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Distributed representations of structure: A Theory of Analogical Access and Mapping
 Psychological Review
, 1997
"... This article describes an integrated theory of analogical access and mapping, instantiated in a ..."
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Cited by 247 (19 self)
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This article describes an integrated theory of analogical access and mapping, instantiated in a
HighLevel Perception, Representation, and Analogy: A Critique of Artificial Intelligence Methodology
 Journal of Experimental and Theoretical Artificial Intelligence
, 1992
"... Highlevel perception—the process of making sense of complex data at an abstract, conceptual level—is fundamental to human cognition. Through highlevel perception, chaotic environmental stimuli are organized into the mental representations that are used throughout cognitive processing. Much work ..."
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Cited by 94 (7 self)
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Highlevel perception—the process of making sense of complex data at an abstract, conceptual level—is fundamental to human cognition. Through highlevel perception, chaotic environmental stimuli are organized into the mental representations that are used throughout cognitive processing. Much work in traditional artificial intelligence has ignored the process of highlevel perception, by starting with handcoded representations. In this paper, we argue that this dismissal of perceptual processes leads to distorted models of human cognition. We examine some existing artificialintelligence models—notably BACON, a model of scientific discovery, and the StructureMapping Engine, a model of analogical thought—and argue that these are flawed precisely because they downplay the role of highlevel perception. Further, we argue that perceptual processes cannot be separated from other cognitive processes even in principle, and therefore that traditional artificialintelligence models cannot be defended by supposing the existence of a “representation module ” that supplies representations readymade. Finally, we describe a model of highlevel perception and analogical thought in which perceptual processing is integrated with analogical mapping, leading to the flexible buildup of representations appropriate to a given context. 1 The Problem of Perception One of the deepest problems in cognitive science is that of understanding how people make sense of the vast amount of raw data constantly bombarding them from their environment. The essence of human perception lies in the ability of the mind to hew order from this chaos, whether this means simply detecting movement in the visual field, recognizing sadness in a tone of voice, perceiving a threat on a chessboard, or coming to understand the Iran–Contra affair in terms of
Reachability Analysis Using Polygonal Projections
 IN HYBRID SYSTEMS: COMPUTATION AND CONTROL
, 1999
"... Coho is a reachability analysis tool for systems modeled by nonlinear, ordinary differential equations. Coho represents highdimensional objects using projections onto planes corresponding to pairs of variables. This representation is compact and allows efficient algorithms from computational geome ..."
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Cited by 43 (5 self)
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Coho is a reachability analysis tool for systems modeled by nonlinear, ordinary differential equations. Coho represents highdimensional objects using projections onto planes corresponding to pairs of variables. This representation is compact and allows efficient algorithms from computational geometry to be exploited while also capturing dependencies in the behaviour of related variables. Reachability is performed by integration where methods from linear programming and linear systems theory are used to bound trajectories emanating from each face of the object. This paper has two contributions: first, we describe the implementation of Coho and, second, we present analysis results obtained by using Coho on several simple models.
Exploring the symbolic/subsymbolic continuum: A case study of raam
 The Symbolic and Connectionist Paradigms: Closing the Gap
, 1992
"... It is di cult to clearly de ne the symbolic and subsymbolic paradigms; each is usually described by its tendencies rather than any one de nitive property. Symbolic processing is generally characterized by hardcoded, explicit rules operating on discrete, static tokens, while subsymbolic processing i ..."
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Cited by 39 (4 self)
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It is di cult to clearly de ne the symbolic and subsymbolic paradigms; each is usually described by its tendencies rather than any one de nitive property. Symbolic processing is generally characterized by hardcoded, explicit rules operating on discrete, static tokens, while subsymbolic processing is associated with learned, fuzzy constraints a ecting continuous,
Reachability analysis of nonlinear systems using conservative approximation
 In Oded Maler and Amir Pnueli, editors, Hybrid Systems: Computation and Control, LNCS 2623
, 2003
"... ..."
Computational Techniques for the Verification and Control of Hybrid Systems
 PROCEEDINGS OF THE IEEE
, 2003
"... Hybrid system theory lies at the intersection of the fields of engineering control theory and computer science verification. It is defined as the modeling, analysis, and control of systems which involve the interaction of both discrete state systems, represented by finite automata, and continuous ..."
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Cited by 22 (0 self)
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Hybrid system theory lies at the intersection of the fields of engineering control theory and computer science verification. It is defined as the modeling, analysis, and control of systems which involve the interaction of both discrete state systems, represented by finite automata, and continuous state dynamics, represented by differential equations. The embedded autopilot of a modern commercial jet is a prime example of a hybrid system: the autopilot modes correspond to the application of different control laws, and the logic of mode switching is determined by the continuous state dynamics of the aircraft, as well as through interaction with the pilot. Embedded
Integrating Analogical Mapping and General Problem Solving: The PathMapping Theory
, 1999
"... This article describes the pathmapping theory of how humans integrate analogical mapping and general problem solving. The theory posits that humans represent analogs with declarative roles, map analogs by lowerlevel retrieval of analogous role paths, and coordinate mappings with higherlevel organ ..."
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Cited by 21 (11 self)
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This article describes the pathmapping theory of how humans integrate analogical mapping and general problem solving. The theory posits that humans represent analogs with declarative roles, map analogs by lowerlevel retrieval of analogous role paths, and coordinate mappings with higherlevel organizational knowledge. Implemented in the ACTR cognitive architecture, the pathmapping theory enables models of analogical mapping behavior to incorporate and interface with other problemsolving knowledge. Pathmapping models thus can include taskspecific skills such as encoding analogs or generating responses, and can make behavioral predictions at the level of realworld metrics such as latency or correctness. We show that the pathmapping theory can successfully account for the major phenomena addressed by previous theories of analogy. We also describe a pathmapping model that can account for subjects’ incremental eyemovement and typing behavior in a storymapping task. We discuss extensions and implications of this work to other areas of analogy and problemsolving research.
Approximate reachability computation for polynomial systems
 in HSCC’06, vol. 3927 in LNCS
, 2006
"... Abstract. In this paper we propose an algorithm for approximating the reachable sets of systems defined by polynomial differential equations. Such systems can be used to model a variety of physical phenomena. We first derive an integration scheme that approximates the state reachable in one time ste ..."
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Cited by 17 (10 self)
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Abstract. In this paper we propose an algorithm for approximating the reachable sets of systems defined by polynomial differential equations. Such systems can be used to model a variety of physical phenomena. We first derive an integration scheme that approximates the state reachable in one time step by applying some polynomial map to the current state. In order to use this scheme to compute all the states reachable by the system starting from some initial set, we then consider the problem of computing the image of a set by a multivariate polynomial. We propose a method to do so using the Bézier control net of the polynomial map and the blossoming technique to compute this control net. We also prove that our overall method is of order 2. In addition, we have successfully applied our reachability algorithm to two models of a biological system. 1
Casebased reasoning: an overview
 AI Communications
, 1997
"... Abstract. An important step in the solution of a target problem in casebased reasoning (CBR) is the retrieval of similar previous cases that can be used to solve the target problem. We review a selection of papers from the CBR literature on aspects of retrieval, such as approaches to the assessment ..."
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Cited by 13 (0 self)
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Abstract. An important step in the solution of a target problem in casebased reasoning (CBR) is the retrieval of similar previous cases that can be used to solve the target problem. We review a selection of papers from the CBR literature on aspects of retrieval, such as approaches to the assessment of surface and structural similarity and techniques for automating the construction and maintenance of similarity measures. We also examine a number of retrieval techniques that have been developed to address the limitations of retrieval based purely on similarity. 1