A classification of all order-preserving homeomorphism groups of the reals that satisfy finite uniqueness

The only real relational structures of scale type (m, n) with 1 ≤ m ≤ n < ∞ are of scale type (1, 1), (1, 2), and (2, 2), and so are conjugate to structures whose automorphism groups are subgroups of the affines containing the group of translations. All real relational structures of scale type (0, n) with n < ∞ have automorphism groups abstractly isomorphic to; moreover, each contains subchain of order type theta, invariant under the action of the automorphism group, s.t. the action of the automorphisms on this subchain is conjugate to that of a sub-group of the affines.     

Classification of concatenation measurement structures according to scale type

A relational structure is said to be of scale type (M,N) iff M is the largest degree of homogeneity and N the least degree of uniqueness (Narens, 1981a, Narens, 1981b) of its automorphism group.Roberts (in Proceedings of the first Hoboken Symposium on graph theory, New York: Wiley, 1984; in Proceedings of the fifth international conference on graph theory and its applications, New York: Wiley, 1984) has shown that such a structure on the reals is either ordinal or M is less than the order of at least one defining relation (Theorem 1.2). A scheme for characterizing N is outlined in Theorem 1.3. The remainder of the paper studies the scale type of concatenation structures 〈X, ?, ° 〉, where ? is a total ordering and ° is a monotonic operation. Section 2 establishes that for concatenation structures with M>0 and N<∞ the only scale types are (1,1), (1,2), and (2,2), and the structures for the last two are always idempotent. Section 3 is concerned with such structures on the real numbers (i.e., candidates for representations), and it uses general results of Narens for real relational structures of scale type (M, M) (Theorem 3.1) and of Alper (Journal of Mathematical Psychology, 1985, 29, 73–81) for scale type (1, 2) (Theorem 3.2). For M>0, concatenation structures are all isomorphic to numerical ones for which the operation can be written $\text{x°y = yf(}\text{x}\text{y}\text{)}$, where f is strictly increasing and $\text{f(x)}\text{x}$ is strictly decreasing (unit structures). The equation f(x^?)=f(x)^? is satisfied for all x as follows: for and only for ? = 1 in the (1,1) case; for and only for ?=kⁿ, k > 0 fixed, and n ranging over the integers, in the (1, 2) case; and for all ?>0 in the (2, 2) case (Theorems 3.9, 3.12, and 3.13). Section 4 examines relations between concatenation catenation and conjoint structures, including the operation induced on one component by the ordering of a conjoint structure and the concept of an operation on one component being distributive in a conjoint structure. The results, which are mainly of interest in proving other results, are mostly formulated in terms of the set of right translations of the induced operation. In Section 5 we consider the existence of representations of concatenation structures. The case of positive ones was dealt with earlier (Narens & Luce (Journal of Pure & Applied Algebra27, 1983, 197–233). For idempotent ones, closure, density, solvability, and Archimedean are shown to be sufficient (Theorem 5.1). The rest of the section is concerned with incomplete results having to do with the representation of cases with M>0. A variety of special conditions, many suggested by the conjoint equivalent of a concatenation structure, are studied in Section 6. The major result (Theorem 6.4) is that most of these concepts are equivalent to bisymmetry for idempotent structures that are closed, dense, solvable, and Dedekind complete. This result is important in Section 7, which is devoted to a general theory of scale type (2, 2) for the utility of gambles. The representation is a generalization of the usual SEU model which embodies a distinctly bounded form of rationality; by the results of Section 6 it reduces to the fully rational SEU model when rationality is extended beyond the simplest equivalences. Theorem 7.3 establishes that under plausible smoothness conditions, the ratio scale case does not introduce anything different from the (2, 2) case. It is shown that this theory is closely related to, but somewhat more general, than Kahneman and Tversky's (Econometrica47, 1979, 263–291) prospect theory.     

