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Mathematics - Probability Theory and Stochastic Processes | Inference on the Low Level - An Investigation into Deduction, Nonmonotonic Reasoning, and the

Inference on the Low Level

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

Series: Applied Logic Series, Vol. 30

Leitgeb, Hannes

2004, X, 386 p.

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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.

Content Level » Research

Keywords » epistemology - idea - logic - logical reasoning - nonmonotonic reasoning - programming - reason - semantics

Related subjects » Artificial Intelligence - Complexity - Logic & Philosophy of Language - Philosophy - Probability Theory and Stochastic Processes

Table of contents 

1. Introduction. 2. Preliminaries. I: The Explication of Monotonic and Nonmonotonic Inference.- 3. Belief. 4. Inference. II: The Justification of Monotonic and Nonmonotonic Inference. -5. General Remarks on Justification and Justified Belief. 6. An Informal Account of Our Theory of Justified Inference. 7. A Discussion of Reliability. 8. A Theory of Justified Inference. III: The Logic of Justified Monotonic and Nonmonotonic Inference.- 9. The Semantics of Deductive and Nonmonotonic Logic. 10. Systems of Deductive and Nonmonotonic Logic. 11. Soundness and Completeness Results. 12. Further Consequences for Justified Inference. IV: The Cognition of Justified Monotonic and Nonmonotonic Inference by Low-Level Agents. -13. Introductory Remarks. 14. Inhibition Nets as Simple Neural Networks. 15. Interpreted Inhibition Net Agents. 16. Cumulative-Ordered Interpreted Inh. Net Agents and the System CL. 17. Cumulative-Ordered Interpreted Inhibition Net Agents as Ideal Agents. 18. Inhibition Nets and Other Forms of Nonmonotonic Reasoning. 19. Inhibition Nets and Artificial Neural Networks. 20. Discussion. V: Appendix.- 21. Digression on States, Dispositions, Causation, Processes. 22. Goldman's Reliability Account of Justified Belief. 23. A Sketch of Logic Programming. 24. Preferential Interpreted Inhibition Net Agents and the System P. 25. Cumulative Interpreted Inhibition Net Agents and the System PM. 26. Simple Preferential Interpreted Inhibition Net Agentsand the System M.

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