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)

People are habitual explanation generators. At its most mundane, our propensity to explain allows us to infer that we should not drink milk that smells sour; at the other extreme, it allows us to establish facts (e.g., theorems in mathematical logic) whose truth was not even known prior to the existence of the explanation (proof). What do the cognitive operations underlying the inference that the milk is sour have in common with the proof that, say, the square root of two (...) is irrational? Our ability to generate explanations bears striking similarities to our ability to make analogies. Both reflect a capacity to generate inferences and generalizations that go beyond the featural similarities between a novel problem and familiar problems in terms of which the novel problem may be understood. However, a notable difference between analogy-making and explanation-generation is that the former is a process in which a single source situation is used to reason about a single target, whereas the latter often requires the reasoner to integrate multiple sources of knowledge. This seemingly small difference poses a challenge to the task of marshaling our understanding of analogical reasoning to understanding explanation. We describe a model of explanation, derived from a model of analogy, adapted to permit systematic violations of this one-to-one mapping constraint. Simulation results demonstrate that the resulting model can generate explanations for novel explananda and that, like the explanations generated by human reasoners, these explanations vary in their coherence. (shrink)

Research on language processing has shown that the disruption of conceptual integration gives rise to specific patterns of event-related brain potentials —N400 and P600 effects. Here, we report similar ERP effects when adults performed cross-domain conceptual integration of analogous semantic and mathematical relations. In a problem-solving task, when participants generated labeled answers to semantically aligned and misaligned arithmetic problems, the second object label in misaligned problems yielded an N400 effect for addition problems. In a verification task, when participants judged arithmetically (...) correct but semantically misaligned problem sentences to be “unacceptable,” the second object label in misaligned sentences elicited a P600 effect. Thus, depending on task constraints, misaligned problems can show either of two ERP signatures of conceptual disruption. These results show that well-educated adults can integrate mathematical and semantic relations on the rapid timescale of within-domain ERP effects by a process akin to analogical mapping. (shrink)

Relational reasoning is a complex form of human cognition involving the evaluation of relations between mental representations of information. Prior studies have modified stimulus properties of relational reasoning problems and examined differences in difficulty between different problem types. While subsets of these stimulus properties have been addressed in separate studies, there has not been a comprehensive study, to our knowledge, which investigates all of these properties in the same set of stimuli. This investigative gap has resulted in different findings across (...) studies which vary in task design, making it challenging to determine what stimulus properties make relational reasoning—and the putative formation of mental models underlying reasoning—difficult. In this article, we present the Multidimensional Relational Reasoning Task, a task which systematically varied an array of stimulus properties within a single set of relational reasoning problems. Using a mixed-effects framework, we demonstrate that reasoning problems containing a greater number of the premises as well as multidimensional relations led to greater task difficulty. The MRRT has been made publicly available for use in future research, along with normative data regarding the relative difficulty of each problem. (shrink)

Children’s cognitive control and knowledge at school entry predict growth rates in analogical reasoning skill over time; however, the mechanisms by which these factors interact and impact learning are unclear. We propose that inhibitory control (IC) is critical for developing both the relational representations necessary to reason and the ability to use these representations in complex problem solving. We evaluate this hypothesis using computational simulations in a model of analogical thinking, Discovery of Relations by Analogy/Learning and Inference with Schemas and (...) Analogy (DORA/LISA; Doumas et al., 2008 ). Longitudinal data from children who solved geometric analogy problems repeatedly over 6 months show three distinct learning trajectories though all gained somewhat: analogical reasoners throughout, non-analogical reasoners throughout, and transitional – those who start non-analogical and grew to be analogical. Varying the base level of top-down lateral inhibition in DORA affected the model’s ability to learn relational representations, which, in conjunction with inhibition levels used in LISA during reasoning, simulated accuracy rates and error types seen in the three different learning trajectories. These simulations suggest that IC may not only impact reasoning ability but may also shape the ability to acquire relational knowledge given reasoning opportunities. (shrink)

Quantum theory is a powerful framework for probabilistic modeling of cognition. Strong empirical evidence suggests the context- and order-dependent representation of human judgment and decision-making processes, which falls beyond the scope of classical Bayesian probability theories. However, considering behavior as the output of underlying neurobiological processes, a fundamental question remains unanswered: Is cognition a probabilistic process at all?

May's careful examination of empirical evidence makes a compelling case against the primacy of emotion in driving moral judgments. At the same time, emotion certainly is involved in moral judgments. We argue that emotion interacts with beliefs, values, and moral principles through a process of coherence-based reasoning (operating at least partially below the level of conscious awareness) in generating moral judgments and decisions.