On the theory of uniqueness in measurement

This paper describes problems in the theory of uniqueness which occur when there are two different measurement homomorphisms f and g with g not attainable from f by a transformation on the range of f. In this case, the theories of scale type and of meaningfulness of statements using scales are in trouble. It is shown that unless extreme care is taken in the definitions, it is possible for two measurement homomorphisms of the same fixed relational system to have different scale type and it is possible for seemingly meaningless statements to be judged meaningful.     

Polite responses to polite requests

Indirect requests vary in politeness; for example, Can you tell me where Jordan Hall is? is more polite than Shouldn't you tell me where Jordan Hall is? By one theory, the more the literal meaning of a request implies personal benefits for the listener, within reason, the more polite is the request. This prediction was confirmed in Experiment 1. Responses to indirect requests also vary in politeness. For Can you tell me where Jordan Hall is?, the response Yes, I can — it's up the street is more polite than It's up the street. By an extension of that theory, the more attentive the responder is to all of the requester's meaning, the more polite is the response. This prediction was confirmed in Experiments 2, 3 and 4. From this evidence, we argued that people ordinarily compute both the literal and the indirect meanings of indirect requests. They must if they are to recognize when the speaker is and isn't being polite, and if they are to respond politely, impolitely, or even neutrally.     

An algorithm for clustering relational data with applications to social network analysis and comparison with multidimensional scaling

A method of hierarchical clustering for relational data is presented, which begins by forming a new square matrix of product-moment correlations between the columns (or rows) of the original data (represented as an n × m matrix). Iterative application of this simple procedure will in general converge to a matrix that may be permuted into the blocked form [_?1¹₁^?1]. This convergence property may be used as the basis of an algorithm (CONCOR) for hierarchical clustering. The CONCOR procedure is applied to several illustrative sets of social network data and is found to give results that are highly compatible with analyses and interpretations of the same data using the blockmodel approach of White (White, Boorman & Breiger, 1976). The results using CONCOR are then compared with results obtained using alternative methods of clustering and scaling (MDSCAL, INDSCAL, HICLUS, ADCLUS) on the same data sets.     

Responding to indirect speech acts

Indirect speech acts, like the request Do you know the time?, have both a literal meaning, here “I ask you whether you know the time,” and an indirect meaning “I request you to tell me the time.” In this paper I outline a model of how listeners understand such speech acts and plan responses to them. The main proposals are these. The literal meaning of indirect speech acts can be intended to be taken seriously (along with the indirect meaning) or merely pro forma. In the first case listeners are expected to respond to both meanings, as in Yes, I do—it's six, but in the second case only to the indirect meaning, as in It's six. There are at least six sources of information listeners use in judging whether the literal meaning was intended seriously or pro forma, as well as whether there was intended to be any indirect meaning. These proposals were supported in five experiments in which ordinary requests for information were made by telephone of 950 local merchants.     

The analysis of semigroups of multirelational systems

A finite family of binary relations on a finite set, termed here a relational system, generates a finite semigroup under the operation of relational composition. The relationship between simplifications of the semigroup of a relational system in the form of homomorphic images, and simplifications of the relational system itself is examined. First of all, the list of relational conditions establishing a relationship between a homomorphic image of the semigroup of a relational system and a simplified, or derived, version of that relational system, is reviewed and extended. Then a definition of empirical relationship is introduced (the Correspondence Definition) and it is shown how, in conjunction with a factorization procedure for finite semigroups (P. E. Pattison & W. K. Bartlett, Journal of Mathematical Psychology, 1982, in press), it leads to a systematic and efficient analysis for a relational system. Applications of the procedure to an empirical blockmodel and to a class of simple relational systems are presented.     

Biased extensive measurement: The homogeneous case

In the homogeneous case of one type of objects, we prove the existence of an additive scale unique up to a positive scaling transformation without transitivity of indifference and with a property of homothetic invariance weaker than monotonicity. The representation, which is a particular case of a semiorder representation, reveals a unique positive factor α?1 that biases extensive structures and explains departures from these standard axioms of extensive measurement (α=1). We interpret α as characterizing the qualitative influence of the underlying measurement process and we show that it induces a proportional indifference threshold.     

