Logical Reasoning
logical reasoning
Analogy and Law
Abstracts: https://sites.google.com/site/analogylist/analogical-minds-seminar/analogy-and-law-symposium
Analogical Reasoning and Generalization for Interactive Task Learning in Physical Machines
Humans are natural teachers; learning through instruction is one of the most fundamental ways that we learn. Interactive Task Learning (ITL) is an emerging research agenda that studies the design of complex intelligent robots that can acquire new knowledge through natural human teacher-robot learner interactions. ITL methods are particularly useful for designing intelligent robots whose behavior can be adapted by humans collaborating with them. In this talk, I will summarize our recent findings on the structure that human instruction naturally has and motivate an intelligent system design that can exploit their structure. The system – AILEEN – is being developed using the common model of cognition. Architectures that implement the Common Model of Cognition - Soar, ACT-R, and Sigma - have a prominent place in research on cognitive modeling as well as on designing complex intelligent agents. However, they miss a critical piece of intelligent behavior – analogical reasoning and generalization. I will introduce a new memory – concept memory – that integrates with a common model of cognition architecture and supports ITL.
How Children Design by Analogy: The Role of Spatial Thinking
Analogical reasoning is a common reasoning tool for learning and problem-solving. Existing research has extensively studied children’s reasoning when comparing, or choosing from ready-made analogies. Relatively less is known about how children come up with analogies in authentic learning environments. Design education provides a suitable context to investigate how children generate analogies for creative learning purposes. Meanwhile, the frequent use of visual analogies in design provides an additional opportunity to understand the role of spatial reasoning in design-by-analogy. Spatial reasoning is one of the most studied human cognitive factors and is critical to the learning of science, technology, engineering, arts, and mathematics (STEAM). There is growing interest in exploring the interplay between analogical reasoning and spatial reasoning. In this talk, I will share qualitative findings from a case study, where a class of 11-to-12-year-olds in the Netherlands participated in a biomimicry design project. These findings illustrate (1) practical ways to support children’s analogical reasoning in the ideation process and (2) the potential role of spatial reasoning as seen in children mapping form-function relationships in nature analogically and adaptively to those in human designs.
Cognitive supports for analogical reasoning in rational number understanding
In cognitive development, learning more than the input provides is a central challenge. This challenge is especially evident in learning the meaning of numbers. Integers – and the quantities they denote – are potentially infinite, as are the fractional values between every integer. Yet children’s experiences of numbers are necessarily finite. Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input. However, retrieving proper analogy requires cognitive supports. In this talk, I seek to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning. To examine these hypotheses, I will present a series of educational intervention studies with third-to-fifth graders. Results showed that a short, unsupervised intervention of spatial alignment between integers and fractions on number lines produced broad and durable gains in fractional magnitudes. Additionally, training on conceptual knowledge of fractions – that fractions denote magnitude and can be placed on number lines – facilitates explicit analogical reasoning. Together, these studies indicate that analogies can play an important role in rational number learning with the help of number lines as schemas. These studies shed light on helpful practices in STEM education curricula and instructions.
Multimodal Blending
In this talk, I’ll consider how new ideas emerge from old ones via the process of conceptual blending. I’ll start by considering analogical reasoning in problem solving and the role conceptual blending plays in these problem-solving contexts. Then I’ll consider blending in multi-modal contexts, including timelines, memes (viz. image macros), and, if time allows, zoom meetings. I suggest mappings analogy researchers have traditionally considered superficial are often important for the development of novel abstractions. Likewise, the analogue portion of multimodal blends anchors their generative capacity. Overall, these observations underscore the extent to which meaning is a socially distributed process whose intermediate products are stored in cognitive artifacts such as text and digital images.
Do large language models solve verbal analogies like children do?
