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Continuous Formal Systems: A Unifying Model in Language and Cognition

MacLennan, Bruce J. (1995) Continuous Formal Systems: A Unifying Model in Language and Cognition. [Conference Paper]

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Abstract

The idea of a calculus or discrete formal system is central to traditional models of language, knowledge, logic, cognition and computation, and it has provided a unifying framework for these and other disciplines. Nevertheless, research in psychology, neuroscience, philosophy and computer science has shown the limited ability of this model to account for the flexible, adaptive and creative behavior exhibited by much of the animal kingdom. Promising alternate models replace discrete structures by structured continua and discrete rule-following by continuous dynamical processes. However, we believe that progress in these alternate models is retarded by the lack of a unifying theoretical construct analogous to the discrete formal system. In this paper we outline the general characteristics of continuous formal systems (simulacra), which we believe will be a unifying element in future models of language, knowledge, logic, cognition and computation. Therefore, we discuss syntax, semantics, inference and computation in the context of continuous formal systems. In addition, we address an issue that the discrete models were inadequate to address: the gradual emergence of (approximately) discrete structures from a continuum. This is relevant to the emergence of linguistic structures, including semantics and syntax, and to the emergence of rule-like regularities in behavior.

Item Type:Conference Paper
Keywords:continuous formal system, continuous computation, analog computation, analogue computation, calculus, syntax, semantics, formality, well-formed, Peirce, image, interpretation, continuous process, dynamical system, program, continuous language, nondeterminism, determinism, continuous grammar, object recognition, invariance, Gabor, multiresolution, uncertainty principle, indeterminacy principle, representation, primary visual cortex, wavelet, rule, formal system
Subjects:Computer Science > Artificial Intelligence
Philosophy > Logic
ID Code:541
Deposited By:MacLennan, Bruce
Deposited On:14 Jun 1999
Last Modified:11 Mar 2011 08:54

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