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Applied Logic

An Investigation into Deduction, Nonmonotonic Reasoning, and the Philosophy of Cognition

By: Hannes Leitgeb

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Hardcover | 13 August 2004

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Hardcover
398 Pages

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24.13 x 16.51 x 2.54

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In contrast to the prevailing tradition in epistemology, the focus in this book is on low-level inferences, i.e., those inferences that we are usually not consciously aware of and that we share with the cat nearby which infers that the bird which she sees picking grains from the dirt, is able to fly. Presumably, such inferences are not generated by explicit logical reasoning, but logical methods can be used to describe and analyze such inferences.

Part 1 gives a purely system-theoretic explication of belief and inference. Part 2 adds a reliabilist theory of justification for inference, with a qualitative notion of reliability being employed. Part 3 recalls and extends various systems of deductive and nonmonotonic logic and thereby explains the semantics of absolute and high reliability. In Part 4 it is proven that qualitative neural networks are able to draw justified deductive and nonmonotonic inferences on the basis of distributed representations. This is derived from a soundness/completeness theorem with regard to cognitive semantics of nonmonotonic reasoning. The appendix extends the theory both logically and ontologically, and relates it to A. Goldman's reliability account of justified belief.

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"The ambitious goal of the book is the formal development of realistic (in particular: dynamic and neuronal) models of the cognitive process of reasoning. ... In sum, Leitgeb's book contains highly original and far-reaching results concerning the relation between three important areas: the epistemology of belief, the logic of reasoning, and the structure and dynamics of neuronal networks. The book is recommended for every reader who is interested in at least one of these areas ... ." (Gerhard Schurz, Journal for General Philosophy of Science, Vol. 38, 2007)

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You Can Find This Book In

Non-Fiction Psychology Cognition & Cognitive Psychology Philosophy Philosophy & Logic Epistemology & The Theory of Knowledge Computing & I.T.Computer Science Artificial Intelligence Mathematics Probability & Statistics Science

Physics Mathematical Physics Reference, Information & Interdisciplinary Subjects Research & Information Information theory Cybernetics & Systems Theory

Introduction	p. 1
Preliminaries	p. 7
The explication of monotonic and nonmonotonic inference	p. 23
Belief	p. 25
Inference	p. 55
The justification of monotonic and nonmonotonic inference	p. 87
General remarks on justification and justified belief	p. 89
An informal account of our theory of justified inference	p. 101
A discussion of reliability	p. 121
A theory of justified inference	p. 145
The logic of justified monotonic and nonmonotonic inference	p. 163
The semantics of deductive and nonmonotonic logic	p. 165
Systems of deductive and nonmonotonic logic	p. 189
Soundness and completeness results	p. 197
Further consequences for justified inference	p. 203
The cognition of justified monotonic and non-monotonic inference by low-level agents	p. 209
Introductory remarks	p. 211
Inhibition nets as simple neural networks	p. 225
Interpreted inhibition net agents	p. 241
Cumulative-ordered interpreted Inh. net agents and the system CL	p. 261
Cumulative-ordered interpreted inhibition net agents as ideal agents	p. 281
Inhibition nets and other forms of nonmonotonic reasoning	p. 285
Inhibition nets and artificial neural networks	p. 291
Discussion	p. 295
Appendix	p. 299
Digression on states, dispositions, causation, processes	p. 301
Goldman's reliability account of justified belief	p. 327
A sketch of logic programming	p. 345
Preferential interpreted inhibition net agents and the system P	p. 349
Cumulative interpreted inhibition net agents and the system C	p. 361
Simple cumulative interpreted inhibition net agents and the system CM	p. 367
Simple preferential interpreted inhibition net agents and the system M	p. 371
Table of Contents provided by Blackwell. All Rights Reserved.

Applied Logic

An Investigation into Deduction, Nonmonotonic Reasoning, and the Philosophy of Cognition

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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