Categorization generated by extended prototypes—An axiomatic approach

We suggest a model of categorization based on prototypes. A set of entities, identified with some finite dimensional Euclidian space, is partitioned into a finite number of categories. Such a categorization is said to be generated by extended prototypes if there is a set of distinguished entities, one for each category, such that the categorization is determined by proximity to these prototypical entities. The prototypes are called extended since they are described by points in a higher dimensional space than the entities. Sufficient conditions for a categorization to be generated by extended prototypes are provided. These conditions are also necessary if the prototypes are in general position.     

Difference measurement spaces

An absolute-difference measurement space is a pair (X, e) where the real-valued function e on X² satisfies conditions which are shown in the paper to be necessary and sufficient for its representability by the absolute distance on the real line. A positive-difference measurement space is a pair (X, l), where the real-valued function l on X² satisfies conditions necessary and sufficient for its representability by positive distances on the real line. The conditions imposed on e and l make these functions extensive measurements of proximity and dominance, the two basic predicates of social enquiry. Another way of treating these conditions is to translate them to the formal language of multivalued logic. The translation is easy and the sentences obtained have plausible intuitive meanings such as reflexivity, symmetry, and transitivity. The two sets of conditions thus become formal theories of proximity and dominance. Our difference measurement spaces are relational structures for the multi-valued logic and models of the two formal theories. Thus proximity and dominance are considered dichotomous in principle and the multiple truth-values represent degrees of error. We suggest adopting multivalued logic as a framework within which the problem of measurement error can be treated together with the formal axiomatization of social and phychological theories.     

An Interactional Approach to Dysfunctional Silencing in Family Therapy

This paper presents an interactional approach to the problem of dysfunctional silencing in family therapy. Silencing is classified as dysfunctional if it satisfies two conditions: (a) it occurs repeatedly and independently of content, and (b) it functions as negative feedback that limits change in the family system. Dysfunctional silencing is defined as those efforts of one or more family members to limit change by repeatedly blocking the communication of another family member, who in turn colludes by tacitly agreeing to remain silent. The interactional approach presented utilizes conflict-resolution techniques and videotape feedback; it is illustrated by a case example.     

Taking Frege's name in vain

A widely held view about Fregean Sense has it that the determination of a sign's referent by the sign's sense is achieved viasatisfaction: the sense specifies a condition (or set of conditions) and the referent is that entity, if any, which uniquely satisfies that (set of) condition(s). This is usually held in conjunction with the claim that the sense is existentially and qualitatively independent of the referent: if the referent did not exist, or did not uniquely satisfy the sense, the sense would still exist and would still specify the same condition(s) that it actually does (and might determine a different referent than its actual one). Proponents of this view give several reasons for holding it. I describe these reasons and argue that they are not convincing. More generally, I try to show that the notion of satisfaction has no useful application within Frege's system. I then suggest an alternative account of the determination of a referent by a sense that I think is truer to Frege and more illuminating. Compared to the satisfaction view, my account construes determination as a more naturalistic and epistemically real relation between speakers and things in the world.     

Hypothesis generation, sparse categories, and the positive test strategy

We consider the situation in which a learner must induce the rule that explains an observed set of data but the hypothesis space of possible rules is not explicitly enumerated or identified. The first part of the article demonstrates that as long as hypotheses are sparse (i.e., index less than half of the possible entities in the domain) then a positive test strategy is near optimal. The second part of this article then demonstrates that a preference for sparse hypotheses (a sparsity bias) emerges as a natural consequence of the family resemblance principle; that is, it arises from the requirement that good rules index entities that are more similar to one another than they are to entities that do not satisfy the rule.     

