It has been suggested that the enterprise of developing mechanistic theories of the human cognitive architecture is flawed because the theories produced are not directly falsifiable. Newell attempted to sidestep this criticism by arguing for a Lakatosian model of scientific progress in which cognitive architectures should be understood as theories that develop over time. However, Newell's own candidate cognitive architecture adhered only loosely to Lakatosian principles. This paper reconsiders the role of falsification and the potential utility of Lakatosian principles in (...) the development of cognitive architectures. It is argued that a lack of direct falsifiability need not undermine the scientific development of a cognitive architecture if broadly Lakatosian principles are adopted. Moreover, it is demonstrated that the Lakatosian concepts of positive and negative heuristics for theory development and of general heuristic power offer methods for guiding the development of an architecture and for evaluating the contribution and potential of an architecture's research program. (shrink)

We consider approaches to explanation within the cognitive sciences that begin with Marr's computational level or Marr's implementational level and argue that each is subject to fundamental limitations which impair their ability to provide adequate explanations of cognitive phenomena. For this reason, it is argued, explanation cannot proceed at either level without tight coupling to the algorithmic and representation level. Even at this level, however, we argue that additional constraints relating to the decomposition of the cognitive system into a set (...) of interacting subfunctions are required. Integrated cognitive architectures that permit abstract specification of the functions of components and that make contact with the neural level provide a powerful bridge for linking the algorithmic and representational level to both the computational level and the implementational level. (shrink)

In this introduction we discuss the motivation behind the workshop “Towards a New Epistemology of Mathematics” of which this special issue constitutes the proceedings. We elaborate on historical and empirical aspects of the desired new epistemology, connect it to the public image of mathematics, and give a summary and an introduction to the contributions to this issue.

When, how, and why students use conceptual knowledge during math problem solving is not well understood. We propose that when solving routine problems, students are more likely to recruit conceptual knowledge if their procedural knowledge is weak than if it is strong, and that in this context, metacognitive processes, specifically feelings of doubt, mediate interactions between procedural and conceptual knowledge. To test these hypotheses, in two studies (Ns = 64 and 138), university students solved fraction and decimal arithmetic problems while (...) thinking aloud; verbal protocols and written work were coded for overt uses of conceptual knowledge and displays of doubt. Consistent with the hypotheses, use of conceptual knowledge during calculation was not significantly positively associated with accuracy, but was positively associated with displays of doubt, which were negatively associated with accuracy. In Study 1, participants also explained solutions to rational arithmetic problems; using conceptual knowledge in this context was positively correlated with calculation accuracy, but only among participants who did not use conceptual knowledge during calculation, suggesting that the correlation did not reflect “online” effects of using conceptual knowledge. In Study 2, participants also completed a nonroutine problem‐solving task; displays of doubt on this task were positively associated with accuracy, suggesting that metacognitive processes play different roles when solving routine and nonroutine problems. We discuss implications of the results regarding interactions between procedural knowledge, conceptual knowledge, and metacognitive processes in math problem solving. (shrink)

A novel explanation of belief bias in relational reasoning is presented based on the role of working memory and retrieval in deductive reasoning, and the influence of prior knowledge on this process. It is proposed that belief bias is caused by the believability of a conclusion in working memory which influences its activation level, determining its likelihood of retrieval and therefore its effect on the reasoning process. This theory explores two main influences of belief on the activation levels of these (...) conclusions. First, believable conclusions have higher activation levels and so are more likely to be recalled during the evaluation of reasoning problems than unbelievable conclusions, and therefore, they have a greater influence on the reasoning process. Secondly, prior beliefs about the conclusion have a base level of activation and may be retrieved when logically irrelevant, influencing the evaluation of the problem. The theory of activation and memory is derived from the Atomic Components of Thought-Rational (ACT-R) cognitive architecture and so this account is formalized in an ACT-R cognitive model. Two experiments were conducted to test predictions of this model. Experiment 1 tested strength of belief and Experiment 2 tested the impact of a concurrent working memory load. Both of these manipulations increased the main effect of belief overall and in particular raised belief-based responding in indeterminately invalid problems. These effects support the idea that the activation level of conclusions formed during reasoning influences belief bias. This theory adds to current explanations of belief bias by providing a detailed specification of the role of working memory and how it is influenced by prior knowledge. (shrink)