On the scales of measurement

Let $\text{X}$ = 〈X, ≧, R₁, R₂…〉 be a relational structure, 〈$\text{X, ≧}$〉 be a Dedekind complete, totally ordered set, and n be a nonnegative integer. $\text{X}$ is said to satisfy n-point homogeneity if and only if for each x₁,…, x_n, y₁,…, y_n such that x₁ ? x₂ ? … ? x_n and y₁ ? y₂ … ? y_n, there exists an automorphism α of $\text{X}$ such that α(x₁) = y_i. $\text{X}$ is said to satisfy n-point uniqueness if and only if for all automorphisms β and γ of $\text{X}$, if β and γ agree at n distinct points of $\text{X}$, then β and γ are identical. It is shown that if $\text{X}$ satisfies n-point homogeneity and n-point uniqueness, then n ≦ 2, and for the case n = 1, $\text{X}$ is ratio scalable, and for the case n = 2, interval scalable. This result is very general and may in part provide an explanation of why so few scale types have arisen in science. The cases of 0-point homogeneity and infinite point homogeneity are also discussed.     

The Role of Placement History and Current Family Environment in Children’s Aggression in Foster Care

Predictors of the physical and relational aggressive behavior of children in foster care were examined (N?=?160, 50.9% male, M age?=?7.57, SD?=?2.39). First, predictors representative of children’s placement histories were examined in relation to the children’s aggression at T1. Next, predictors representing characteristics of the current family environment were examined in relation to the children’s aggression at T2 (4 months later). Results revealed that a greater number of prior group home placements and being in a non-kinship home were associated with higher physical aggression at T1. A greater number of prior group home placements, a fewer number of regular home placements, being in a non-kinship home, and prior removal from the home due to neglect were associated with higher relational aggression at T1. The results also revealed that higher foster sibling relational aggression at T1 predicted lower child physical aggression at T2. If foster siblings were biological children of the foster parent, higher levels of a foster sibling’s physical aggression at T1 predicted reduced child physical aggression at T2. The opposite pattern was observed if foster siblings were not biological children of the foster parent. Lastly, longer time in the current placement, more children in the home, and the presence of a sibling that was a biological child of the parent predicted higher child relational aggression at T2. These findings provide initial insights into how placement history and current family environment are associated with the physical and relational aggressive behavior of children in foster care.     

Comparison of reinforcement and punishment functions produced by the same contingent event in the same subjects

The same event, forced running, was used to reinforce the lever-pressing of six rats in one component of a multiple schedule and to punish their drinking in another component. When the durations of running were converted to probabilities that Ss would not be running at t + n sec, given that the run gegan at t = 0 sec, both reinforcement and punishment were found to be linear (inverse) functions of the probability of not-running. A high concordance (0.90) between slopes of the reinforcement and punishment functions indicated that individual Ss were either sensitive to both reinforcement and punishment or sensitive to neither.     

Relational self-construal moderates the effect of social support on life satisfaction

While social support is associated with a host of important physical and psychological benefits, these effects are not always straightforward. Still, the moderating factors that might underlie individual differences in reactions to social support are not well-understood. In the current studies, we examined individual differences in relational self-construal in the typically positive relationship between social support and life satisfaction. In Study 1 (N = 79) relational self-construal moderated the relationship between social support and life satisfaction such that social support was especially beneficial for those with high relational self-construal. We replicated this effect in Study 2 (N = 284), and also found that social support was especially important for individuals with high relational self-construal in the context of high feelings of stress. These studies suggest that social support has differently gauged effects on life satisfaction depending on an individual’s relational self-construal.     

