There is an active debate within the field of phonology concerning the cognitive status of substantive phonetic factors such as ease of articulation and perceptual distinctiveness. A new framework is proposed in which substance acts as a bias, or prior, on phonological learning. Two experiments tested this framework with a method in which participants are first provided highly impoverished evidence of a new phonological pattern, and then tested on how they extend this pattern to novel contexts and novel sounds. Participants (...) were found to generalize velar palatalization (e.g., the change from [k] as in keep to [t⌢∫S] as in cheap) in a way that accords with linguistic typology, and that is predicted by a cognitive bias in favor of changes that relate perceptually similar sounds. Velar palatalization was extended from the mid front vowel context (i.e., before [e] as in cape) to the high front vowel context (i.e., before [i] as in keep), but not vice versa. The key explanatory notion of perceptual similarity is quantified with a psychological model of categorization, and the substantively biased framework is formalized as a conditional random field. Implications of these results for the debate on substance, theories of phonological generalization, and the formalization of similarity are discussed. (shrink)

An abstract mathematical theory is presented for a common variety of soritical arguments, treated here in terms of responses of a system, say, a biological organism, a gadget, or a set of normative linguistic rules, to stimuli. Any characteristic of the system's responses which supervenes on stimuli is called a stimulus effect upon the system. Classificatory sorites is about the identity of or difference between the effects of stimuli that differ 'only microscopically'. We formulate the classificatory sorites on arguably the (...) highest possible level of generality and show that the 'paradox' is dissolved on grounds unrelated to vague predicates or other linguistic issues traditionally associated with it. If stimulus effects are properly defined (i.e., they are uniquely determined by stimuli), and if the space of the stimuli is endowed with appropriate (not necessarily metric) closeness and connectedness properties, then this space must contain points in every vicinity of which, 'however small', the stimulus effect is not constant. The effects can only be 'tolerant' to very small differences between stimuli if the closeness structure that is used to define very close stimuli does not render the space of stimuli appropriately connected: in this case the 'paradox' cannot be formulated. Nor can it be formulated if the response properties considered are not true effects, i.e., if they do not supervene on stimuli. (shrink)

We develop a mathematical theory for comparative sorites, considered in terms of a system mapping pairs of stimuli into a binary response characteristic whose values supervene on stimulus pairs and are interpretable as the complementary relations 'are the same' and 'are not the same' (overall or in some respect). Comparative sorites is about hypothetical sequences of stimuli in which every two successive elements are mapped into the relation 'are the same', while the pair comprised of the first and the last (...) elements of the sequence is mapped into 'are not the same'. Although soritical sequences of this kind are logically possible, we argue that their existence is grounded in no empirical evidence and show that it is excluded by a certain psychophysical principle proposed for human comparative judgements in a context unrelated to soritical issues. We generalize this principle to encompass all conceivable situations for which comparative sorites can be formulated. (shrink)

Between‐trial effects in Stroop‐like interference tasks are linked to differences in the amount of cognitive control. Trials following an incongruent trial show less interference, an effect suggested to result from the increased control caused by the incongruent previous trial (known as the Gratton effect). In this study, we show that cognitive control not only results in a different amount of interference but also in a different locus of the interference. That is, the stage of the task that shows the most (...) interference changes as a function of the preceding trial. Using computational cognitive modeling, we explain these effects by a difference in the amount of processing of the irrelevant dimension of the stimulus. (shrink)

In this article, 41 models of covariation detection from 2 × 2 contingency tables were evaluated against past data in the literature and against data from new experiments. A new model was also included based on a limiting case of the normative phi‐coefficient under an extreme rarity assumption, which has been shown to be an important factor in covariation detection (McKenzie & Mikkelsen, 2007) and data selection (Hattori, 2002; Oaksford & Chater, 1994, 2003). The results were supportive of the new (...) model. To investigate its explanatory adequacy, a rational analysis using two computer simulations was conducted. These simulations revealed the environmental conditions and the memory restrictions under which the new model best approximates the normative model of covariation detection in these tasks. They thus demonstrated the adaptive rationality of the new model. (shrink)

The prominence of Bayesian modeling of cognition has increased recently largely because of mathematical advances in specifying and deriving predictions from complex probabilistic models. Much of this research aims to demonstrate that cognitive behavior can be explained from rational principles alone, without recourse to psychological or neurological processes and representations. We note commonalities between this rational approach and other movements in psychology – namely, Behaviorism and evolutionary psychology – that set aside mechanistic explanations or make use of optimality assumptions. Through (...) these comparisons, we identify a number of challenges that limit the rational program's potential contribution to psychological theory. Specifically, rational Bayesian models are significantly unconstrained, both because they are uninformed by a wide range of process-level data and because their assumptions about the environment are generally not grounded in empirical measurement. The psychological implications of most Bayesian models are also unclear. Bayesian inference itself is conceptually trivial, but strong assumptions are often embedded in the hypothesis sets and the approximation algorithms used to derive model predictions, without a clear delineation between psychological commitments and implementational details. Comparing multiple Bayesian models of the same task is rare, as is the realization that many Bayesian models recapitulate existing (mechanistic level) theories. Despite the expressive power of current Bayesian models, we argue they must be developed in conjunction with mechanistic considerations to offer substantive explanations of cognition. We lay out several means for such an integration, which take into account the representations on which Bayesian inference operates, as well as the algorithms and heuristics that carry it out. We argue this unification will better facilitate lasting contributions to psychological theory, avoiding the pitfalls that have plagued previous theoretical movements. (shrink)

Judging similarities among objects, events, and experiences is one of the most basic cognitive abilities, allowing us to make predictions and generalizations. The main assumption in similarity judgment is that people selectively attend to salient features of stimuli and judge their similarities on the basis of the common and distinct features of the stimuli. However, it is unclear how people select features from stimuli and how they weigh features. Here, we present a computational method that helps address these questions. Our (...) procedure combines image-processing techniques with a machine-learning algorithm and assesses feature weights that can account for both similarity and categorization judgment data. Our analysis suggests that a small number of local features are particularly important to explain our behavioral data. (shrink)