Effects of stimulus order on discrimination processes in comparative and equality judgements: Data and models

In typical discrimination experiments, participants are presented with a constant standard and a variable comparison stimulus and their task is to judge which of these two stimuli is larger (comparative judgement). In these experiments, discrimination sensitivity depends on the temporal order of these stimuli (Type B effect) and is usually higher when the standard precedes rather than follows the comparison. Here, we outline how two models of stimulus discrimination can account for the Type B effect, namely the weighted difference model (or basic Sensation Weighting model) and the Internal Reference Model. For both models, the predicted psychometric functions for comparative judgements as well as for equality judgements, in which participants indicate whether they perceived the two stimuli to be equal or not equal, are derived and it is shown that the models also predict a Type B effect for equality judgements. In the empirical part, the models' predictions are evaluated. To this end, participants performed a duration discrimination task with comparative judgements and with equality judgements. In line with the models' predictions, a Type B effect was observed for both judgement types. In addition, a time-order error, as indicated by shifts of the psychometric functions, and differences in response times were observed only for the equality judgement. Since both models entail distinct additional predictions, it seems worthwhile for future research to unite the two models into one conceptual framework.     

Overshadowing by fixed- and variable-duration stimuli

Two experiments investigated the effect of the temporal distribution form of a stimulus on its ability to produce an overshadowing effect. The overshadowing stimuli were either of the same duration on every trial, or of a variable duration drawn from an exponential distribution with the same mean duration as that of the fixed stimulus. Both experiments provided evidence that a variable-duration stimulus was less effective than a fixed-duration cue at overshadowing conditioning to a target conditioned stimulus (CS); moreover, this effect was independent of whether the overshadowed CS was fixed or variable. The findings presented here are consistent with the idea that the strength of the association between CS and unconditioned stimulus (US) is, in part, determined by the temporal distribution form of the CS. These results are discussed in terms of time-accumulation and trial-based theories of conditioning and timing.     

The other modality: Auditory stimuli in language switching

Language switching studies typically implement visual stimuli and visual language cues to trigger a concept and a language response, respectively. In the present study we set out to generalise this to another stimulus modality by investigating language switching with auditory stimuli next to visual stimuli. The results showed that switch costs can be obtained with both auditory and visual stimuli. Yet, switch costs were relatively larger with visual stimuli than with auditory stimuli. Both methodological and theoretical implications of these findings are discussed.     

Experimental analysis of human vocal behavior: applications of speech-recognition technology

Recent developments in speech recognition make it feasible to apply the technology to study vocal behavior. The present study illustrates the use of this technology to establish functional stimulus classes. Eight students were taught to say nonsense words in the presence of arbitrarily assigned sets of symbols consistent with three three-member experimenter-defined stimulus classes. Computer-controlled speech-recognition software was used to record, analyze, and differentially reinforce vocal responses. When the stimulus classes were established, students were taught to say a new nonsense word in the presence of one member of each stimulus class. Transfer of function was tested subsequently to determine if the novel stimulus names transferred to the remaining stimulus class members. Most subjects required two iterations of the training and testing procedures before transfer occurred. The data illustrate the usefulness of recording vocal behavior during stimulus control procedures and demonstrate the use of speech-recognition technology. The paper also describes the current state of speech-recognition technology and suggests several other areas of research that might benefit from using vocal behavior as its primary datum.     

Equivalence classes in individuals with minimal verbal repertoires

Studies from two different laboratories tested for equivalence classes in individuals with severe mental retardation and minimal verbal repertoires. In the first study, 3 individuals learned several matching-to-sample performances: matching picture comparison stimuli to dictated-word sample stimuli (AB), matching those same pictures to printed letter samples (CB), and also matching the pictures to nonrepresentative forms (DB). On subsequent tests, all individuals immediately displayed Emergent Relations AC, AD, BC, BD, CD, and DC, together constituting a positive demonstration of equivalence (as defined by Sidman). The second study obtained a positive equivalence test outcome in 1 of 2 individuals with similarly minimal verbal repertoires. Taken together, these studies call into question previous assertions that equivalence classes are demonstrable only in individuals with well-developed language repertoires.     