The development of features in object concepts

According to one productive and influential approach to cognition, categorization, object recognition, and higher level cognitive processes operate on a set of fixed features, which are the output of lower level perceptual processes. In many situations, however, it is the higher level cognitive process being executed that influences the lower level features that are created. Rather than viewing the repertoire of features as being fixed by low-level processes, we present a theory in which people create features to subserve the representation and categorization of objects. Two types of category learning should be distinguished. Fixed space category learning occurs when new categorizations are representable with the available feature set. Flexible space category learning occurs when new categorizations cannot be represented with the features available. Whether fixed or flexible, learning depends on the featural contrasts and similarities between the new category to be represented and the individuals existing concepts. Fixed feature approaches face one of two problems with tasks that call for new features: If the fixed features are fairly high level and directly useful for categorization, then they will not be flexible enough to represent all objects that might be relevant for a new task. If the fixed features are small, subsymbolic fragments (such as pixels), then regularities at the level of the functional features required to accomplish categorizations will not be captured by these primitives. We present evidence of flexible perceptual changes arising from category learning and theoretical arguments for the importance of this flexibility. We describe conditions that promote feature creation and argue against interpreting them in terms of fixed features. Finally, we discuss the implications of functional features for object categorization, conceptual development, chunking, constructive induction, and formal models of dimensionality reduction.     

The response-cued completion hypothesis and the nature of residual cost in regular switch

Three experiments are presented that compare the residual cost found when shifting from one task to another under different extra-response conditions, to test whether the response is the main factor to complete mental set reconfiguration. We investigated whether residual costs can be eliminated if participants carry out a response prior to completing switch trials. In all experiments, participants were required to press an extra key during the inter-trial interval (ITI) to proceed. In experiment 1, this extra response consisted of pressing the space bar. In experiment 2, the response consisted of pressing one of the two possible keys that belonged to the alternating tasks response set. In experiment 3, the interpolated response involved pressing one of the two possible keys, not belonging to the response set of the alternating tasks. We found no residual cost in the second or the third experiments. To explain the nature of residual cost we discuss the data in the context of a response cued completion hypothesis.     

Internal approach to external sets and universes

A problem which enthusiasts ofIST, Nelson's internal set theory, usually face is how to treat external sets in the internal universe which does not contain them directly. To solve this problem, we considerBST,bounded set theory, a modification ofIST which is, briefly, a theory for the family of thoseIST sets which are members of standard sets.We show thatBST is strong enough to incorporate external sets in the internal universe in a way sufficient to develop the most advanced applications of nonstandard methods. In particular, we define inBST an enlargement of theBST universe which satisfies the axioms ofHST, an external theory close to a theory introduced by Hrbaek. HST includes Replacement and Saturation for all formulas but contradicts the Power Set and Choice axioms (either of them is incompatible with Replacement plus Saturation), therefore to get an external universe which satisfies all ofZFC minus Regularity one has to pay by a restriction of Saturation. We prove thatHST admits a system of subuniverses which modelZFC (minus Regularity but with Power Set and Choice) and Saturation in a form restricted by a fixed but arbitrary standard cardinal.Thus the proposed system of set theoretic foundations for nonstandard mathematics, based on the simple and natural axioms of the internal theoryBST, provides the treatment of external sets sufficient to carry out elaborate external constructions.Partially supported by AMS grants in 1993 and 1994 and DFG grant in 1994.Presented byRobert Goldblatt     

Bounded Revision: Two-Dimensional Belief Change Between Conservative and Moderate Revision

This paper presents the model of ‘bounded revision’ that is based on two-dimensional revision functions taking as arguments pairs consisting of an input sentence and a reference sentence. The key idea is that the input sentence is accepted as far as (and just a little further than) the reference sentence is ‘cotenable’ with it. Bounded revision satisfies the AGM axioms as well as the Same Beliefs Condition (SBC) saying that the set of beliefs accepted after the revision does not depend on the reference sentence (although the posterior belief state does depend on it). Bounded revision satisfies the Darwiche–Pearl (DP) axioms for iterated belief change. If the reference sentence is fixed to be a tautology or a contradiction, two well-known one-dimensional revision operations result. Bounded revision thus naturally fills the space between conservative revision (also known as natural revision) and moderate revision (also known as lexicographic revision). I compare this approach to the two-dimensional model of ‘revision by comparison’ investigated by Fermé and Rott (Artif Intell 157:5–47, 2004) that satisfies neither the SBC nor the DP axioms. I conclude that two-dimensional revision operations add substantially to the expressive power of qualitative approaches that do not make use of numbers as measures of degrees of belief.     

