Axiomatic justifications of the utility principle: A formal investigation

It is argued that existing axiomatic theories of utility do not provide the utility principle or the principle of maximising expected utility with a formal justification. It is also argued that these theories only put mild constraints on a decision-maker in a decision-context. Finally, it is argued that the prospects are not particularly bright for finding formal non-circular arguments for the utility principle that do not rely on the law of large numbers.     

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.     

Cut-free sequent and tableau systems for propositional Diodorean modal logics

We present sound, (weakly) complete and cut-free tableau systems for the propositional normal modal logicsS4.3, S4.3.1 andS4.14. When the modality is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear discrete sequence of points; and as a branching tree where each branch is a linear discrete sequence of points.Although cut-free, the last two systems do not possess the subformula property. But for any given finite set of formulaeX the superformulae involved are always bounded by a finite set of formulaeX* _L depending only onX and the logicL. Thus each system gives a nondeterministic decision procedure for the logic in question. The completeness proofs yield deterministic decision procedures for each logic because each proof is constructive.Each tableau system has a cut-free sequent analogue proving that Gentzen's cut-elimination theorem holds for these latter systems. The techniques are due to Hintikka and Rautenberg.Presented byDov M. Gabbay     

Authenticity as a foundational principle of medical ethics

Increasingly, contemporary medical ethicists have become aware of the need to explicate a foundation for their various models of applied ethics. Many of these theories are inspired by the apparent incompatibility of patient autonomy and provider beneficence. The principle of patient autonomy derives its current primacy to a large extent from its legal origins. However, this principle seems at odds with the clinical reality. In the bioethical literature, the notion of authenticity has been proposed as an alternative foundational principle to autonomy. This article examines this proposal in reference to various existentialist philosophers (Heidegger, Sartre, Camus and Marcel). It is concluded that the principle of autonomy fails to do what it is commonly supposed to do: provide a criterion of distinction that can be invoked to settle moral controversies between patients and providers. The existentialist concept of authenticity is more promising in at least one crucial respect: It acknowledges that the essence of human life disappears from sight if life's temporal character is reduced to a series of present decisions and actions. This also implies that the very quest for a criterion that allows physicians to distinguish between sudden, unexpected decisions of their patients to be or not to be respected, without recourse to the patient's past or future, is erroneous.     

Classical geometric illusion effects with nonclassical stimuli: Angular induction from decomposing lines into point arrays

Angular induction is the process by which one line segment can bias judgment of orientation and/or collinearity of another segment, and it has been established that the magnitude of error is a determinate function of the relative angle between the two. We examined how these known relationships are affected by decomposing the induction segment into an array of scattered points. The bias that was produced by such arrays was found to be consistent with a formal model of angular induction, with the strength of the effect decreasing as the scatter among the points was increased. This decline in strength was almost linear with a logarithmic transform of the dimensions of the stimulus array. We also evaluated the hypothesis that the induction stimulus is detected by one or more channels—for example, neurons—for which the sensitivity profiles are modeled as Gabor wavelets. The change in induction strength with increasing point scatter was not predicted by a single width of channel. However, the combined activity of an ensemble of channels that differed in width did match the perceptual effects if one also stipulated that each channel would respond maximally to a fine-line stimulus.     

Local and global factors of similarity in visual search

Effects of the similarity between target and distractors in a visual search task were investigated in several experiments. Both familiar (numerals and letters) and unfamiliar (connected figures in a 5 × 5 matrix) stimuli were used. The observer had to report on the presence or absence of a target among a variable number of homogeneous distractors as fast and as accurately as possible. It was found that physical difference had the same clear effect on processing time far familiar and for unfamiliar stimuli: processing time decreased monotonically with increasing physical difference. Distractors unrelated to the target and those related to the target by a simple transformation (180° rotation, horizontal or vertical reflection) were also compared, while the physical difference was kept constant. For familiar stimuli, transformational relatedness increased processing time in comparison with that fort unrelated stimulus pairs. It was further shown in a scaling experiment that this effect could be accounted for by the amount of perceived similarity of the target-distractor pairs. For unfamiliar stimuli, transformational relatedness did have a smaller and less pronounced effect. Various comparable unrelated distractors resulted in a full range of processing times. Results from a similarity scaling experiment correlated well with the outcome of the experiments with unfamiliar stimuli. These results are interpreted in terms of an underlying continuum of perceived similarity as the basis of the speed of visual search, rather than a dichotomy of parallel versus serial processing.     

Some uniqueness results for PARAFAC2

Whereas the unique axes properties of PARAFAC1 have been examined extensively, little is known about uniqueness properties for the PARAFAC2 model for covariance matrices. This paper is concerned with uniqueness in the rank two case of PARAFAC2. For this case, Harshman and Lundy have recently shown, subject to mild assumptions, that PARAFAC2 is unique when five (covariance) matrices are analyzed. In the present paper, this result is sharpened. PARAFAC2 is shown to be usually unique with four matrices. With three matrices it is not unique unless a certain additional assumption is introduced. If, for instance, the diagonal matrices of weights are constrained to be non-negative, three matrices are enough to have uniqueness in the rank two case of PARAFAC2. The authors are obliged to Richard Harshman for stimulating this research, and to the Associate Editor and reviewers for suggesting major improvements in the presentation.