Analogical reasoning –learning about new things by relating it to previous knowledge– lies at the heart of human intelligence and creativity and forms the core of educational practice. Children start creating and using analogies early on, making incredible progress moving from associative processes to successful analogical reasoning. For example, if we ask a four-year-old “Horse belongs to stable like chicken belongs to …?” they may use association and reply “egg”, whereas older children will likely give the intended relational response “chicken coop” (or other term to refer to a chicken’s home). Interestingly, despite state-of-the-art AI-language models having superhuman encyclopedic knowledge and superior memory and computational power, our pilot studies show that these large language models often make mistakes providing associative rather than relational responses to verbal analogies. For example, when we asked four- to eight-year-olds to solve the analogy “body is to feet as tree is to …?” they responded “roots” without hesitation, but large language models tend to provide more associative responses such as “leaves”. In this study we examine the similarities and differences between children's and six large language models' (Dutch/multilingual models: RobBERT, BERT-je, M-BERT, GPT-2, M-GPT, Word2Vec and Fasttext) responses to verbal analogies extracted from an online adaptive learning environment, where >14,000 7-12 year-olds from the Netherlands solved 20 or more items from a database of 900 Dutch language verbal analogies.
Learning by Analogy in Mathematics
Analogies between old and new concepts are common during classroom instruction. While previous studies of transfer focus on how features of initial learning guide later transfer to new problem solving, less is known about how to best support analogical transfer from previous learning while children are engaged in new learning episodes. Such research may have important implications for teaching and learning in mathematics, which often includes analogies between old and new information. Some existing research promotes supporting learners' explicit connections across old and new information within an analogy. In this talk, I will present evidence that instructors can invite implicit analogical reasoning through warm-up activities designed to activate relevant prior knowledge. Warm-up activities "close the transfer space" between old and new learning without additional direct instruction.
Learning Relational Rules from Rewards
Humans perceive the world in terms of objects and relations between them. In fact, for any given pair of objects, there is a myriad of relations that apply to them. How does the cognitive system learn which relations are useful to characterize the task at hand? And how can it use these representations to build a relational policy to interact effectively with the environment? In this paper we propose that this problem can be understood through the lens of a sub-field of symbolic machine learning called relational reinforcement learning (RRL). To demonstrate the potential of our approach, we build a simple model of relational policy learning based on a function approximator developed in RRL. We trained and tested our model in three Atari games that required to consider an increasingly number of potential relations: Breakout, Pong and Demon Attack. In each game, our model was able to select adequate relational representations and build a relational policy incrementally. We discuss the relationship between our model with models of relational and analogical reasoning, as well as its limitations and future directions of research.
AI-assisted language learning: Assessing learners who memorize and reason by analogy
Vocabulary learning applications like Duolingo have millions of users around the world, but yet are based on very simple heuristics to choose teaching material to provide to their users. In this presentation, we will discuss the possibility to develop more advanced artificial teachers, which would be based on modeling of the learner’s inner characteristics. In the case of teaching vocabulary, understanding how the learner memorizes is enough. When it comes to picking grammar exercises, it becomes essential to assess how the learner reasons, in particular by analogy. This second application will illustrate how analogical and case-based reasoning can be employed in an alternative way in education: not as the teaching algorithm, but as a part of the learner’s model.
Is Theory of Mind Analogical? Evidence from the Analogical Theory of Mind cognitive model
Theory of mind, which consists of reasoning about the knowledge, belief, desire, and similar mental states of others, is a key component of social reasoning and social interaction. While it has been studied by cognitive scientists for decades, none of the prevailing theories of the processes that underlie theory of mind reasoning and development explain the breadth of experimental findings. I propose that this is because theory of mind is, like much of human reasoning, inherently analogical. In this talk, I will discuss several theory of mind findings from the psychology literature, the challenges they pose for our understanding of theory of mind, and bring in evidence from the Analogical Theory of Mind (AToM) cognitive model that demonstrates how these findings fit into an analogical understanding of theory of mind reasoning.
Analogy and Spatial Cognition: How and Why they matter for STEM learning
Space is the universal donor for relations" (Gentner, 2014). This quote is the foundation of my talk. I will explore how and why visual representations and analogies are related, and why. I will also explore how considering the relation between analogy and spatial reasoning can shed light on why and how spatial thinking is correlated with learning in STEM fields. For example, I will consider children’s numbers sense and learning of the number line from the perspective of analogical reasoning.
