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.

Uncertainty is an intrinsic part of life; most events, affairs, and questions are uncertain. A key problem in behavioral sciences is how the mind copes with uncertain information. Quantum probability theory offers a set of principles for inference, which align well with intuition about psychological processes in certain cases: cases when it appears that inference is contextual, the mental state changes as a result of previous judgments, or there is interference between different possibilities. We motivate the use of quantum theory in cognition and its key characteristics. For each of these characteristics, we review relevant quantum cognitive models and empirical support. The scope of quantum cognitive models encompasses fallacies in decision-making (such as the conjunction fallacy or the disjunction effect), question order effects, conceptual combination, evidence accumulation, perception, over-/underdistribution effects in memory, and more. Quantum models often formalize psychological ideas previously expressed in heuristic terms, allow unified explanations of previously disparate findings, and have led to several surprising, novel predictions. We also cast a critical eye on quantum models and consider some of their shortcomings and issues regarding their further development.

No other study has had as great an impact on the development of the similarity literature as that of Tversky (1977), which provided compelling demonstrations against all the fundamental assumptions of the popular, and extensively employed, geometric similarity models. Notably, similarity judgments were shown to violate symmetry and the triangle inequality and also be subject to context effects, so that the same pair of items would be rated differently, depending on the presence of other items. Quantum theory provides a generalized geometric approach to similarity and can address several of Tversky's main findings. Similarity is modeled as quantum probability, so that asymmetries emerge as order effects, and the triangle equality violations and the diagnosticity effect can be related to the context-dependent properties of quantum probability. We so demonstrate the promise of the quantum approach for similarity and discuss the implications for representation theory in general.

All mental representations change with time. A baseline intuition is that mental representations have specific values at different time points, which may be more or less accessible, depending on noise, forgetting processes, etc. We present a radical alternative, motivated by recent research using the mathematics from quantum theory for cognitive modelling. Such cognitive models raise the possibility that certain possibilities or events may be incompatible, so that perfect knowledge of one necessitates uncertainty for the others. In the context of time-dependence, in physics, this issue is explored with the so-called temporal Bell (TB) or Leggett–Garg inequalities. We consider in detail the theoretical and empirical challenges involved in exploring the TB inequalities in the context of cognitive systems. One interesting conclusion is that we believe the study of the TB inequalities to be empirically more constrained in psychology than in physics. Specifically, we show how the TB inequalities, as applied to cognitive systems, can be derived from two simple assumptions: cognitive realism and cognitive completeness. We discuss possible implications of putative violations of the TB inequalities for cognitive models and our understanding of time in cognition in general. Overall, this paper provides a surprising, novel direction in relation to how time should be conceptualized in cognition.

Significance: Faced with a violation of Bell inequalities, a committed realist might pursue an explanation of the observed correlations on the basis of violations of the locality or free choice (sometimes called measurement independence) assumptions. The question of whether it is better to abandon (partially or completely) locality or free choice has been strongly debated since the inception of Bell inequalities, with ardent supporters on either side. We offer a comprehensive treatment that allows a comparison of both assumptions on an equal footing, demonstrating a deep interchangeability. This both advances the foundational debate and provides quantitative answers regarding the weight of each assumption for causal (or realist) explanations of observed correlations.

Developmental language disorder (DLD, also called specific language impairment, SLI) is a common developmental disorder comprising the largest disability group in pre-school-aged children. Approximately 7% of the population is expected to have developmental language difficulties. However, the specific etiological factors leading to DLD are not yet known and even the typical linguistic features appear to vary by language. We present here a project that investigates DLD at multiple levels of analysis and aims to make the reliable prediction and early identification of the difficulties possible. Following the multiple deficit model of developmental disorders, we investigate the DLD phenomenon at the etiological, neural, cognitive, behavioral, and psychosocial levels, in a longitudinal study of preschool children. In January 2013, we launched the Helsinki Longitudinal SLI study (HelSLI) at the Helsinki University Hospital ( http://tiny.cc/HelSLI ). We will study 227 children aged 3–6 years with suspected DLD and their 160 typically developing peers. Five subprojects will determine how the child’s psychological characteristics and environment correlate with DLD and how the child’s well-being relates to DLD, the characteristics of DLD in monolingual versus bilingual children, nonlinguistic cognitive correlates of DLD, electrophysiological underpinnings of DLD, and the role of genetic risk factors. Methods include saliva samples, EEG, computerized cognitive tasks, neuropsychological and speech and language assessments, video-observations, and questionnaires. The project aims to increase our understanding of the multiple interactive risk and protective factors that affect the developing heterogeneous cognitive and behavioral profile of DLD, including factors affecting literacy development. This accumulated knowledge will form a heuristic basis for the development of new interventions targeting linguistic and non-linguistic aspects of DLD.