Inference on the Low Level: An Investigation Into Deduction, Nonmonotonic Reasoning, and the Philosophy of Cognition

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Springer Science & Business Media, Aug 13, 2004 - Computers - 383 pages

This monograph provides a new account of justified inference as a cognitive process. In contrast to the prevailing tradition in epistemology, the focus 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.

This text will be of interest to epistemologists and logicians, to all computer scientists who work on nonmonotonic reasoning and neural networks, and to cognitive scientists.

 

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Contents

INTRODUCTION
1
PRELIMINARIES
7
The Explication of Monotonic and Nonmonotonic Inference
23
BELIEF
25
31 Perceptual Beliefs and Central State Beliefs
30
32 Total Beliefs
32
33 Occurrent Beliefs and Dispositional Beliefs
35
34 Singular Beliefs and General Beliefs
45
The Cognition of Justified Monotonic and Nonmonotonic Inference by LowLevel Agents
209
INTRODUCTORY REMARKS
211
131 Two Paradigms of Cognitive Science
212
1312 The Dynamical Systems Paradigm
213
1313 Connectionism as a Special Case of the Dynamical Systems Paradigm
215
1314 Comparison
217
132 The Cognitive Architecture of Ideal Agents
220
1322 Ideal Symbolic Computation Agents and Why They Fail for Practical Reasons
221

INFERENCE
55
42 A Sketch of Our Theory of Inference
58
43 Dispositions to Change to Beliefs and to Remain in Beliefs
63
44 Direct Reasons and Inferences
69
Deductive High Probability Normic
76
46 Reasons and Inferences
80
Deductive High Probability Normic
83
The Justification of Monotonic and Nonmonotonic Inference
87
GENERAL REMARKS ON JUSTIFICATION AND JUSTIFIED BELIEF
89
512 Externalist Justification of Beliefs
92
513 Comparison
96
52 The Ascription of Justified Belief
99
AN INFORMAL ACCOUNT OF OUR THEORY OF JUSTIFIED INFERENCE
101
612 Externalist Justification of Inferences
103
62 The LowLevel Postulate
104
63 A Reliabilist Account of Justified BasicAcquired Inferences
106
632 The Generality Problem Affecting the Reliabilist Justification of Inferences Inductive Reasoning Processes as SecondOrder Processes
110
633 The Ascription of Justified Inference
119
A DISCUSSION OF RELIABILITY
121
72 Quality Criteria for Notions of FirstOrder Reliability
122
73 Quantitative Notions of FirstOrder Reliability
123
74 Qualitative Notions of FirstOrder Reliability
124
75 Comparison of Quantitative and Qualitative Reliability wrt Strength
127
76 Quantitative Reliability Fails Our LowLevel Quality Criteria
129
Why We Opt for Qualitative Reliability
135
78 Qualitative Reliability Fails Rationality But That Does Not Matter
137
79 Qualitative Reliability vs Monotonic and Nonmonotonic Inferences
139
710 SecondOrder Reliability
141
A THEORY OF JUSTIFIED INFERENCE
145
82 Reliability for Inferences
151
83 Reliability for Reasoning Processes
152
84 The Explication of Justified Inference
153
85 Two Consequences of the Theory
158
86 Ideal Agents
160
The Logic of Justified Monotonic and Nonmonotonic Inference
163
THE SEMANTICS OF DEDUCTIVE AND NONMONOTONIC LOGIC
165
91 Semantics for Universal Conditionals
167
92 Semantics for High Probability Conditionals
168
93 Semantics for Normic Conditionals
180
SYSTEMS OF DEDUCTIVE AND NONMONOTONIC LOGIC
189
SOUNDNESS AND COMPLETENESS RESULTS
197
FURTHER CONSEQUENCES FOR JUSTIFIED INFERENCE
203
INHIBITION NETS AS SIMPLE NEURAL NETWORKS
225
142 Inhibition Nets
226
143 Inhibition Nets as Dynamical Systems
230
INTERPRETED INHIBITION NET AGENTS
241
152 Singular Occurrent Beliefs in Net Agents
246
153 General Defeasible Dispos Beliefs and Nonmon Inferences in Net Agents
251
154 Universal Dispositional Beliefs in Net Agents
258
CUMULATIVEORDERED INTERPRETED INH NET AGENTS AND THE SYSTEM CL
261
162 The Representation Theorem for CL
274
1622 The Completeness Lemma for CL
277
CUMULATIVEORDERED INTERPRETED INHIBITION NET AGENTS AS IDEAL AGENTS
281
INHIBITION NETS AND OTHER FORMS OF NONMONOTONIC REASONING
285
INHIBITION NETS AND ARTIFICIAL NEURAL NETWORKS
291
DISCUSSION
295
Appendix
299
DIGRESSION ON STATES DISPOSITIONS CAUSATION PROCESSES
301
212 States
305
213 Disposition Ascriptions
307
214 Belief States
309
215 Direct Causation and Sustaining of Belief States by Belief States
319
216 Processes
321
GOLDMANS RELIABILITY ACCOUNT OF JUSTIFIED BELIEF
327
222 The Reliability Approach in Epistemology and Cognition
328
223 The Reliability Approach in Strong and Weak Justification
334
224 The Rel Approach in Epistemic Folkways and Scientific Epistemology
335
The Problems for Goldmans Approaches
336
2252 The Generality Problem
341
2253 Problems of Defining Reliability
342
2254 Problems of Subjective Justification
343
A SKETCH OF LOGIC PROGRAMMING
345
PREFERENTIAL INTERPRETED INHIBITION NET AGENTS AND THE SYSTEM P
349
242 The Network Semantics for Pref Partially Interpreted Inh Net Agents
355
243 The Representation Theorem for P
356
CUMULATIVE INTERPRETED INHIBITION NET AGENTS AND THE SYSTEM C
361
252 The Representation Theorem for C
362
2522 The Completeness Lemma for C
364
SIMPLE CUMULATIVE INTERPRETED INHIBITION NET AGENTS AND THE SYSTEM CM
367
262 The Representation Theorem for CM
368
SIMPLE PREFERENTIAL INTERPRETED INHIBITION NET AGENTS AND THE SYSTEM M
371
272 The Representation Theorem for M
372
References
375
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Philosophy of Logic

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