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57
The empirical case for two systems of reasoning
 Psychological Bulletin
, 1996
"... Distinctions have been proposed between systems of reasoning for centuries. This article distills properties shared by many of these distinctions and characterizes the resulting systems in light of recent findings and theoretical developments. One system is associative because its computations refle ..."
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Cited by 321 (3 self)
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Distinctions have been proposed between systems of reasoning for centuries. This article distills properties shared by many of these distinctions and characterizes the resulting systems in light of recent findings and theoretical developments. One system is associative because its computations reflect similarity structure and relations of temporal contiguity. The other is "rule based " because it operates on symbolic structures that have logical content and variables and because its computations have the properties that are normally assigned to rules. The systems serve complementary functions and can simultaneously generate different solutions to a reasoning problem. The rulebased system can suppress the associative system but not completely inhibit it. The article reviews evidence in favor of the distinction and its characterization. One of the oldest conundrums in psychology is whether people are best conceived as parallel processors of information who operate along diffuse associative links or as analysts who operate by deliberate and sequential manipulation of internal representations. Are inferences drawn through a network of learned associative pathways or through application of a kind of "psychologic"
The Race, the Hurdle, and the Sweet Spot: Lessons from Genetic Algorithms for the Automation of Design Innovation and Creativity
, 1998
"... this article, I will argue rather strongly that computational innovationat least certain important facets of the processes of innovationhas been achieved, and that computational creativity is plausibly within our sights. Specifically, I will argue that modern research in genetic algorithmss ..."
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Cited by 43 (17 self)
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this article, I will argue rather strongly that computational innovationat least certain important facets of the processes of innovationhas been achieved, and that computational creativity is plausibly within our sights. Specifically, I will argue that modern research in genetic algorithmssearch
Studies of scientific discovery: Complementary approaches and convergent findings
 Psychological Bulletin
, 1999
"... This review integrates 4 major approaches to the study of science—historical accounts of scientific discoveries, psychological experiments with nonscientists working on tasks related to scientific discoveries, direct observation of ongoing scientific laboratories, and computational modeling of scien ..."
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Cited by 27 (2 self)
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This review integrates 4 major approaches to the study of science—historical accounts of scientific discoveries, psychological experiments with nonscientists working on tasks related to scientific discoveries, direct observation of ongoing scientific laboratories, and computational modeling of scientific discovery processes—by viewing them through the lens of the theory of human problem solving. The authors provide a brief justification for the study of scientific discovery, a summary of the major approaches, and criteria for comparing and contrasting them. Then, they apply these criteria to the different approaches and indicate their complementarities. Finally, they provide several examples of convergent principles of the process of scientific discovery. The central thesis of this article is that although research on scientific discovery has taken many different paths, these paths show remarkable convergence on key aspects of the discovery processes, allowing one to aspire to a general theory of scientific discovery. This convergence is often obscured by the disparate cultures, research methodologies, and theoretical foundations of the various disciplines that study scientific discovery, including
Diagrammatic representation and reasoning
 Machine GRAPHICS & VISION 3(1/2
, 1994
"... Abstract. The rapidly developing field of diagrammatic knowledge representation and reasoning is surveyed. The origins and rationale of the field, basic principles and methodologies, as well as selected applications are discussed. Closely related areas, like visual languages, data presentation, and ..."
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Cited by 21 (2 self)
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Abstract. The rapidly developing field of diagrammatic knowledge representation and reasoning is surveyed. The origins and rationale of the field, basic principles and methodologies, as well as selected applications are discussed. Closely related areas, like visual languages, data presentation, and visualization are briefly introduced as well. Basic sources of material for further study are indicated. Key words: diagrammatic representation, diagrammatic reasoning, visual languages, diagrams, visual programming, data presentation, visualization, knowledge representation, computer graphics, qualitative physics, geometry theorem proving. 1.
Computer Learning and the Scientific Method: A Proposed Solution to the Information Theoretical Problem of Meaning
, 1965
"... This discussion outlines and implements the theory of an inductive inference technique that automatically discovers classes among large numbers of input patterns, generates operational definitions of class membership with explicit levels of confidence, creates a continuously updated "selforganized" ..."
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Cited by 9 (3 self)
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This discussion outlines and implements the theory of an inductive inference technique that automatically discovers classes among large numbers of input patterns, generates operational definitions of class membership with explicit levels of confidence, creates a continuously updated "selforganized" coded hierarchical taxonomic classification of patterns, and recognizes to which already discovered class or classes, if any, a new input belongs in an informationtheoretically efficient way. Relationships to the "scientific method" and learning are discussed.