The representational nature of human cognition and thought in general has been a source of controversies. This is particularly so in the context of studies of unconscious cognition, in which representations tend to be ontologically and structurally segregated with regard to their conscious status. However, it appears evolutionarily and developmentally unwarranted to posit such segregations, as,otherwise, artifact structures and ontologies must be concocted to explain them from the viewpoint of the human cognitive architecture. Here, from a by-and-large Classical cognitivist viewpoint, (...) I show why this segregation is wrong, and elaborate on the need to postulate an ontological and structural continuity between unconscious and conscious representations. Specifically, I hypothesize that this continuity is to be found in the symbolic-based interplay between the syntax and the semantics of thought, and I propose a model of human information processing characterized by the integration of syntactic and semantic representations. (shrink)

Multi-voxel pattern recognition techniques combined with Hidden Markov models can be used to discover the mental states that people go through in performing a task. The combined method identifies both the mental states and how their durations vary with experimental conditions. We apply this method to a task where participants solve novel mathematical problems. We identify four states in the solution of these problems: Encoding, Planning, Solving, and Respond. The method allows us to interpret what participants are doing on individual (...) problem-solving trials. The duration of the planning state varies on a trial-to-trial basis with novelty of the problem. The duration of solution stage similarly varies with the amount of computation needed to produce a solution once a plan is devised. The response stage similarly varies with the complexity of the answer produced. In addition, we identified a number of effects that ran counter to a prior model of the task. Thus, we were able to decompose the overall problem-solving time into estimates of its components and in way that serves to guide theory. (shrink)

The ability to reason and problem‐solve in novel situations, as measured by the Raven's Advanced Progressive Matrices (RAPM), is highly predictive of both cognitive task performance and real‐world outcomes. Here we provide evidence that RAPM performance depends on the ability to reallocate attention in response to self‐generated feedback about progress. We propose that such an ability is underpinned by the basal ganglia nuclei, which are critically tied to both reward processing and cognitive control. This hypothesis was implemented in a neurocomputational (...) model of the RAPM task, which was used to derive novel predictions at the behavioral and neural levels. These predictions were then verified in one neuroimaging and two behavioral experiments. Furthermore, an effective connectivity analysis of the neuroimaging data confirmed a role for the basal ganglia in modulating attention. Taken together, these results suggest that individual differences in a neural circuit related to reward processing underpin human fluid reasoning abilities. (shrink)

Several attempts have been made previously to provide a biological grounding for cognitive architectures by relating their components to the computations of specific brain circuits. Often, the architecture's action selection system is identified with the basal ganglia. However, this identification overlooks one of the most important features of the basal ganglia—the existence of a direct and an indirect pathway that compete against each other. This characteristic has important consequences in decision-making tasks, which are brought to light by Parkinson's disease as (...) well as genetic differences in dopamine receptors. This paper shows that a standard model of action selection in a cognitive architecture cannot replicate any of these findings, details an alternative solution that reconciles action selection in the architecture with the physiology of the basal ganglia, and extends the domain of application of cognitive architectures. The implication of this solution for other architectures and existing models are discussed. (shrink)

Previous accounts of cognitive skill acquisition have demonstrated how procedural knowledge can be obtained and transformed over time into skilled task performance. This article focuses on a complementary aspect of skill acquisition, namely the integration and reuse of previously known component skills. The article posits that, in addition to mechanisms that proceduralize knowledge into more efficient forms, skill acquisition requires tight integration of newly acquired knowledge and previously learned knowledge. Skill acquisition also benefits from reuse of existing knowledge across disparate (...) task domains, relying on indexicals to reference and share necessary information across knowledge components. To demonstrate these ideas, the article proposes a computational model of skill acquisition from instructions focused on integration and reuse, and applies this model to account for behavior across seven task domains. (shrink)

