Classical (Bayesian) probability (CP) theory has led to an influential research tradition for modeling cognitive processes. Cognitive scientists have been trained to work with CP principles for so long that it is hard even to imagine alternative ways to formalize probabilities. However, in physics, quantum probability (QP) theory has been the dominant probabilistic approach for nearly 100 years. Could QP theory provide us with any advantages in cognitive modeling as well? Note first that both CP and QP theory share the (...) fundamental assumption that it is possible to model cognition on the basis of formal, probabilistic principles. But why consider a QP approach? The answers are that (1) there are many well-established empirical findings (e.g., from the influential Tversky, Kahneman research tradition) that are hard to reconcile with CP principles; and (2) these same findings have natural and straightforward explanations with quantum principles. In QP theory, probabilistic assessment is often strongly context- and order-dependent, individual states can be superposition states (that are impossible to associate with specific values), and composite systems can be entangled (they cannot be decomposed into their subsystems). All these characteristics appear perplexing from a classical perspective. However, our thesis is that they provide a more accurate and powerful account of certain cognitive processes. We first introduce QP theory and illustrate its application with psychological examples. We then review empirical findings that motivate the use of quantum theory in cognitive theory, but also discuss ways in which QP and CP theories converge. Finally, we consider the implications of a QP theory approach to cognition for human rationality. (shrink)

In a famous critique, Goodman dismissed similarity as a slippery and both philosophically and scientifically useless notion. We revisit his critique in the light of important recent work on similarity in psychology and cognitive science. Specifically, we use Tversky’s influential set-theoretic account of similarity as well as Gärdenfors’s more recent resuscitation of the geometrical account to show that, while Goodman’s critique contained valuable insights, it does not warrant a dismissal of similarity.

Advocates of dynamic systems have suggested that higher mental processes are based on continuous representations. In order to evaluate this claim, we first define the concept of representation, and rigorously distinguish between discrete representations and continuous representations. We also explore two important bases of representational content. Then, we present seven arguments that discrete representations are necessary for any system that must discriminate between two or more states. It follows that higher mental processes require discrete representations. We also argue that discrete (...) representations are more influenced by conceptual role than continuous representations. We end by arguing that the presence of discrete representations in cognitive systems entails that computationalism (i.e., the view that the mind is a computational device) is true, and that cognitive science should embrace representational pluralism. (shrink)

According to a recent proposal, natural concepts are represented in an optimally designed similarity space, adhering to principles a skilled engineer would use for creatures with our perceptual and cognitive capacities. One key principle is that natural concepts should be easily learnable. While evidence exists for parts of this optimal design proposal, there has been no direct evidence linking naturalness to learning until now. This article presents results from a computational study on perceptual color space, demonstrating that naturalness indeed facilitates (...) learning. (shrink)

Tenenbaum and Griffiths (2001) have proposed that their Bayesian model of generalisation unifies Shepard’s (1987) and Tversky’s (1977) similarity-based explanations of two distinct patterns of generalisation behaviours by reconciling them under a single coherent task analysis. I argue that this proposal needs refinement: instead of unifying the heterogeneous notion of psychological similarity, the Bayesian approach unifies generalisation by rendering the distinct patterns of behaviours informationally relevant. I suggest that generalisation as a Bayesian inference should be seen as a complement to, (...) instead of a replacement of, similarity-based explanations. Furthermore, I show that the unificatory powers of the Bayesian model of generalisation can contribute to the selection of one of these models of psychological similarity. (shrink)

Tenenbaum and Griffiths (Behavioral and Brain Sciences 24(4):629–640, 2001) have proposed that their Bayesian model of generalisation unifies Shepard’s (Science 237(4820): 1317–1323, 1987) and Tversky’s (Psychological Review 84(4): 327–352, 1977) similarity-based explanations of two distinct patterns of generalisation behaviours by reconciling them under a single coherent task analysis. I argue that this proposal needs refinement: instead of unifying the heterogeneous notion of psychological similarity, the Bayesian approach unifies generalisation by rendering the distinct patterns of behaviours informationally relevant. I suggest that (...) generalisation as a Bayesian inference should be seen as a complement to, instead of a replacement of, similarity-based explanations. Furthermore, I show that the unificatory powers of the Bayesian model of generalisation can contribute to the selection of one of these models of psychological similarity. (shrink)

Similarity‐based theories of concepts have a broad intuitive appeal and have been successful in accounting for various phenomena related to the formation and application of concepts. Their adequacy as theories of concepts has been questioned, however, as similarity is often taken as too flexible, too unconstrained, to be explanatory of categorization. In this article, I propose an account of similarity that takes the “foil” against which the target items are measured as integral to the process of comparison, making the similarity (...) relation a fundamentally triadic one. I argue that this account delivers more internal constraints on the process of comparison than the traditional, dyadic account of similarity does. Finally, I propose that this account is advantageous for a similarity‐based theory of concepts, as it easily integrates with the notion of conceptual taxonomy and uses it to deliver additional constraints on categorization. On such a theory of concepts, the foil, whose variability is in large part responsible for the flexible nature of similarity judgements, is turned within the framework of conceptual taxonomy to the very element that constrains similarity judgements in categorization. Therefore, this notion of similarity mitigates the worry that similarity is too flexible to be explanatory of categorization. (shrink)