On Categorical Equivalences of Commutative BCK-algebras

A commutative BCK-algebra with the relative cancellation property is a commutative BCK-algebra (X;*,0) which satisfies the condition: if a ≤ x, a ≤ y and x * a = y * a, then x = y. Such BCK-algebras form a variety, and the category of these BCK-algebras is categorically equivalent to the category of Abelian ℓ-groups whose objects are pairs (G, G ₀), where G is an Abelian ℓ-group, G ₀ is a subset of the positive cone generating G ⁺ such that if u, v ∈ G ₀, then 0 ∨ (u - v) ∈ G ₀, and morphisms are ℓ-group homomorphisms h: (G, G ₀) → (G′,G′₀) with f(G ₀) ⫅ G′₀. Our methods in particular cases give known categorical equivalences of Cornish for conical BCK-algebras and of Mundici for bounded commutative BCK-algebras (= MV-algebras). This revised version was published online in June 2006 with corrections to the Cover Date.     

Generalization of deferred imitation during the first year of life

Infants first generalize across contexts and cues at 3 months of age in operant tasks but not until 12 months of age in imitation tasks. Three experiments using an imitation task examined whether infants younger than 12 months of age might generalize imitation if conditions were more like those in operant studies. Infants sat on a distinctive mat in a room in their home (the context) while an adult modeled actions on a hand puppet (the cue). When they were tested 24 h later, 6-month-olds generalized imitation when either the mat or the room (but not both) differed, whereas 9-month-olds generalized when both the mat and the room differed. In addition, 9-month-olds who imitated immediately also generalized to a novel test cue, whereas 6-month-olds did not. These results parallel results from operant studies and reveal that the similarity between the conditions of encoding and retrieval-not the type of task-determines whether infants generalize. The findings offer further evidence that memory development during infancy is a continuous function.     

Equivalent MIRID models

It is shown that in the context of the Model with Internal Restrictions on the Item Difficulties (MIRID), different componential theories about an item set may lead to equivalent models. Furthermore, we provide conditions for the identifiability of the MIRID model parameters, and it will be shown how the MIRID model relates to the Linear Logistic Test Model (LLTM). While it is known that the LLTM is a special case of the MIRID, we show that it is possible to construct an LLTM that encompasses the MIRID. The MIRID model places a bilinear restriction on the item parameters of the Rasch model. It is explained how this fact is used to simplify the results of Bechger, Verhelst, and Verstralen (2001) and Bechger, Verstralen, and Verhelst (2002), and extend their scope to a wider class of models.     

On aims and methods in the neuroimaging of derived relations

Ingenious and seemingly powerful technologies have been developed recently that enable the visualization in some detail of events in the brain concomitant upon the ongoing behavioral performance of a human participant. Measurement of such brain events offers at the very least a new set of dependent variables in relation to which the independent variables familiarly manipulated in the operant laboratory may be explored. Two related paradigms in which a start has been made in such research concern the derivation of novel or emergent relations from a baseline set of trained relations, and include the phenomenon of transitive inference (TI), observed in studies of stimulus equivalence (SE) and serial learning (SL) or seriation. This paper reviews some published and forthcoming neuroimaging studies of these and related phenomena, and considers how this line of research both demands and represents a welcome synthesis between types of question and levels of explanation in behavioral science that often have been seen as antithetical.     

A functional analytic approach to computer-interactive mathematics

Following a pretest, 11 participants who were naive with regard to various algebraic and trigonometric transformations received an introductory lecture regarding the fundamentals of the rectangular coordinate system. Following the lecture, they took part in a computer-interactive matching-to-sample procedure in which they received training on particular formula-to-formula and formula-to-graph relations as these formulas pertain to reflections and vertical and horizontal shifts. In training A-B, standard formulas served as samples and factored formulas served as comparisons. In training B-C, factored formulas served as samples and graphs served as comparisons. Subsequently, the program assessed for mutually entailed B-A and C-B relations as well as combinatorially entailed C-A and A-C relations. After all participants demonstrated mutual entailment and combinatorial entailment, we employed a test of novel relations to assess 40 different and complex variations of the original training formulas and their respective graphs. Six of 10 participants who completed training demonstrated perfect or near-perfect performance in identifying novel formula-to-graph relations. Three of the 4 participants who made more than three incorrect responses during the assessment of novel relations showed some commonality among their error patterns. Derived transfer of stimulus control using mathematical relations is discussed.