Analogical retrieval across disparate task domains
Previous experiments have shown that a comparison of two written narratives highlights their shared relational structure, which in turn facilitates the retrieval of analogous narratives from the past (e.g., Gentner, Loewenstein, Thompson, & Forbus, 2009). However, analogical retrieval occurs across domains that appear more conceptually distant than merely different narratives, and the deepest analogies use matches in higher-order relational structure. The present study investigated whether comparison can facilitate analogical retrieval of higher-order relations across written narratives and abstract symbolic problems. Participants read stories which became retrieval targets after a delay, cued by either analogous stories or letter-strings. In Experiment 1 we replicated Gentner et al. who used narrative retrieval cues, and also found preliminary evidence for retrieval between narrative and symbolic domains. In Experiment 2 we found clear evidence that a comparison of analogous letter-string problems facilitated the retrieval of source stories with analogous higher-order relations. Experiment 3 replicated the retrieval results of Experiment 2 but with a longer delay between encoding and recall, and a greater number of distractor source stories. These experiments offer support for the schema induction account of analogical retrieval (Gentner et al., 2009) and show that the schemas abstracted from comparison of narratives can be transferred to non-semantic symbolic domains.
Analogy Use in Parental Explanation
How and why are analogies spontaneously generated? Despite the prominence of analogy in learning and reasoning, there is little research on whether and how analogy is spontaneously generated in everyday settings. Here we fill this gap by gathering parents' answers to children's real questions, and examining analogy use in parental explanations. Study 1 found that parents used analogy spontaneously in their explanations, despite no prompt nor mention of analogy in the instruction. Study 2 found that these analogical explanations were rated highly by parents, schoolteachers, and university students alike. In Study 3, six-year-olds also rated good analogical explanations highly, but unlike their parents, did not rate them higher than causal, non-analogical explanations. We discuss what makes an analogy a good explanation, and how theories from both explanation and analogy research explain one’s motivation for spontaneously generating analogies.
Exploration-Based Approach for Computationally Supported Design-by-Analogy
Engineering designers practice design-by-analogy (DbA) during concept generation to retrieve knowledge from external sources or memory as inspiration to solve design problems. DbA is a tool for innovation that involves retrieving analogies from a source domain and transferring the knowledge to a target domain. While DbA produces innovative results, designers often come up with analogies by themselves or through serendipitous, random encounters. Computational support systems for searching analogies have been developed to facilitate DbA in systematic design practice. However, many systems have focused on a query-based approach, in which a designer inputs a keyword or a query function and is returned a set of algorithmically determined stimuli. In this presentation, a new analogical retrieval process that leverages a visual interaction technique is introduced. It enables designers to explore a space of analogies, rather than be constrained by what’s retrieved by a query-based algorithm. With an exploration-based DbA tool, designers have the potential to uncover more useful and unexpected inspiration for innovative design solutions.
Semantic Distance and Beyond: Interacting Predictors of Verbal Analogy Performance
Prior studies of A:B::C:D verbal analogies have identified several factors that affect performance, including the semantic similarity between source and target domains (semantic distance), the semantic association between the C-term and incorrect answers (distracter salience), and the type of relations between word pairs (e.g., categorical, compositional, and causal). However, it is unclear how these stimulus properties affect performance when utilized together. Moreover, how do these item factors interact with individual differences such as crystallized intelligence and creative thinking? Several studies reveal interactions among these item and individual difference factors impacting verbal analogy performance. For example, a three-way interaction demonstrated that the effects of semantic distance and distracter salience had a greater impact on performance for compositional and causal relations than for categorical ones (Jones, Kmiecik, Irwin, & Morrison, 2022). Implications for analogy theories and future directions are discussed.