Cognitive architectures are theories of cognition that try to capture the essential representations and mechanisms that underlie cognition. Research in cognitive architectures has gradually moved from a focus on the functional capabilities of architectures to the ability to model the details of human behavior, and, more recently, brain activity. Although there are many different architectures, they share many identical or similar mechanisms, permitting possible future convergence. In judging the quality of a particular cognitive model, it is pertinent to not just (...) judge its fit to the experimental data but also its simplicity and ability to make predictions. (shrink)

This paper presents two cognitive models that simulate the production of referring expressions in the iMAP task—a task-oriented dialog. One general model is based on Dale and Reiter’s (1995)incremental algorithm, and the other is a simple template model that has a higher correlation with the data but is specifically geared toward the properties of the iMAP task. The property of the iMAP task environment that is modeled here is that the color feature is unreliable for identifying referents while other features (...) are reliable. The low computational cost of the incremental algorithm for generating referring expressions makes it an interesting starting point for a cognitive model. However, its explanatory power is limited, because it generates uniquely distinguishing referring expressions and because it considers features for inclusion in the referring expression in a fixed order. The first model extends the original incremental algorithm by an ability to adapt to feedback of whether a referring expression was used successfully, but it seems to overpredict the frequency with which distinguishing expressions are made and underpredict the frequency of overspecified referring expressions. The second model produces features for referring expressions purely based on its current estimate of a feature’s utility. Both models predict the observed human behavior of decreasing use of color terms and increasing use of useful feature terms. (shrink)

This paper presents an attempt to bridge the gap between logical and cognitive treatments of strategic reasoning in games. There have been extensive formal debates about the merits of the principle of backward induction among game theorists and logicians. Experimental economists and psychologists have shown that human subjects, perhaps due to their bounded resources, do not always follow the backward induction strategy, leading to unexpected outcomes. Recently, based on an eye-tracking study, it has turned out that even human subjects who (...) produce the outwardly correct ‘backward induction answer’ use a different internal reasoning strategy to achieve it. The paper presents a formal language to represent different strategies on a finer-grained level than was possible before. The language and its semantics help to precisely distinguish different cognitive reasoning strategies, that can then be tested on the basis of computational cognitive models and experiments with human subjects. The syntactic framework of the formal system provides a generic way of constructing computational cognitive models of the participants of the Marble Drop game. (shrink)

Marr’s seminal distinction between computational, algorithmic, and implementational levels of analysis has inspired research in cognitive science for more than 30 years. According to a widely-used paradigm, the modelling of cognitive processes should mainly operate on the computational level and be targeted at the idealised competence, rather than the actual performance of cognisers in a specific domain. In this paper, we explore how this paradigm can be adopted and revised to understand mathematical problem solving. The computational-level approach applies methods from (...) computational complexity theory and focuses on optimal strategies for completing cognitive tasks. However, human cognitive capacities in mathematical problem solving are essentially characterised by processes that are computationally sub-optimal, because they initially add to the computational complexity of the solutions. Yet, these solutions can be optimal for human cognisers given the acquisition and enactment of mathematical practices. Here we present diagrams and the spatial manipulation of symbols as two examples of problem solving strategies that can be computationally sub-optimal but humanly optimal. These aspects need to be taken into account when analysing competence in mathematical problem solving. Empirically informed considerations on enculturation can help identify, explore, and model the cognitive processes involved in problem solving tasks. The enculturation account of mathematical problem solving strongly suggests that computational-level analyses need to be complemented by considerations on the algorithmic and implementational levels. The emerging research strategy can help develop algorithms that model what we call enculturated cognitive optimality in an empirically plausible and ecologically valid way. (shrink)