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

Hannes Leitgeb

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.

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
• 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
• 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
• 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

Bibliographic information

• Title: Inference on the Low Level: An Investigation Into Deduction, Nonmonotonic Reasoning, and the Philosophy of Cognition; Volume 30 of Applied Logic Series, ISSN 1386-2790
• Author: Hannes Leitgeb
• Edition: illustrated
• Publisher: Springer Science & Business Media, 2004
• ISBN: 1402024924, 9781402024924
• Length: 383 pages
• Subjects: Computers / Artificial Intelligence / General; Mathematics / Probability & Statistics / General; Mathematics / Probability & Statistics / Stochastic Processes; Philosophy / Epistemology; Philosophy / Logic; Science / Physics / General; Science / Physics / Mathematical & Computational