Children’s inference of verb meanings: Inductive, analogical and abductive inference
Children need inference in order to learn the meanings of words. They must infer the referent from the situation in which a target word is said. Furthermore, to be able to use the word in other situations, they also need to infer what other referents the word can be generalized to. As verbs refer to relations between arguments, verb learning requires relational analogical inference, something which is challenging to young children. To overcome this difficulty, young children recruit a diverse range of cues in their inference of verb meanings, including, but not limited to, syntactic cues and social and pragmatic cues as well as statistical cues. They also utilize perceptual similarity (object similarity) in progressive alignment to extract relational verb meanings and further to gain insights about relational verb meanings. However, just having a list of these cues is not useful: the cues must be selected, combined, and coordinated to produce the optimal interpretation in a particular context. This process involves abductive reasoning, similar to what scientists do to form hypotheses from a range of facts or evidence. In this talk, I discuss how children use a chain of inferences to learn meanings of verbs. I consider not only the process of analogical mapping and progressive alignment, but also how children use abductive inference to find the source of analogy and gain insights into the general principles underlying verb learning. I also present recent findings from my laboratory that show that prelinguistic human infants use a rudimentary form of abductive reasoning, which enables the first step of word learning.
A new experimental paradigm to study analogy transfer
Analogical reasoning is one of the most complex cognitive functions in humans that allows abstract thinking, high-level reasoning, and learning. Based on analogical reasoning, one can extract an abstract and general concept (i.e., an analogy schema) from a familiar situation and apply it to a new context or domain (i.e., analogy transfer). These processes allow us to solve problems we never encountered before and generate new ideas. However, the place of analogy transfer in problem solving mechanisms is unclear. This presentation will describe several experiments with three main findings. First, we show how analogy transfer facilitates problem-solving, replicating existing empirical data largely based on the radiation/fortress problems with four new riddles. Second, we propose a new experimental task that allows us to quantify analogy transfer. Finally, using science network methodology, we show how restructuring the mental representation of a problem can predict successful solving of an analogous problem. These results shed new light on the cognitive mechanism underlying solution transfer by analogy and provide a new tool to quantify individual abilities.
Assessing the potential for learning analogy problem-solving: does EF play a role?
Analogical reasoning is related to everyday learning and scholastic learning and is a robust predictor of g. Therefore, children's ability to reason by analogy is often measured in a school context to gain insight into children's cognitive and intellectual functioning. Often, the ability to reason by analogy is measured by means of conventional, static instruments. Static tests are criticised by researchers and practitioners to provide an overview of what individuals have learned in the past and for this reason are assumed not to tap into the potential for learning, based on Vygotsky's zone of proximal development. This seminar will focus on children's potential for reasoning by analogy, as measured by means of a dynamic test, which has a test-training-test design. In so doing, the potential relationship between dynamic test outcomes and executive functioning will be explored.
Symposium on cross-cultural research in analogical reasoning
Abstracts: https://www.sites.google.com/site/analogylist/cross-cultural-symposium
Implementing structure mapping as a prior in deep learning models for abstract reasoning
Building conceptual abstractions from sensory information and then reasoning about them is central to human intelligence. Abstract reasoning both relies on, and is facilitated by, our ability to make analogies about concepts from known domains to novel domains. Structure Mapping Theory of human analogical reasoning posits that analogical mappings rely on (higher-order) relations and not on the sensory content of the domain. This enables humans to reason systematically about novel domains, a problem with which machine learning (ML) models tend to struggle. We introduce a two-stage neural net framework, which we label Neural Structure Mapping (NSM), to learn visual analogies from Raven's Progressive Matrices, an abstract visual reasoning test of fluid intelligence. Our framework uses (1) a multi-task visual relationship encoder to extract constituent concepts from raw visual input in the source domain, and (2) a neural module net analogy inference engine to reason compositionally about the inferred relation in the target domain. Our NSM approach (a) isolates the relational structure from the source domain with high accuracy, and (b) successfully utilizes this structure for analogical reasoning in the target domain.
