Modal and amodal cognition: an overarching principle in various domains of psychology.

Accounting for how the human mind represents the internal and external world is a crucial feature of many theories of human cognition. Central to this question is the distinction between modal as opposed to amodal representational formats. It has often been assumed that one but not both of these two types of representations underlie processing in specific domains of cognition (e.g., perception, mental imagery, and language). However, in this paper, we suggest that both formats play a major role in most cognitive domains. We believe that a comprehensive theory of cognition requires a solid understanding of these representational formats and their functional roles within and across different domains of cognition, the developmental trajectory of these representational formats, and their role in dysfunctional behavior. Here we sketch such an overarching perspective that brings together research from diverse subdisciplines of psychology on modal and amodal representational formats so as to unravel their functional principles and their interactions.

Complete Q-matrices in conjunctive models on general attribute structures.

In cognitive diagnostic assessment a property of the Q-matrix, usually referred to as completeness, warrants that the cognitive attributes underlying the observed behaviour can be uniquely assessed. Characterizations of completeness were first derived under the assumption of independent attributes, and are currently under investigation for interdependent attributes. The dominant approach considers so-called attribute hierarchies, which are conceptualized through a partial order on the set of attributes. The present paper extends previously published results on this issue obtained for conjunctive attribute hierarchy models. Drawing upon results from knowledge structure theory, it provides novel sufficient and necessary conditions for completeness of the Q-matrix, not only for conjunctive models on attribute hierarchies, but also on more general attribute structures.

Internal references in cross-modal judgments: A global psychophysical perspective.

We are able to compare intensities across different sorts of stimuli, like in matching the brightness of visual stimuli of different hue, or the loudness of auditory stimuli of different spectral shapes. We can even match the brightness of a visual stimulus to the loudness of a tone, and vice versa. The term cross-dimensional matching is used to subsume these kinds of intra- and cross-modal tasks. The often replicated regression effect in cross-dimensional matching relates to the observation that the intensity of whatever stimulus is adjusted exhibits a tendency toward some mean magnitude, which is interpreted as serving as an internal reference. Internal references, however, are not part of psychophysical theory in the tradition of Stevens. They form a key ingredient for the theory of global psychophysics initiated by R. Duncan Luce, which also makes explicit Stevens' assumption of an underlying ratio scale of perceived intensity to which all sensations map, and renders it empirically testable. The present article generalizes Luce's theory of cross-dimensional magnitude production (Luce et al., 2010) to integrate potentially role-dependent internal references (pertaining to the standard, or the adjusted stimulus) as suggested by the regression effect. Reconsidering available empirical evidence for magnitude production and matching experiments in the light of these theoretical developments leads to a coherent picture. The results indicate that internal references are role-dependent in cross-dimensional tasks (intra- or cross-modal), but role-independent in intra-dimensional tasks. Moreover, predictions derived from the generalized theory provide a close fit to classical matching data. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

The interaction of linguistic and arithmetic factors affects adult performance on arithmetic word problems.

Performance on word problems is influenced by linguistic and arithmetic factors, and by their interaction. To study these factors and interactions, we manipulated linguistic and arithmetic factors independently in a within-participant design that included complexity parameters (a) in the domain of arithmetic: carry/borrow (no-carry/borrow vs. carry/borrow), operation (addition vs. subtraction), (b) in the domain of linguistics: nominalization (nominalized vs. verbalized form), and (c) linking the two domains: lexical consistency (linguistic predicate locally consistent vs. inconsistent with mathematical operation). Response times of 25 students solving 320 one-step word problems were measured. All four factors showed a main effect on response times, and interactions between linguistic and arithmetic factors affected response times. These interactions were observed when the linguistic and arithmetic factors were conceptually linked. Our results highlight that not only the linguistic and arithmetic complexities of an item contribute to the difficulty of a word problem, but linguistic and arithmetic factors interact. We discuss the theoretical implications for the numerical and the linguistic domain as well as the possible impact of domain-general characteristics, such as working memory limitations as a potential reason for the observed interactions between numerical and linguistic attributes.

On a Generalization of Local Independence in Item Response Theory Based on Knowledge Space Theory.

Knowledge space theory (KST) structures are introduced within item response theory (IRT) as a possible way to model local dependence between items. The aim of this paper is threefold: firstly, to generalize the usual characterization of local independence without introducing new parameters; secondly, to merge the information provided by the IRT and KST perspectives; and thirdly, to contribute to the literature that bridges continuous and discrete theories of assessment. In detail, connections are established between the KST simple learning model (SLM) and the IRT General Graded Response Model, and between the KST Basic Local Independence Model and IRT models in general. As a consequence, local independence is generalized to account for the existence of prerequisite relations between the items, IRT models become a subset of KST models, IRT likelihood functions can be generalized to broader families, and the issues of local dependence and dimensionality are partially disentangled. Models are discussed for both dichotomous and polytomous items and conclusions are drawn on their interpretation. Considerations on possible consequences in terms of model identifiability and estimation procedures are also provided.

On the Link between Cognitive Diagnostic Models and Knowledge Space Theory.

The present work explores the connections between cognitive diagnostic models (CDM) and knowledge space theory (KST) and shows that these two quite distinct approaches overlap. It is proved that in fact the Multiple Strategy DINA (Deterministic Input Noisy AND-gate) model and the CBLIM, a competence-based extension of the basic local independence model (BLIM), are equivalent. To demonstrate the benefits that arise from integrating the two theoretical perspectives, it is shown that a fairly complete picture on the identifiability of these models emerges by combining results from both camps. The impact of the results is illustrated by an empirical example, and topics for further research are pointed out.

Assessing the local identifiability of probabilistic knowledge structures.

Given a collection Q of problems, in knowledge space theory Doignon & Falmagne, (International Journal of Man-Machine Studies 23:175-196, 1985) the knowledge state of a student is the collection K ⊆ Q of all problems that this student is capable of solving. A knowledge structure is a pair (Q, ), where is a collection of knowledge states that contains at least the empty set and Q. A probabilistic knowledge structure (PKS) is a knowledge structure (Q, , π), where π is a probability distribution on the knowledge states. The PKS that has received the most attention is the basic local independence model BLIM; Falmagne & Doignon, (British Journal of Mathematical and Statistical Psychology 41:1-23, 1988a, Journal of Mathematical Psychology 32:232-258, 1988b). To the best of our knowledge, systematic investigations in the literature concerning the identifiability of the BLIM are totally missing. Based on the theoretical work of Bamber and van Santen (Journal of Mathematical Psychology 29:443-473, 1985), the present article is aimed to present a method and a corresponding computerized procedure for assessing the local identifiability of the BLIM, which is applicable to any finite knowledge structure of moderate size.

The locus of perceived equidistance in binocular vision.

Empirical studies of the locus of perceived equidistance in binocular vision have revealed a characteristic change of its form, depending on absolute distance. This result is commonly taken to indicate influence of vergence-related binocular information, a conclusion that is by no means exclusively dictated by the data. Heller (1997) has suggested an alternative theoretical account that is based on the idea of independently combining the outcome of monocular input transformations without any form of binocular interaction. This article provides an experimental test of the structural assumption lying at the core of the axiomatic foundation of Heller's theory. I test the so-called Reidemeister condition under reduced cue conditions in two settings for each of 7 subjects. The results provide strong evidence for the validity of the Reidemeister condition and thus challenge the view that the locus of perceived equidistance depends on vergence-related binocular information. The discussion of the factors contributing to the monocular input transformations emphasizes the role of the optical properties of the eyes.