Inferences about spatial, temporal, and other relations are ubiquitous. This article presents a novel model-based theory of such reasoning. The theory depends on 5 principles. (a) The structure of mental models is iconic as far as possible. (b) The logical consequences of relations emerge from models constructed from the meanings of the relations and from knowledge. (c) Individuals tend to construct only a single, typical model. (d) They spontaneously develop their own strategies for relational reasoning. (e) Regardless of strategy, the difficulty of an inference depends on the process of integration of the information from separate premises, the number of entities that have to be integrated to form a model, and the depth of the relation. The article describes computer implementations of the theory and presents experimental results corroborating its main principles.

This book is about the interface between natural language and the sensorimotor system. It is obvious that there is an interface between language and sensorimotor cognition, because we can talk about what we see and do. The main proposal in the book is that the interface is more direct than is commonly assumed. To argue for this proposal I focus on a simple concrete episode—a man grabbing a cup—which can be reported in a simple transitive sentence (e.g. the English sentence The man grabbed a cup). In the first part of the book I present a detailed model of the sensorimotor processes involved in experiencing this episode, both as the agent bringing it about and as an observer watching it happen. The model draws on a large body of research in neuroscience and psychology. I also present a model of the syntactic structure of the associated transitive sentence, developed within the entirely separate discipline of theoretical linguistics. This latter model is a version of Chomsky’s ‘Minimalist ’ syntactic theory, which assumes that a sentence reporting the episode has the same underlying syntactic structure (called ‘logical form’) regardless of which language it is in. My main proposal is that these two independently motivated models are in fact closely

recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Keywords: computational modeling, cognitive modeling, instructional theory, machine learning, learning science, second language learning, mathematics learning, science learning, robust learning, learning theory, knowledge componentsExecutive Summary The volume of research on learning and instruction is enormous. Yet progress in improving educational outcomes has been slow at best. Many learning science results have not been translated into general practice and it appears that most that have been fielded have not yielded significant results in randomized control trials. Addressing the chasm between learning science and educational practice will require massive efforts from many constituencies, but one of these efforts is to develop a theoretical framework that permits a more systematic accumulation of the relevant research base. A key piece in such a theoretical framework is the development of levels of analyses that are fine enough to be supported by cognitive science and cognitive neuroscience, but also at levels appropriate to guide the design of effective educational practices. An ideal scientific solution would be a small set of universal instructional principles that can be applied to produce efficient

We examine the possibility of distributed sensemaking: improving a user’s sensemaking by leveraging previous users ’ work without those users directly collaborating or even knowing one another. We asked users to engage in sensemaking by organizing and annotating web search results into “knowledge maps, ” either with or without previous users ’ maps to work from. We also recorded gaze patterns as users examined others ’ knowledge maps. Our findings show the conditions under which distributed sensemaking can improve sensemaking quality; that a user’s sensemaking process is readily apparent to a subsequent user via a knowledge map; and that the organization of content was more useful to subsequent users than the content itself, especially when those users had differing goals. We discuss the role distributed sensemaking can play in schema induction by helping users make a mental model of an information space and make recommendations for new tool and system development. Author Keywords Sensemaking, search, collaboration, knowledge mapping.

Theories of analogical reasoning have viewed relational structure as the dominant determinant of analogical mapping and inference, while assigning lesser importance to similarity between individual objects. An experiment is reported in which these two sources of constraints on analogy are placed in competition under conditions of high relational complexity. Results demonstrate equal importance for relational structure and object similarity, both in analogical mapping and in inference generation. The human data were successfully simulated using a computational analogy model (LISA) that treats both relational correspondences and object similarity as soft constraints that operate within a limited-capacity working memory; but not with a model (SME) that treats relational structure as pre-eminent. Analogies provide a valuable source of new inferences and a means of expanding knowledge. Analogical reasoning is generally viewed as involving four major subprocesses: (1) retrieving an appropriate source analogue from long-term memory to compare with a novel target analogue, (2) mapping elements of the two analogues, (3) making inferences about the target as a function of its mapping to the source, and (4) using the source and target together to induce a more general schema or rule (e.g., Carbonell, 1983;