Analogical Reasoning with Neuro-Symbolic AI
Knowledge discovery with computers requires a huge amount of search. Analogical reasoning is effective for efficient knowledge discovery. Therefore, we proposed analogical reasoning systems based on first-order predicate logic using Neuro-Symbolic AI. Neuro-Symbolic AI is a combination of Symbolic AI and artificial neural networks and has features that are easy for human interpretation and robust against data ambiguity and errors. We have implemented analogical reasoning systems by Neuro-symbolic AI models with word embedding which can represent similarity between words. Using the proposed systems, we efficiently extracted unknown rules from knowledge bases described in Prolog. The proposed method is the first case of analogical reasoning based on the first-order predicate logic using deep learning.
Do we reason differently about affectively charged analogies? Insights from EEG research
Affectively charged analogies are commonly used in literature and art, but also in politics and argumentation. There are reasons to think we may process these analogies differently. Notably, analogical reasoning is a complex process that requires the use of cognitive resources, which are limited. In the presence of affectively charged content, some of these resources might be directed towards affective processing and away from analogical reasoning. To investigate this idea, I investigated effects of affective charge on differences in brain activity evoked by sound versus unsound analogies. The presentation will detail the methods and results for two such experiments, one in which participants saw analogies formed of neutral and negative words and one in which they were created by combining conditioned symbols. I will also briefly discuss future research aiming to investigate the effects of analogical reasoning on brain activity related to affective processing.
Understanding and Enhancing Creative Analogical Reasoning
This talk will focus on our lab's extensive research on understanding and enhancing creative analogical reasoning. I will cover the development of the analogy finding matrix task, evidence for conscious augmentation of creative state during this task, and the real-world implications this ability has for college STEM education. I will also discuss recent research aimed at enhancing performance on this creative analogical reasoning task using both transcranial direct current stimulation (tDCS) and transcranial alternating current stimulation (tACS).
Scaffolding up from Social Interactions: A proposal of how social interactions might shape learning across development
Social learning and analogical reasoning both provide exponential opportunities for learning. These skills have largely been studied independently, but my future research asks how combining skills across previously independent domains could add up to more than the sum of their parts. Analogical reasoning allows individuals to transfer learning between contexts and opens up infinite opportunities for innovation and knowledge creation. Its origins and development, so far, have largely been studied in purely cognitive domains. Constraining analogical development to non-social domains may mistakenly lead researchers to overlook its early roots and limit ideas about its potential scope. Building a bridge between social learning and analogy could facilitate identification of the origins of analogical reasoning and broaden its far-reaching potential. In this talk, I propose that the early emergence of social learning, its saliency, and its meaningful context for young children provides a springboard for learning. In addition to providing a strong foundation for early analogical reasoning, the social domain provides an avenue for scaling up analogies in order to learn to learn from others via increasingly complex and broad routes.
Causal Reasoning: Its role in the architecture and development of the mind
The seminar will first outline the architecture of the human mind, specifying general and domain-specific mental processes. The place of causal reasoning and its relations with the other processes will be specified. Experimental, psychometric, developmental, and brain-based evidence will be summarized. The main message of the talk is that causal thought involves domain-specific core processes rooted in perception and served by special brain networks which capture interactions between objects. With development, causal reasoning is increasingly associated with a general abstraction system which generates general principles underlying inductive, analogical, and deductive reasoning and also heuristics for specifying causal relations. These associations are discussed in some detail. Possible implications for artificial intelligence and educational implications are also discussed.
A Functional Approach to Analogical Reasoning in Scientific Practice
The talk argues for a new approach to analysing analogical reasoning in scientific practice. Traditionally, philosophers of science tend to analyse analogical reasoning in either a top-down way or a bottom-up way. Examples of top-down approaches include Mary Hesse’s seminal work (1963) and Paul Bartha’s articulation model (2010), while most popular bottom-up approach is John Norton’s material approach (2018). I will address the problems of these traditional approaches and introduce an alternative approach, which is motivated by my exemplar-based approach to the history of science, defended in my recent book (2020).