Acategoriality as mental instability
 Journal of Mind and Behavior, submitted
, 2005
"... Mental representations are based upon categories in which the state of a mental system is stable. Acategorial states, on the other hand, are distinguished by unstable behavior. A refined and compact terminology for the description of categorial and acategorial mental states and their stability prope ..."
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Cited by 8 (4 self)
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Mental representations are based upon categories in which the state of a mental system is stable. Acategorial states, on the other hand, are distinguished by unstable behavior. A refined and compact terminology for the description of categorial and acategorial mental states and their stability properties is introduced within the framework of the theory of dynamical systems. The relevant concepts are illustrated by selected empirical observations in cognitive neuroscience. Alterations of the category of the first person singular and features of creative activity will be discussed as examples for the phenomenology of acategorial states. Harald Atmanspacher is also associate member of the MaxPlanckCenter for Interdisciplinary
Formal notations are diagrams: Evidence from a production task
"... Although a general sense of the magnitude, quantity, or numerosity of objects is common in both untrained people and animals, the abilities to deal exactly with large quantities and to reason precisely in complex but wellspecified situations—to behave formally, that is—are skills unique to people t ..."
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Cited by 8 (3 self)
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Although a general sense of the magnitude, quantity, or numerosity of objects is common in both untrained people and animals, the abilities to deal exactly with large quantities and to reason precisely in complex but wellspecified situations—to behave formally, that is—are skills unique to people trained in symbolic notations. These symbolic notations typically employ complex, hierarchically embedded structures, which all extant analyses assume are constructed by concatenative, rulebased processes. The primary goal of this article is to establish, using behavioral measures on naturalistic tasks, that some of the same cognitive resources involved in representing spatial relations and proximities are also involved in representing symbolic notations—in short, that formal notations are a kind of diagram. We examined selfgenerated productions in the domains of handwritten arithmetic expressions and typewritten statements in a formal logic. In both tasks, we found substantial evidence for spatial representational schemes even in these highly symbolic domains. It is clear that mathematical equations written in modern notation are, in general, visual forms and that they share some properties with diagrammatic or imagistic displays. Equations and mathematical expressions are often set off from the main text, use nonstandard characters and shapes, and deviate substantially from linear symbol placement. Furthermore, evidence indicates that at least some mathematical processing is sensitive to the particular visual form of its presentation notation (Cambell, 1999; McNeil & Alibali, 2004, 2005). Despite these facts, notational mathematical representation is typically considered sentential and is placed in opposition to diagrammatic representations in fields as diverse as education
Computers, Reasoning and Mathematical Practice
"... ion in itself is not the goal: for Whitehead [117]"it is the large generalisation, limited by a happy particularity, which is the fruitful conception." As an example consider the theorem in ring theory, which states that if R is a ring, f(x) is a polynomial over R and f(r) = 0 for every element of ..."
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Cited by 6 (2 self)
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ion in itself is not the goal: for Whitehead [117]"it is the large generalisation, limited by a happy particularity, which is the fruitful conception." As an example consider the theorem in ring theory, which states that if R is a ring, f(x) is a polynomial over R and f(r) = 0 for every element of r of R then R is commutative. Special cases of this, for example f(x) is x 2 \Gamma x or x 3 \Gamma x, can be given a first order proof in a few lines of symbol manipulation. The usual proof of the general result [20] (which takes a semester's postgraduate course to develop from scratch) is a corollary of other results: we prove that rings satisfying the condition are semisimple artinian, apply a theorem which shows that all such rings are matrix rings over division rings, and eventually obtain the result by showing that all finite division rings are fields, and hence commutative. This displays von Neumann's architectural qualities: it is "deep" in a way in which the symbol manipulati...
A Perspective On Symbolic Mathematical Computing And Artificial Intelligence
 Annals of Mathematics and Artificial Intelligence
, 1997
"... . The nature and history of the research area common to artificial intelligence and symbolic mathematical computation are examined, with particular reference to the topics having the greatest current amount of activity or potential for further development: mathematical knowledgebased computing envi ..."
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Cited by 6 (1 self)
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. The nature and history of the research area common to artificial intelligence and symbolic mathematical computation are examined, with particular reference to the topics having the greatest current amount of activity or potential for further development: mathematical knowledgebased computing environments, autonomous agents and multiagent systems, transformation of problem descriptions in logics into algebraic forms, exploitation of machine learning, qualitative reasoning, and constraintbased programming. Knowledge representation, for mathematical knowledge, is identified as a central focus for much of this work. Several promising topics for further research are stated. As an introduction to the proceedings of the first international conference that was devoted specifically to symbolic mathematical computing (SMC) and artificial intelligence, we wrote a combination of a short survey and a summary of our predictions and suggestions for the future development of the territory common ...