Fuzzy Logic and Arithmetical Hierarchy,II

A very simple many-valued predicate calculus is presented; a completeness theorem is proved and the arithmetical complexity of some notions concerning provability is determined.     

Promoting the Culturally Sensitive Diagnosis of Mexican Americans: Some Personal Insights

This article presents a series of personal guidelines for promoting the culturally sensitive psychiatric diagnosis of Mexican American/Chicano clients. These guidelines are primarily based on the authors' collective experiences in diagnosing and treating this population.     

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.     

Il quadro generale di una fenomenologia statunitense della musica

This article sets out the overall framework within which American music phenomenologists operates. A widely accepted definition of the word phenomenology, together with a basically eclectic attitude and a boundary issue between musicology and philosophy, is identified. The impetus to the article is provided by an anti-positivistic polemic and a plea in defence of the meaning and concreteness of musical experience. These aspects then combine in a critique of traditional musical analysis in its positivistic matrix. S.K. Langer's philosophy, as the inspiration of this polemic, is examined in the central part of the article. However, the author's distancing from the idealistic aspects of his esthetics is covered, in particular the downplaying of the sound-sensitive level and the condemnation of musicology in general. Sense and sensitive materials, wide philosophical options and concrete procedures of music analysis are what these authors look for in phenomenology as a means to reconcile humanistic and technical culture. Therefore, the article is not so much a condemnation as an attempt to refound musicology in its entirety, with particular reference to contemporary music.     

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.     

Towards authentic conversations. Authenticity in the patient-professional relationship

The purpose of this paper is to evaluate the significance of the existential notion of authenticity for medical ethics. This is done by analyzing authenticity and examining its implications for the patient-professional relationship and for ethical decision-making in medical situations. It is argued that while authenticity implies important demand for individual responsibility, which has therapeutic significance, it perpetuates ideas which are antithetical both to authentic interaction between patients and professionals and to fruitful deliberation of moral dilemmas. In order to counteract these consequences, an alternative idea of authenticity is introduced. According to this idea, authenticity is not regarded primarily as individual sovereignty, but as an ability to participate in a dialogue in which the subjectivity of both partners is respected. Such practice, based on mutual trust and responsibility, would enhance common decision-making and overcome the alienation between patients and professionals.     

Sensorimotor synchronization: Motor responses to pseudoregular auditory patterns

Musically trained and untrained subjects (N=30) were asked to synchronize their finger tapping with stimuli in auditory patterns. Each pattern comprised six successive tonal stimuli of the same duration, the first of which was accented by a different frequency. The duration of interstimulus onset intervals (ISIs) gradually increased or decreased in constant steps toward the end of the patterns. Four values of such steps were used in different trials: 20, 30, 45, and 60 msec. Various time-control mechanisms are hypothesized as being simultaneously responsible for subjects’ incorrect reproduction of the internal temporal ratios of the stimulus patterns. The mechanism of assimilation (of a central tendency) led subjects to enforce a regular (isochronous) structure on the patterns. The influence of other time-control mechanisms (distinction, subjective expression of an accent, sequential transfer) was expressed mainly in differences between intertap onset intervals (ITIs) and the corresponding ISIs at the beginning of the patterns. The duration of the first two ITIs was in the majority of the trials in an inverse ratio to the ratio of the respective ISIs. The distortions resulting from the timing mechanisms concerned were more pronounced in the performance of nonmusicians than in that of musicians.     

Modifications of the Poggendorff effect as a function of random dot textures between the verticals

In the present research, we investigated the modification of the strength of the Poggendortf illusion as a function of different densities ofrandom dot textures failing the space between the verticals. The results ofExperiment 1 show that the illusory effect is a nonlinear function ofthe texture parameterr, the ratio of black pixels to white and black pixels, with a minimum forr=0.5, approximately, and a maximum forr=0 andr=1. The results may be interpreted by an analytical model of perceptual space dynamics, in which the effect dependson the amount of interaction between points of different light intensity. A computer simulation performed by applying the analytical model to different values ofr shows a good agreement between the predictions and the experimental data. To test the hypothesis underlying the model, a second experiment was carried out to measure the magnitude of the expansion ofthe space between the verticals as a function of the parameterr. The results are consistent with the hypothesis of the model. The overall data are discussed in terms of their implications on various theories proposed for the Poggeadorff illusion.     

Quantum MV algebras

We introduce the notion of quantum MV algebra (QMV algebra) as a generalization of MV algebras and we show that the class of all effects of any Hilbert space gives rise to an example of such a structure. We investigate some properties of QMV algebras and we prove that QMV algebras represent non-idempotent extensions of orthomodular lattices.I should like to thank Prof. M.L. Dalla Chiara and Dr. P. Minari for many interesting comments and remarks. Daniele Mundici