Children's relational noun generalization strategies
A common result is that comparison settings (i.e., several stimuli introduced simultaneously) favor conceptualization and generalization. However still little is known of the solving strategies used by children to compare and generalize novel words. Understanding the temporal dynamics of children’s solving strategies may help assess which processes underlie generalization. We tested children in noun and relational noun generalization tasks and collected eye tracking data. To analyze and interpret the data we followed predictions made by existing models of analogical reasoning and generalization. The data reveals clear patterns of exploration in which participants compare learning items before searching for a solution. Analyses of the beginning of trials show that early comparisons favor generalization and that errors may be caused by a lake of early comparison. Children then pursue their search in different ways according to the task. In this presentation I will present the generalization strategies revealed by eye tracking, compare the strategies from both tasks and confront them to existing models.
Beyond the binding problem: From basic affordances to symbolic thought
Human cognitive abilities seem qualitatively different from the cognitive abilities of other primates, a difference Penn, Holyoak, and Povinelli (2008) attribute to role-based relational reasoning—inferences and generalizations based on the relational roles to which objects (and other relations) are bound, rather than just the features of the objects themselves. Role-based relational reasoning depends on the ability to dynamically bind arguments to relational roles. But dynamic binding cannot be sufficient for relational thinking: Some non-human animals solve the dynamic binding problem, at least in some domains; and many non-human species generalize affordances to completely novel objects and scenes, a kind of universal generalization that likely depends on dynamic binding. If they can solve the dynamic binding problem, then why can they not reason about relations? What are they missing? I will present simulations with the LISA model of analogical reasoning (Hummel & Holyoak, 1997, 2003) suggesting that the missing pieces are multi-role integration (the capacity to combine multiple role bindings into complete relations) and structure mapping (the capacity to map different systems of role bindings onto one another). When LISA is deprived of either of these capacities, it can still generalize affordances universally, but it cannot reason symbolically; granted both abilities, LISA enjoys the full power of relational (symbolic) thought. I speculate that one reason it may have taken relational reasoning so long to evolve is that it required evolution to solve both problems simultaneously, since neither multi-role integration nor structure mapping appears to confer any adaptive advantage over simple role binding on its own.
Analogical Reasoning Plus: Why Dissimilarities Matter
Analogical reasoning remains foundational to the human ability to forge meaningful patterns within the sea of information that continually inundates the senses. Yet, meaningful patterns rely not only on the recognition of attributional similarities but also dissimilarities. Just as the perception of images rests on the juxtaposition of lightness and darkness, reasoning relationally requires systematic attention to both similarities and dissimilarities. With that awareness, my colleagues and I have expanded the study of relational reasoning beyond analogous reasoning and attributional similarities to highlight forms based on the nature of core dissimilarities: anomalous, antinomous, and antithetical reasoning. In this presentation, I will delineate the character of these relational reasoning forms; summarize procedures and measures used to assess them; overview key research findings; and describe how the forms of relational reasoning work together in the performance of complex problem solving. Finally, I will share critical next steps for research which has implications for instructional practice.
Conceptual Change Induced by Analogical Reasoning Sparks “Aha!” Moments
Although analogical reasoning has been assumed to involve insight and its associated “aha!” experience, the relationship between these phenomena has never been directly probed empirically. In this study we investigated the relationship between representational change and the “aha!” experience during analogical reasoning. A novel set of verbal analogy stimuli were developed for use as an insight task. Across two experiments, participants reported significantly stronger aha moments and showed greater evidence of representational change on trials with more semantically distant analogies. Further, the strength of reported aha moments was correlated with the degree to which participants’ descriptions of the analogies changed over the course of each trial. Lastly, we probed the individual differences associated with a tendency to report stronger "aha" experiences, particularly related to mood, curiosity, and reward responsiveness. The findings shed light on the affective components of analogical reasoning and suggest that measuring affective responses during such tasks may elucidate novel insights into the mechanisms of creative analogical reasoning.
A role for cognitive maps in metaphors and analogy?
