted at global minima when the symmetric matrices are not Gramian, or when these matrices are Gramian but the solution not globally optimal.Part of this research has been supported by The Netherlands Organization for Scientific Research (NWO), PSYCHON-grant (560-267-011).     

Semantic congruity effects in judgments of loudness

This research uses comparative judgments of the relative loudness of sounds to make a critical test of one theory of the mental representation of continuous physical attributes. The first two experiments find a semantic congruity effect, which is an interaction such that subjects can pick the louder of two loud sounds faster than the softer, and the softer of two quiet sounds faster than the louder. According to the theory under test, physical quantities are stored as points on a representational continuum, with a variance as well as a mean placement on it. The theory predicts the semantic congruity effect by assuming that the variance of placement of intensities on the representational continuum is a function of the direction of judgment: a soft sound will have less variance than a loud one when judged for softness and more when judged for loudness. Since the speed of making a judgment increases as variance decreases, the theory predicts a semantic congruity effect. However, for loudness, it can be shown that variance does not change in the manner assumed. The finding of a semantic congruity effect therefore disconfirms the theory. Alternative models are discussed. This research was supported by NSF Grant BNS 78-17442.