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Plato, Diagrammatic Reasoning and Mental Models
This book analyses the role of diagrammatic reasoning in Plato’s philosophy: the readers will realize that Plato, describing the stages of human cognitive development using a diagram, poses a logic problem to stimulate the general reasoning abilities of his readers. Following the examination of mental models in this book, the readers will reflect on what inferences can be useful to approach this kind of logic problem. Plato calls for a collaboration between writer and readers. In this book the readers will examine the connection between diagrams and discovery, realizing the important epistemic role of visualization. They will recognize the crucial role that diagrams play in problem solving. The logic problem elaborated by Plato is addressed considering the epistemic function of mental models. These models introduce to an advanced stage of cognitive development, in which reasoning uses in its investigations a higher-level of mathematical complexity, represented by structuralism.
Asleep at the Switch
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Psychology and Cognitive Science
This special issue includes revised versions of papers presented at the IUPsyS Symposium "Psychology and Cognitive Science", held during the XXVIth International Congress of Psychology in Montreal, August 1996. The introductory article reports the results of an international survey conducted for the IUPsyS on the place and role of psychology in cognitive science; the next three papers are illustrations of interdisciplinary approaches to cognitive issues. Approaches to discourse comprehension by cognitive psychology, artificial intelligence, linguistics, and neurobiology are discussed, and it is considered how the human mind and machines represent knowledge from discourse and text. Finally, there is a description of a computational approach to vision and language inspired by psychological theories.
Arrays, Functional Languages, and Parallel Systems
During a meeting in Toronto last winter, Mike Jenkins, Bob Bernecky and I were discussing how the two existing theories on arrays influenced or were in fluenced by programming languages and systems. More's Army Theory was the basis for NIAL and APL2 and Mullin's A Mathematics of A rmys(MOA) , is being used as an algebra of arrays in functional and A-calculus based pro gramming languages. MOA was influenced by Iverson's initial and extended algebra, the foundations for APL and J respectively. We discussed that there is a lot of interest in the Computer Science and Engineering communities concerning formal methods for languages that could support massively parallel operations in scientific com...
Proceedings of the Fourteenth Annual Conference of the Cognitive Science Society
This volume features the complete text of all regular papers, posters, and summaries of symposia presented at the 14th annual meeting of the Cognitive Science Society.
A Combination of Geometry Theorem Proving and Nonstandard Analysis, with Application to Newton's Principia
Abstract: "Sir Isaac Newton's Philosophiæ Naturalis Principia Mathematica (the Principia) was first published in 1687 and set much of the foundations that led to profound changes in modern science. Despite the influence of the work, the elegance of the geometrical techniques used by Newton is little known since the demonstrations of most of the theorems set out in it are usually done using calculus. Newton's reasoning also goes beyond the traditional boundaries of Euclidean geometry with the presence of both motion and infinitesimals. This thesis describes the mechanization of Lemmas and Propositions from the Principia using formal tools developed in the generic theorem prover Isabelle. We ...
AI Magazine
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