In human and non-human animals, conceptual knowledge is partially organized according to low-dimensional geometries that rely on brain structures and computations involved in spatial representations. Recently, two separate lines of research have investigated cognitive maps, that are associated with the hippocampal formation and are similar to world-centered representations of the environment, and image spaces, that are associated with the parietal cortex and are similar to self-centered spatial relationships. I will suggest that cognitive maps and image spaces may be two manifestations of a more general propensity of the mind to create low-dimensional internal models, and may play a role in analogical reasoning and metaphorical thinking. Finally, I will show some data suggesting that the metaphorical relationship between colors and emotions can be accounted for by the structural alignment of low-dimensional conceptual spaces.
Representations of abstract relations in infancy
Abstract relations are considered the pinnacle of human cognition, allowing analogical and logical reasoning, and possibly setting humans apart from other animal species. Such relations cannot be represented in a perceptual code but can easily be represented in a propositional language of thought, where relations between objects are represented by abstract discrete symbols. Focusing on the abstract relations same and different, I will show that (1) there is a discontinuity along ontogeny with respect to the representations of abstract relations, but (2) young infants already possess representations of same and different. Finally, (3) I will investigate the format of representation of abstract relations in young infants, arguing that those representations are not discrete, but rather built by juxtaposing abstract representations of entities.
Transforming task representations
Humans can adapt to a novel task on our first try. By contrast, artificial intelligence systems often require immense amounts of data to adapt. In this talk, I will discuss my recent work (https://www.pnas.org/content/117/52/32970) on creating deep learning systems that can adapt on their first try by exploiting relationships between tasks. Specifically, the approach is based on transforming a representation for a known task to produce a representation for the novel task, by inferring and then using a higher order function that captures a relationship between the tasks. This approach can be interpreted as a type of analogical reasoning. I will show that task transformation can allow systems to adapt to novel tasks on their first try in domains ranging from card games, to mathematical objects, to image classification and reinforcement learning. I will discuss the analogical interpretation of this approach, an analogy between levels of abstraction within the model architecture that I refer to as homoiconicity, and what this work might suggest about using deep-learning models to infer analogies more generally.
Analogical reasoning and metaphor processing in autism - Similarities & differences
In this talk, I will present the results of two recent systematic reviews and meta-analyses related to analogical reasoning and metaphor processing in autism, together with the results of a study that investigated verbal analogical reasoning and metaphor processing in the same sample of participants. Both metaphors and analogies rely on exploiting similarities, and they necessitate contextual processing. Nevertheless, our findings relating to metaphor processing and analogical reasoning showed distinct patterns. Whereas analogical reasoning emerged as a relative strength in autism, metaphor processing was found to be a relative weakness. Additionally, both meta-analytic studies investigated the relations between the level of intelligence of participants included in the studies, and the effect size of group differences between the autistic and typically developing (TD) samples. These analyses suggested in the case of analogical reasoning that the relative advantage of ASD participants might only be present in the case of individuals with lower levels of intelligence. By contrast, impairments in metaphor processing appeared to be more pronounced in the case of individuals with relatively lower levels of (verbal) intelligence. In our experimental study, we administered both verbal analogies and metaphors to the same sample of high-functioning autistic participants and TD controls. The two groups were matched on age, verbal IQ, working memory and educational background. Our aim was to understand better the similarities and differences between processing analogies and metaphors, and to see whether the advantage in analogical reasoning and disadvantage in metaphor processing is universal in autism.
One Instructional Sequence Fits all? A Conceptual Analysis of the Applicability of Concreteness Fading
According to the concreteness fading approach, instruction should start with concrete representations and progress stepwise to representations that are more idealized. Various researchers have suggested that concreteness fading is a broadly applicable instructional approach. In this talk, we conceptually analyze examples of concreteness fading in mathematics and various science domains. In this analysis, we draw on theories of analogical and relational reasoning and on the literature about learning with multiple representations. Furthermore, we report on an experimental study in which we employed concreteness fading in advanced physics education. The results of the conceptual analysis and the experimental study indicate that concreteness fading may not be as generalizable as has been suggested. The reasons for this limited generalizability are twofold. First, the types of representations and the relations between them differ across different domains. Second, the instructional goals between domains and the subsequent roles of the representations vary.