Consider two individuals, John and Mary, who each possess a number of concepts. How can we determine that John and Mary both have a concept of, say, Horse? John and Mary may not have exactly the same knowledge of horses, but it is important to be able to place their horse concepts into correspondence with one another, if only so that we can say things like, “Mary’s concept of horse is much more sophisticated than John’s. ” Concepts should be public in the sense that they can be possessed by more than one person (Fodor, 1998; Fodor & Lepore, 1992), and for this to be the possible, we must be able to determine correspondences, or translations, between two individuals ’ concepts. There have been two major approaches in cognitive science to conceptual meaning that could potentially provide a solution to finding translations between conceptual systems. According to an “external grounding” account, concepts ’ meanings depend on their connection to the external world (this account is more thoroughly defined in the next section). By this account, the concept Horse means what it does because our perceptual apparatus can identify features that characterize horses. According to what we will call a “Conceptual web ” account, concepts ’ meanings depend on their connections to each other. By this account, Horse’s meaning depends on Gallop, Domesticated, and Quadruped, and in turn, these concepts depend on other concepts, including Horse (Quine & Ullian, 1970). In this chapter, we will first present a brief tour of some of the main proponents of conceptual web and external grounding accounts of conceptual meaning. Then, we will describe a computer algorithm that translates between conceptual systems. The initial goal of this computational work is to show how translating across systems is possible using only withinsystem relations, as is predicted by a conceptual web account. However, the subsequent goal is to show how the synthesis of external and internal information can dramatically improve translation. This work suggests that the external grounding and conceptual web accounts should not be

Most models of categorization learn categories defined by characteristic features but some categories are described more naturally in terms of relations. We present a generative model that helps to explain how relational categories are learned and used. Our model learns abstract schemata that specify the relational similarities shared by instances of a category, and our emphasis on abstraction departs from previous theoretical proposals that focus instead on comparison of concrete instances. Our first experiment suggests that abstraction can help to explain some of the findings that have previously been used to support comparison-based approaches. Our second experiment focuses on one-shot schema learning, a problem that raises challenges for comparison-based approaches but is handled naturally by our abstraction-based account. Categories such as family, sonnet, above, betray, and imitate differ in many respects but all of them depend critically on relational information. Members of a family are typically related by blood or marriage, and the lines that make up a sonnet must rhyme with each other according to a certain

A fundamental aspect of human intelligence is the ability to represent and reason about relations. Examples of relational thinking include our ability to appreciate analogies between different objects or events (Gentner, 1983; Holyoak & Thagard, 1995), our ability to apply abstract rules in novel situations (e.g., Smith, Langston & Nisbett, 1992), our ability to understand and learn language (e.g., Kim, Pinker, Prince & Prasada, 1991), our

We describe a way of learning matrix representations of objects and relationships. The goal of learning is to allow multiplication of matrices to represent symbolic relationships between objects and symbolic relationships between relationships, which is the main novelty of the method. We demonstrate that this leads to excellent generalization in two different domains: modular arithmetic and family relationships. We show that the same system can learn first-order propositions such as (2,5) ∈ +3 or (Christopher, Penelope) ∈ has wife, and higher-order propositions such as (3,+3) ∈ plus and (+3, −3) ∈ inverse or (has husband, has wife) ∈ higher oppsex. We further demonstrate that the system understands how higher-order propositions are related to first-order ones by showing that it can correctly answer questions about first-order propositions involving the relations +3 or has wife even though it has not been trained on any first-order examples involving these relations. 1

capacities of human cognition are not entirely amodal and disembodied. The present study presents two empirical studies which aim to demonstrate that relational reasoning is grounded in our sensory-motor experience. Experiment 1 shows that the affordances of tool-like objects have an effect on comparing functional relations. Experiment 2 makes sure that this finding can not be explained by an automatic activation of motor systems. The results are interpreted as evidence that at least certain functional relations are perceived by simulating interactions with the environment. It is also asserted that the process of comparing such relations is constrained by the properties of the human body such as hand-dominance.