The link between logic and mathematics has long been recognized by theorists from various fields. For instance, the mathematician, Bertrand Russell (1919), described logic and math as intrinsically...

Computational modeling of sketch understanding is interesting both scientifically and for creating systems that interact with people more naturally. Scientifically, understanding sketches requires modeling aspects of visual processing, spatial representations, and conceptual knowledge in an integrated way. Software that can understand sketches is starting to be used in classrooms, and it could have a potentially revolutionary impact as the models and technologies become more advanced. This paper looks at one such effort, Sketch Worksheets, which have been used in multiple classroom (...) experiments already, with students ranging from elementary school to college. Sketch Worksheets are a software equivalent of pencil and paper worksheets commonly found in classrooms, but they provide on-the-spot feedback based on what students draw. They are built on the CogSketch platform, which provides qualitative visual and spatial representations and analogical processing based on computational models of human cognition. This paper explores three issues. First, we examine how research from cognitive science and artificial intelligence, combined with the constraints of creating new kinds of educational software, led to the representations and processing in CogSketch. Second, we examine how these capabilities have been used in Sketch Worksheets, drawing upon experiments with fifth-grade students in biology and college students in engineering design and in geoscience. Finally, we examine some open issues in sketch understanding that need to be addressed to better model high-level aspects of vision, and for sketch understanding systems to reach their full potential for supporting education. (shrink)

One of the central issues in cognitive science is the nature of human representations. We argue that symbolic representations are essential for capturing human cognitive capabilities. We start by examining some common misconceptions found in discussions of representations and models. Next we examine evidence that symbolic representations are essential for capturing human cognitive capabilities, drawing on the analogy literature. Then we examine fundamental limitations of feature vectors and other distributed representations that, despite their recent successes on various practical problems, suggest (...) that they are insufficient to capture many aspects of human cognition. After that, we describe the implications for cognitive architecture of our view that analogy is central, and we speculate on roles for hybrid approaches. We close with an analogy that might help bridge the gap. (shrink)

Visual comparison is a key process in everyday learning and reasoning. Recent research has discovered the spatial alignment principle, based on the broader framework of structure‐mapping theory in comparison. According to the spatial alignment principle, visual comparison is more efficient when the figures being compared are arranged in direct placement—that is, juxtaposed with parallel structural axes. In this placement, (1) the intended relational correspondences are readily apparent, and (2) the influence of potential competing correspondences is minimized. There is evidence for (...) the spatial alignment principle in adults’ visual comparison (Matlen et al., 2020). Here, we test whether it holds for children. Six‐ and eight‐year‐old children performed a same‐different task over visual pairs. The results indicated that direct placement led to faster and more accurate comparison, both for concrete same‐different matches (matches of both objects and relations) and for purely relational matches—evidence that the same structural alignment process holds for visual comparison in 6‐ and 8‐year‐olds as in adults. These findings have implications for learning and education. (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)

Policymakers are responsible for key decisions about political governance. Usually, they are selected or elected based on experience and then supported in their decision-making by the additional counsel of subject experts. Those satisfied with this system believe these individuals – generally speaking – will have the right intuitions about the best types of action. This is important because political decisions have ethical implications; they affect how we all live in society. Nevertheless, there is a wealth of research that cautions against (...) trusting human judgment as it can be severely flawed. This paper will look at the root causes of the most common errors of human judgment before arguing – contra the instincts of many – that future AI systems could take a range of political decisions more reliably. I will argue that, if/when engineers establish ethically robust systems, governments will have a moral obligation to refer to them as a part of decision-making. (shrink)

Advances in artificial intelligence have raised a basic question about human intelligence: Is human reasoning best emulated by applying task‐specific knowledge acquired from a wealth of prior experience, or is it based on the domain‐general manipulation and comparison of mental representations? We address this question for the case of visual analogical reasoning. Using realistic images of familiar three‐dimensional objects (cars and their parts), we systematically manipulated viewpoints, part relations, and entity properties in visual analogy problems. We compared human performance to (...) that of two recent deep learning models (Siamese Network and Relation Network) that were directly trained to solve these problems and to apply their task‐specific knowledge to analogical reasoning. We also developed a new model using part‐based comparison (PCM) by applying a domain‐general mapping procedure to learned representations of cars and their component parts. Across four‐term analogies (Experiment 1) and open‐ended analogies (Experiment 2), the domain‐general PCM model, but not the task‐specific deep learning models, generated performance similar in key aspects to that of human reasoners. These findings provide evidence that human‐like analogical reasoning is unlikely to be achieved by applying deep learning with big data to a specific type of analogy problem. Rather, humans do (and machines might) achieve analogical reasoning by learning representations that encode structural information useful for multiple tasks, coupled with efficient computation of relational similarity. (shrink)

A problem is a situation in which an agent seeks to attain a given goal without knowing how to achieve it. Human problem solving is typically studied as a search in a problem space composed of states (information about the environment) and operators (to move between states). A problem such as playing a game of chess has possible states, and a traveling salesperson problem with as little as 82 cities already has more than different tours (similar to chess). Biological neurons (...) are slower than the digital switches in computers. An exhaustive search of the problem space exceeds the capacity of current computers for most interesting problems, and it is fairly clear that humans cannot in their lifetime exhaustively search even small fractions of these problem spaces. Yet, humans play chess and solve logistical problems of similar complexity on a daily basis. Even for simple problems humans do not typically engage in exploring even a small fraction of the problem space. This begs the question: How do humans solve problems on a daily basis in a fast and efficient way? Recent work suggests that humans build a problem representation and solve the represented problem—not the problem that is out there. The problem representation that is built and the process used to solve it are constrained by limits of cognitive capacity and a cost–benefit analysis discounting effort and reward. In this article, we argue that better understanding the way humans represent and solve problems using heuristics can help inform how simpler algorithms and representations can be used in artificial intelligence to lower computational complexity, reduce computation time, and facilitate real-time computation in complex problem solving. (shrink)