Self-observation versus flooding in the treatment of agoraphobia

The effects on agoraphobia of (1) self-observation with a minimum of therapeutic intervention. (2) flooding, (3) a combination of flooding and self-observation, and (4) no-treatment control were compared. Assessments were made at the beginning of treatment, during and at the end of treatment and at the follow-up three months later. They were carried out by the therapist (in vivo) measurement; phobic anxiety and phobic avoidance scale) by an independent observer (phobic anxiety scale and phobic avoidance scale) and by the client (phobic anxiety scale; phobic avoidance scale: FSS; social anxiety scale; SDS and I-E scale).Self-observation, flooding and flooding/self-observation resulted in significant improvement on several variables, whereas the no-treatment control group did not improve. No difference in effectiveness was found between the self-observation and flooding treatments. In addition, the results suggest that a combined flooding/self-observation treatment is more effective than each of the individual treatments.     

Relational and item-specific influences on generate–recognize processes in recall

The generate–recognize model and the relational–item-specific distinction are two approaches to explaining recall. In this study, we consider the two approaches in concert. Following Jacoby and Hollingshead (Journal of Memory and Language 29:433–454, 1990), we implemented a production task and a recognition task following production (1) to evaluate whether generation and recognition components were evident in cued recall and (2) to gauge the effects of relational and item-specific processing on these components. An encoding task designed to augment item-specific processing (anagram-transposition) produced a benefit on the recognition component (Experiments 1–3) but no significant benefit on the generation component (Experiments 1–3), in the context of a significant benefit to cued recall. By contrast, an encoding task designed to augment relational processing (category-sorting) did produce a benefit on the generation component (Experiment 3). These results converge on the idea that in recall, item-specific processing impacts a recognition component, whereas relational processing impacts a generation component.     

Some aspects of language comprehension in anterior aphasia

The competency of language comprehension was evaluated in three groups: anterior aphasics, posterior aphasics, and normal control subjects. Test material was divided into two sentence groups (Fill in the Blank and True/False) emphasizing either (1) semantic, “real world,” identity words or (2) syntactic, relational words, and one paragraph interpretation task. Matching auditory and visual (written) presentations were given. The control subjects performed almost flawlessly but many errors were made by each aphasia group. Qualitative study revealed a marked difference in the comprehension problem of the two groups. The anterior aphasic group performed well on semantically weighted sentences but made errors on syntactically weighted material, regardless of mode of presentation. In contrast, the posterior aphasics made almost the same number of errors on both types of material, regardless of mode of presentation. These findings support the concept of defective language comprehension in anterior aphasia and further suggest that the defect centers on the syntactical structures which are also poorly handled in expressive output.     

Transnational families,remittances, cieng and obligation for Dinka women in Australia

This paper explores the narratives of a group of Dinka women living in Australia with a focus on the emotional underpinnings of remittance sending to family in Africa. The sending of remittances is shaped by the Dinka relational ontology of cieng which obliges those who have migrated to Australia to financially support relatives left behind in Africa. Through exploring the ‘emotional content of obligation’ (Clark, 1990) this paper considers how cieng and remittance sending can result in feelings including shame and helplessness but also in reinforcing a sense belonging. In addition, this paper argues that while there is continuity in cieng despite the global dispersal of Dinka people, there has been a change in the degree and type of obligation placed on people through cieng.     

The actual and retrospective-occupational self-concept dimensions of retired educators

A 20-item adjective checklist was used by 118 retired educators to describe their actual and retrospective-occupational self-concepts. The men made their retrospective ratings for middle-aged and preretired occupational roles. The intercorrelations among the self-concept ratings were multiple-set factor analyzed, and seven common dimensions were identified: (1) stability, (2) conventionality, (3) independence, (4) practicality, (5) status, (6) confidence, and (7) cleverness. The results suggested that the retired educators had used the same dimensions in describing their actual and retrospective-occupational self-concepts. The percentages of variance contributed by the dimensions within the self-concept structures were also reported and discussed within the framework of career development.