Hierarchical classes: Model and data analysis

A discrete, categorical model and a corresponding data-analysis method are presented for two-way two-mode (objects × attributes) data arrays with 0, 1 entries. The model contains the following two basic components: a set-theoretical formulation of the relations among objects and attributes; a Boolean decomposition of the matrix. The set-theoretical formulation defines a subset of the possible decompositions as consistent with it. A general method for graphically representing the set-theoretical decomposition is described. The data-analysis algorithm, dubbed HICLAS, aims at recovering the underlying structure in a data matrix by minimizing the discrepancies between the data and the recovered structure. HICLAS is evaluated with a simulation study and two empirical applications.This research was supported in part by a grant from the Belgian NSF (NFWO) to Paul De Boeck and in part by NSF Grant BNS-83-01027 to Seymour Rosenberg. We thank Iven Van Mechelen for clarifying several aspects of the Boolean algebraic formulation of the model and Phipps Arabie for his comments on an earlier draft.     

Birkhoff-like sheaf representation for varieties of lattice expansions

Given a variety we study the existence of a class such that S1 every A can be represented as a global subdirect product with factors in and S2 every non-trivial A is globally indecomposable. We show that the following varieties (and its subvarieties) have a class satisfying properties S1 and S2: p-algebras, distributive double p-algebras of a finite range, semisimple varieties of lattice expansions such that the simple members form a universal class (bounded distributive lattices, De Morgan algebras, etc) and arithmetical varieties in which the finitely subdirectly irreducible algebras form a universal class (f-rings, vector groups, Wajsberg algebras, discriminator varieties, Heyting algebras, etc). As an application we obtain results analogous to that of Nachbin saying that if every chain of prime filters of a bounded distributive lattice has at most length 1, then the lattice is Boolean.We wish to thank Lic. Alfredo Guerin and Dr. Daniel Penazzi for helping us with linguistics aspects. We are indebted to the referee for several helpful suggestions. We also wish to thank Professor Mick Adams for providing us with several reprints and useful e-mail information on the subject.Suported by CONICOR and SECyT (UNC).     

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     

Categorization and abstraction abilities in 3-year-old children: a comparison with monkey data

Three-year-old children were tested on three categorization tasks of increasing levels of abstraction (used with adult baboons in an earlier study): the first was a conceptual categorization task (food vs toys), the second a perceptual matching task (same vs different objects), and the third a relational matching task in which the children had to sort pairs according to whether or not the two items belonged to the same or different categories. The children were tested using two different procedures, the first a replication of the procedure used with the baboons (pulling one rope for a category or a relationship between two objects, and another rope for the other category or relationship), the second a task based upon childrens prior experiences with sorting objects (putting in the same box objects belonging to the same category or a pair of objects exemplifying the same relation). The children were able to solve the first task (conceptual categorization) when tested with the sorting into boxes procedure, and the second task (perceptual matching) when tested with both procedures. The children were able to master the third task (relational matching) only when the rules were clearly explained to them, but not when they could only watch sorting examples. In fact, the relational matching task without explanation requires analogy abilities that do not seem to be fully developed at 3 years of age. The discrepancies in performances between children tested with the two procedures, with the task explained or not, and the discrepancies observed between children and baboons are discussed in relation to differences between species and/or problem-solving strategies.     

Free Łukasiewicz and Hoop Residuation Algebras

Hoop residuation algebras are the {, 1}-subreducts of hoops; they include Hilbert algebras and the {, 1}-reducts of MV-algebras (also known as Wajsberg algebras). The paper investigates the structure and cardinality of finitely generated free algebras in varieties of k-potent hoop residuation algebras. The assumption of k-potency guarantees local finiteness of the varieties considered. It is shown that the free algebra on n generators in any of these varieties can be represented as a union of n subalgebras, each of which is a copy of the {, 1}-reduct of the same finite MV-algebra, i.e., of the same finite product of linearly ordered (simple) algebras. The cardinality of the product can be determined in principle, and an inclusion-exclusion type argument yields the cardinality of the free algebra. The methods are illustrated by applying them to various cases, both known (varieties generated by a finite linearly ordered Hilbert algebra) and new (residuation reducts of MV-algebras and of hoops).     

论八卦是八个逻辑范式

基于太极代数,本文证明八卦是八个逻辑范式,八卦中包含四对矛盾关系,其中"六子"构成辩证逻辑组。八卦是生命生产和思想生产都必须共同遵循的变化法则。学界似有这样的倾向,以为《周易》中只有类推逻辑而没有演绎逻辑,本文证明这种观点是不能成立的。八卦本质上就是演绎逻辑的,卦象的本质是逻辑法则。因此,基于卦象的联想或推理不能脱离八卦的逻辑内涵;否则,想象的灵活性必将导致卦象上的混淆,甚至使八卦沦为象数游戏的工具。     

Preliminary Examination of a Cartoon-Based Hostile Attributional Bias Measure for Urban African American Boys

The current study illustrates how researchers developed and validated a cartoon-based adaptation of a written hostile attributional bias measure for a sample of urban, low-income, African American boys. A series of studies were conducted to develop cartoon illustrations to accompany a standard written hostile attributional bias vignette measure (Study 1), to determine initial psychometric properties (Study 2) and acceptability (Study 3), and to conduct a test–retest reliability trial of the adapted measure in a separate sample (Study 4). These studies utilize a participatory action research approach to measurement design and adaptation, and suggest that collaborations between researchers and key school stakeholders can lead to measures that are psychometrically strong, developmentally appropriate, and culturally sensitive. In addition, the cartoon-based hostile attributional bias measure appears to have promise as an assessment and/or outcome measure for aggression and bullying prevention programs conducted with urban African American boys.     

Maternal and paternal parenting styles associated with relational aggression in children and adolescents: A conceptual analysis and meta-analytic review

How does parenting affect relational aggression in children? The goal of the present series of meta-analyses based on 48 studies (28,097 children) was to analyze and integrate the findings on the associations between various types of parenting behaviors and relational aggression, and to identify potential substantive and methodological factors that may moderate these associations. To distinguish between different parenting strategies, experts sorted the parenting measures used in the studies into 10 groups. Results of a multiple correspondence analysis revealed four separate clusters: Positive parenting, psychologically controlling parenting, negative/harsh parenting, and uninvolved parenting. The meta-analyses demonstrated that more positive parenting was associated with less relational aggression (combined effect sizes r = −.06, p < .05, for mothers, r = −.08, p < .01, for fathers). More harsh parenting (combined effect sizes r = .11, p < .01, for mothers, r = .12, p < .01, for fathers) and more uninvolved parenting (combined effect sizes r = .07, p < .01, for mothers, absent for fathers) were associated with increased relational aggression. Paternal psychologically controlling parenting was positively related to relational aggression (r = .05, p < .01), whereas maternal psychologically controlling parenting was not (combined effect sizes r = .04, p = .09). The effect of several moderators is discussed. The findings of this study suggest that dimensions of positive and negative parenting behaviors of mothers and fathers are associated with children’s relational aggression and that these associations are – in case of fathers – contingent upon a number of sampling and procedural characteristics.