Seven independence concepts and continuous multiattribute utility functions

This paper examines seven independence concepts based on a preference relation on the set of simple probability measures defined on a set of multiattribute consequences. Three of the independence relations involve gambles and the other four are based on riskless preferences over the n-tuples in the consequence set. The main theorems state conditions under which one or more of the risky independence relations can be derived from a riskless independence relation in conjunction with other conditions. The other conditions include a risky independence condition which differs from the one(s) to be derived, the assumption that the consequence set is a convex subset of a finite-dimensional Euclidean space, and the assumption that the individual's von Neumann-Morgenstern utility function on the consequence set is continuous.     

Reliability and dimensionality of judgments of visually textured materials

We extended perceptual studies of the Brodatz set of textured materials. In the experiments, texture perception for different texture sets, viewing distances, or lighting intensities was examined. Subjects compared one pair of textures at a time. The main task was to rapidly rate all of the texture pairs on a number scale for their overall dissimilarities first and then for their dissimilarities according to six specified attributes (e.g., texture contrast). The implied dimensionality of perceptual texture space was usually at least four, rather than three. All six attributes proved to be useful predictors of overall dissimilarity, especially coarseness and regularity. The novel attribute texture lightness, an assessment of mean surface reflectance, was important when viewing conditions were wide-ranging. We were impressed by the general validity of texture judgments across subject, texture set, and comfortable viewing distances or lighting intensities. The attributes are nonorthogonal directions in four-dimensional perceptual space and are probably not narrow linear axes. In a supplementary experiment, we studied a completely different task: identifying textures from a distance. The dimensionality for this more refined task is similar to that for rating judgments, so our findings may have general application.     

What the Humean Should Say About Entanglement

Tim Maudlin has influentially argued that Humeanism about laws of nature stands in conflict with quantum mechanics. Specifically Humeanism implies the principle Separability: the complete physical state of a world is determined by the intrinsic physical state of each space‐time point. Maudlin argues Separability is violated by the entangled states posited by QM. We argue that Maudlin only establishes that a stronger principle, which we call Strong Separability, is in tension with QM. Separability is not in tension with QM. Moreover, while the Humean requires Separability to capture the core tenets of her view, there's no Humean‐specific motivation for accepting Strong Separability. We go on to give a Humean account of entangled states which satisfies Separability. The core idea is that certain quantum states depend upon the Humean mosaic in much the same way as the laws do. In fact, we offer a variant of the Best System account on which the systemization procedure that generates the laws also serves to ground these states. We show how this account works by applying it to the example of Bohmian Mechanics. The 3N‐dimensional configuration space, the world particle in it and the wave function on it are part of the best system of the Humean mosaic, which consists of N particles moving in 3‐dimensional space. We argue that this account is superior to the Humean account of Bohmian Mechanics defended by Loewer and Albert, which takes the 3N‐dimensional space, and its inhabitants, as fundamental.     

Discussion of a set of points in terms of their mutual distances

Necessary and sufficient conditions are given for a set of numbers to be the mutual distances of a set of real points in Euclidean space, and matrices are found whose ranks determine the dimension of the smallest Euclidean space containing such points. Methods are indicated for determining the configuration of these points, and for approximating to them by points in a space of lower dimensionality.This paper was written in response to suggestions by Harold Gulliksen and by M. W. Richardson. The latter is working on a psychophysical problem in which the dimensionality of a set of points whose mutual distances are available is a central idea.     

Direct measurement of the curvature of visual space

We consider the horizontal plane at eye height, that is all objects seen at the horizon. Although this plane visually degenerates into a line in the visual field, the 'depth' dimension nevertheless gives it a two-dimensional structure. We address the problem of intrinsic curvature of this plane. The classical geometric method is based on Gauss's original definition: The angular excess in a triangle equals the integral curvature over the area of the triangle. Angles were directly measured by a novel method of exocentric pointing. Experiments were performed outside, in the natural environment, under natural viewing conditions. The observers were instructed not to move from a set location and to maintain eye height, but were otherwise free to perform eye, head, and body movements. We measured the angular excess for equilateral triangles with sides of 2-20 m, the vantage position at the barycenter. We found angular excesses and deficits of up to 30 degrees. From these data we constructed the metric. The curvature changes from elliptic in near space to hyperbolic in far space. At very large distances the plane becomes parabolic.     

