This article describes an integrated theory of analogical access and mapping, instantiated in a

Abstract. The practice of first-order logic is replete with meta-level concepts. Most notably there are meta-variables ranging over formulae, variables, and terms, and properties of syntax such as alpha-equivalence, capture-avoiding substitution and assumptions about freshness of variables with respect to metavariables. We present one-and-a-halfth-order logic, in which these concepts are made explicit. We exhibit both sequent and algebraic specifications of one-and-a-halfth-order logic derivability, show them equivalent, show that the derivations satisfy cut-elimination, and prove correctness of an interpretation of first-order logic within it. We discuss the technicalities in a wider context as a case-study for nominal algebra, as a logic in its own right, as an algebraisation of logic, as an example of how other systems might be treated, and also as a theoretical foundation

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The authors present a theory of how relational inference and generalization can be accomplished within a cognitive architecture that is psychologically and neurally realistic. Their proposal is a form of symbolic connectionism: a connectionist system based on distributed representations of concept meanings, using temporal synchrony to bind fillers and roles into relational structures. The authors present a specific instantiation of their theory in the form of a computer simulation model, Learning and Inference with Schemas and Analogies (LISA). By using a kind of self-supervised learning, LISA can make specific inferences and form new relational generalizations and can hence acquire new schemas by induction from examples. The authors demonstrate the sufficiency of the model by using it to simulate a body of empirical phenomena concerning analogical inference and relational generalization. A fundamental aspect of human intelligence is the ability to form and manipulate relational representations. Examples of relational thinking include the ability to appreciate analogies between seemingly different objects or events (Gentner, 1983; Holyoak & Thagard, 1995), the ability to apply abstract rules in novel situations (e.g., Smith, Langston, & Nisbett, 1992), the ability to understand and learn language (e.g., Kim, Pinker, Prince, & Prasada, 1991), and even the ability to appreciate perceptual similarities

The use of analogy in human thinking is examined from the perspective of a multiconstraint theory, which postu-lates 3 basic types of constraints: similarity, structure, and purpose. The operation of these constraints is appar-ent in laboratory experiments on analogy and in natural-istic settings, including politics, psychotherapy, and sci-entific research. The multiconstraint theory has been im-plemented in detailed computational simulations of the analogical human mind. ~ ~ any parents know that young children take comfort in getting a kiss on an injury to "make it better. " Little Aaron, aged 24 months, would routinely come to his mother saying things like, "I bump my head. Kiss it. " But one morning, for the first time ever, the tables turned. While his mother was dressing

Recent constraint-satisfaction models of explanation, analogy, and decision making claim that these processes are influenced by bidirectional constraints that promote coherence. College students were asked to reach a verdict in a complex legal case involving multiple conflicting arguments, including alternative analogies to the target case. Participants rated agreement with the individual arguments both in isolation before seeing the case, and again after reaching a verdict. Assessments of the individual arguments (including the competing analogies) shifted so as to cohere with their emerging verdict. Information about the character of the defendant in the initial case triggered a cascade of "spreading coherence", influencing decisions made about a subsequent case involving very different legal issues. Participants ' memory for their initial positions also shifted so as to cohere with their final positions. The coherence shifts were simulated by a constraint satisfaction model. The results demonstrate that an alogical process of constraint satisfaction can transform highly ambiguous inputs into coherent decisions. Bidirectional Reasoning 3 One of the most deep-rooted assumptions about human reasoning is that the flow of

It is assumed that players bundle nodes in which other players must move into analogy classes, and players only have expectations about the average behavior in every class. A solution concept is proposed for multi-stage games with perfect information: at every node players choose best-responses to their analogy-based expectations, and expectations are correct on average over those various nodes pooled together into the same analogy classes. The approach is applied to a variety of games. It is shown that a player may beneÞt from having a coarse analogy partitioning. And for simple analogy partitioning, (1) initial cooperation followed by an end opportunistic behavior may emerge in the Þnitely repeated prisoner’s dilemma (or in the centipede game), (2) an agreement need not be reached immediately in bargaining games with complete information.

This paper presents several challenges to the models of analogy-making, namely the need for building integrated models, the need for using dynamic and emergent representations, the need for using dynamic and emergent computation, and the need to integrate analogy-making with other cognitive processes. Some experimental data are reviewed which substantiate these needs and the main ideas how the AMBR model of analogy-making could meet these challenges are presented. 1. From the Anatomy towards the Physiology of AnalogyMaking: The Need for Integrated and Dynamic Models For a long time now the research on analogy has concentrated on the anatomy of analogymaking, i.e. on decomposing it into pieces (representation building, retrieval, mapping, transfer, evaluation, learning) and trying to understand how each individual piece works. A number of successful models of various subprocesses (mainly of mapping and retrieval) have been built which account for most of the psy...

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This article describes the path-mapping theory of how humans integrate analogical mapping and general problem solving. The theory posits that humans represent analogs with declarative roles, map analogs by lower-level retrieval of analogous role paths, and coordinate mappings with higher-level organizational knowledge. Implemented in the ACT-R cognitive architecture, the path-mapping theory enables models of analogical mapping behavior to incorporate and interface with other problem-solving knowledge. Path-mapping models thus can include task-specific skills such as encoding analogs or generating responses, and can make behavioral predictions at the level of real-world metrics such as latency or correctness. We show that the path-mapping theory can successfully account for the major phenomena addressed by previous theories of analogy. We also describe a path-mapping model that can account for subjects’ incremental eye-movement and typing behavior in a story-mapping task. We discuss extensions and implications of this work to other areas of analogy and problem-solving research.