Shepard’s (1987) universal law of generalisation (ULG) illustrates that an invariant gradient of generalisation across species and across stimuli conditions can be obtained by mapping the probability of a generalisation response onto the representations of similarity between individual stimuli. Tenenbaum and Griffiths (2001) Bayesian account of generalisation expands ULG towards generalisation from multiple examples. Though the Bayesian model starts from Shepard’s account it refrains from any commitment to the notion of psychological similarity to explain categorisation. This chapter presents the conceptual (...) spaces theory (Gärdenfors 2000, 2014) as a mediator between Shepard’s and Tenenbaum & Griffiths’ conflicting views on the role of psychological similarity for a successful model of categorisation. It suggests that the conceptual spaces theory can help to improve the Bayesian model while finding an explanatory role for psychological similarity. (shrink)

Attribute spaces are a type of conceptual spaces which Carnap introduced in his late basic system of inductive logic. This article shows how to extend Carnap's use of them into a full model of inductive reasoning with geometrically represented concepts, extending my earlier work. The proposed model draws on Bayesian non-parametric techniques in order to define a probability distribution over the attribute space and a way of updating it with data. The model is another example of conceptual and formal continuity (...) of Carnapian inductive logic with subsequent developments in statistics. (shrink)

The feature-matching approach pioneered by Amos Tversky remains a groundwork for psychological models of similarity and categorization but is rarely explicitly justified considering recent advances in thinking about cognition. While psychologists often view similarity as an unproblematic foundational concept that explains generalization and conceptual thought, long-standing philosophical problems challenging this assumption suggest that similarity derives from processes of higher-level cognition, including inference and conceptual thought. This paper addresses three specific challenges to Tversky’s approach: (i) the feature-selection problem, (ii) the problem (...) of cognitive implausibility, and (iii) the problem of unprincipled tweaking. It subsequently supports key insights from Tversky’s account based on recent developments in Bayesian modeling of cognition. A novel computational view of similarity as inference is proposed that addresses each challenge by considering the contrast class as constitutive of similarity and selecting for highly informative features. In so doing, this view illustrates the ongoing promise of the feature-matching approach in explaining perception, generalization and conceptual thought by grounding them in principles of probabilistic inference. (shrink)

Since Tversky argued that similarity judgments violate the three metric axioms, asymmetrical similarity judgments have been particularly challenging for standard, geometric models of similarity, such as multidimensional scaling. According to Tversky, asymmetrical similarity judgments are driven by differences in salience or extent of knowledge. However, the notion of salience has been difficult to operationalize, especially for perceptual stimuli for which there are no apparent differences in extent of knowledge. To investigate similarity judgments between perceptual stimuli, across three experiments, we collected (...) data where individuals would rate the similarity of a pair of temporally separated color patches. We identified several violations of symmetry in the empirical results, which the conventional multidimensional scaling model cannot readily capture. Pothos et al. proposed a quantum geometric model of similarity to account for Tversky's findings. In the present work, we extended this model to a more general framework that can be fit to similarity judgments. We fitted several variants of quantum and multidimensional scaling models to the behavioral data and concluded in favor of the quantum approach. Without further modifications of the model, the best-fit quantum model additionally predicted violations of the triangle inequality that we observed in the same data. Overall, by offering a different form of geometric representation, the quantum geometric framework of similarity provides a viable alternative to multidimensional scaling for modeling similarity judgments, while still allowing a convenient, spatial illustration of similarity. (shrink)

We present a novel way of accounting for similarity judgments. Our approach posits that similarity stems from three main sources—familiarity, priming, and inherent perceptual likeness. Here, we explore each of these constructs and demonstrate their individual and combined effectiveness in explaining similarity judgments. Using these three measures, our account of similarity explains ratings of simple, color-based perceptual stimuli that display asymmetry effects, as well as more complicated perceptual stimuli with structural properties; more traditional approaches to similarity solve one or the (...) other and have difficulty accounting for both. Overall, our work demonstrates the importance of each of these components of similarity in explaining similarity judgments, both individually and together, and suggests important implications for other similarity approaches. (shrink)

In the present dissertation, I propose a general, robust, and objective characteristic of the information environment, according to which negative information is more diverse than positive information. I present an explanatory framework for this phenomenon based on the non-extremity of positive qualities. Specifically, most attribute dimensions host one “positive” range which is surrounded by two distinct “negative” ranges, resulting in a greater diversity of negative compared to positive attributes, stimuli, and information in general. Chapter 1 of my dissertation reviews evidence (...) for the proposed greater diversity of negative information, showing that positive stimuli are consistently perceived as more similar than negative stimuli. Chapter 2 presents a line of research that demonstrates the same phenomenon in the domain of person perception. People perceive other people they like as more similar to one another than other people they dislike. I further suggest that the greater diversity of negative information as an “extrapsychic” phenomenon can account for a number of valence asymmetries in information processing that have previously been explained based on “intrapsychic” affective reactions. In line with this idea, Chapter 3 presents research showing that negative words enjoy a recognition advantage over positive words because they are more diverse. Chapter 4 discusses limitations, open questions and further implications of the current empirical findings and of the explanatory framework provided. (shrink)