The Representation of Belief

I derive a sufficient condition for a belief set to be representable by a probability function: if at least one comparative confidence ordering of a certain type satisfies Scott’s axiom, then the belief set used to induce that ordering is representable. This provides support for Kenny Easwaran’s project of analyzing doxastic states in terms of belief sets rather than credences.     

The Crossover of Work‐Family Conflict From One Spouse to the Other1

In a secondary analysis of data from 220 women serving in the U.S. Air Force and their spouses, we examined the effects of job and family stressors on work‐family conflict (WFC) and family‐work conflict (FWC), focusing on the crossover of these experiences from one spouse to the other. We found positive relationships of WFC with both job and family stressors for wives and with job stressors for husbands. We also found that job and family stressors predicted FWC for wives, but not for husbands. Furthermore, spouse's support buffered the relationship between one's job stressors and the experience of WFC for wives but accelerated these relationships for husbands. Our findings support the bidirectional crossover of WFC from one spouse to another.     

Analyzing proximity matrices: The assessment of internal variation in combinatorial structure

A data analysis strategy is discussed for evaluating the degree to which a subset D of a larger object set S satisfies a particular algebraic property. Based on a set measure f(D) and a proximity function on S × S, two separate evaluation tasks, referred to as confirmatory and exploratory, are considered. In a confirmatory task the subset D is identified a priori and f(D) is compared against the distribution of f(·) over all subsets containing the same number of objects. The exploratory task, on the other hand, treats f(·) as an objective function to be optimized over all subsets of a given size. Examples of these two notions include the assessment of symmetry, cluster compactness, and the extent to which D satisfies the error-free conditions for a hierarchical model or a unidimensional scale.     

Family Strain and Adolescent Delinquency in Two Chinese Cities,Guangzhou and Hong Kong

Elucidating the conditions in which family strain takes effect in adolescent delinquency is one avenue along which to substantiate general strain theory. These conditions include family relationship and the type of delinquency. In the context of Chinese societies, the conditions also include the differences between socialist, collectivist Mainland China and capitalist, more individualist Hong Kong. We collected survey data from 1,026 secondary school students in Guangzhou in Mainland China, and from 1,116 in Hong Kong, to demonstrate these conditions. The results, which indicate the intimate relationship between parents and adolescents, verify that family strain has a very strong impact on adolescent delinquency. In this connection, family strain comprised parental support as a negative indicator. However, the effect of parental support on adolescent strain was only weakly negative in Guangzhou and even positive in the case of nonworking mothers. The differentials in parental influence between Guangzhou and Hong Kong are attributable to the different family policies and structures in the two cities. On the other hand, family strain exhibited similar effects on two types of delinquency, violence and status offense.     

Learning Abilities and Disabilities: Generalist Genes, Specialist Environments

ABSTRACT— Twin studies comparing identical and fraternal twins consistently show substantial genetic influence on individual differences in learning abilities such as reading and mathematics, as well as in other cognitive abilities such as spatial ability and memory. Multivariate genetic research has shown that the same set of genes is largely responsible for genetic influence on these diverse cognitive areas. We call these "generalist genes." What differentiates these abilities is largely the environment, especially nonshared environments that make children growing up in the same family different from one another. These multivariate genetic findings of generalist genes and specialist environments have far-reaching implications for diagnosis and treatment of learning disabilities and for understanding the brain mechanisms that mediate these effects.     

Towards a computational theory of experience

A standing challenge for the science of mind is to account for the datum that every mind faces in the most immediate – that is, unmediated – fashion: its phenomenal experience. The complementary tasks of explaining what it means for a system to give rise to experience and what constitutes the content of experience (qualia) in computational terms are particularly challenging, given the multiple realizability of computation. In this paper, we identify a set of conditions that a computational theory must satisfy for it to constitute not just a sufficient but a necessary, and therefore naturalistic and intrinsic, explanation of qualia. We show that a common assumption behind many neurocomputational theories of the mind, according to which mind states can be formalized solely in terms of instantaneous vectors of activities of representational units such as neurons, does not meet the requisite conditions, in part because it relies on inactive units to shape presently experienced qualia and implies a homogeneous representation space, which is devoid of intrinsic structure. We then sketch a naturalistic computational theory of qualia, which posits that experience is realized by dynamical activity-space trajectories (rather than points) and that its richness is measured by the representational capacity of the trajectory space in which it unfolds.