Using Developmental Trajectories to Understand Change in Children’s Analogical Reasoning
Analogical reasoning is a complex ‘high-level’ cognitive process characterised by making inferences based on analogical comparisons. As with other high-level processes, development takes place over a protracted time period and believed to result from changes in multiple ‘lower-level’ systems. In the case of analogical reasoning, changes in systems responsible for conceptual knowledge, task knowledge, inhibition, and working memory have all been causally implicated in development. Whilst there is evidence that each of these systems contributes to development, what the relative contribution of each across development is, and how they interact with each, remain largely unanswered questions. In this presentation, I will describe how cross-sectional trajectory analysis can be used as a complementary method to shed light on these questions.
Analogies, Games and the Learning of Mathematics
Research on analogical processing and reasoning has provided strong evidence that the use of adequate educational analogies has strong and positive effects on the learning of mathematics. In this talk I will show some experimental results suggesting that analogies based on spatial representations might be particularly effective to improve mathematics learning. Since fostering mathematics learning also involves addressing psychosocial factors such as the development of mathematical anxiety, providing social incentives to learn, and fostering engagement and motivation, I will argue that one area to explore with great potential to improve math learning is applying analogical research in the development of learning games aimed to improve math learning. Finally, I will show some early prototypes of an educational project devoted to developing games designed to foster the learning of early mathematics in kindergarten children.
Logical Neural Networks
The work to be presented in this talk proposes a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a highly interpretable disentangled representation. Inference is omnidirectional rather than focused on predefined target variables, and corresponds to logical reasoning, including classical first-order logic theorem proving as a special case. The model is end-to-end differentiable, and learning minimizes a novel loss function capturing logical contradiction, yielding resilience to inconsistent knowledge. It also enables the open-world assumption by maintaining bounds on truth values which can have probabilistic semantics, yielding resilience to incomplete knowledge.
Abstract Semantic Relations in Mind, Brain, and Machines
Abstract semantic relations (e.g., category membership, part-whole, antonymy, cause-effect) are central to human intelligence, underlying the distinctively human ability to reason by analogy. I will describe a computational project (Bayesian Analogy with Relational Transformations) that aims to extract explicit representations of abstract semantic relations from non-relational inputs automatically generated by machine learning. BART’s representations predict patterns of typicality and similarity for semantic relations, as well as similarity of neural signals triggered by semantic relations during analogical reasoning. In this approach, analogy emerges from the ability to learn and compare relations; mapping emerges later from the ability to compare patterns of relations.
Analogical Reasoning and Executive Functions - A Life Span Approach
From a developmental standpoint, it has been argued that two major complementary factors contribute to the development of analogy comprehension: world knowledge and executive functions. Here I will provide evidence in support of the second view. Beyond paradigms that manipulate task difficulty (e.g., number and types of distractors and semantic distance between domains) we will provide eye-tracking data that describes differences in the way children and adults compare the base and target domains in analogy problems. We will follow the same approach with ageing people. This latter population provides a unique opportunity to disentangle the contribution of knowledge and executive processes in analogy making since knowledge is (more than) preserved and executive control is decreasing. Using this paradigm, I will show the extent to which world knowledge (assessed through vocabulary) compensates for decreasing executive control in older populations. Our eye-tracking data suggests that, to a certain extent, differences between younger and older adults are analogous to the differences between younger adults and children in the way they compare the base and the target domains in analogy problems.
Analogy in Cognitive Architecture
Cognitive architectures are attempts to build larger-scale models of minds. This talk will explore how structure-mapping models of analogical matching, retrieval, and generalization are used in the Companion cognitive architecture. Examples will include modeling conceptual change, learning by reading, and analogical Q/A training.