Practical Logic of Cognitive Systems (eBook)
496 Seiten
Elsevier Science (Verlag)
978-0-08-046092-5 (ISBN)
Practical Logic of Cognitive Systems. After having investigated the notion of
relevance in their previous volume, Gabbay and Woods now turn to abduction. In
this highly original approach, abduction is construed as ignorance-preserving
inference, in which conjecture plays a pivotal role. Abduction is a response to a
cognitive target that cannot be hit on the basis of what the agent currently knows.
The abducer selects a hypothesis which were it true would enable the reasoner to attain his target. He concludes from this fact that the hypothesis may be conjectured. In allowing conjecture to stand in for the knowledge he fails to have, the abducer reveals himself to be a satisficer, since an abductive solution is not a solution from knowledge. Key to the authors' analysis is the requirement that a conjectured proposition is not just what a reasoner might allow himself to assume, but a proposition he must defeasibly release as a premiss for further inferences in the domain of enquiry in which the original abduction problem has arisen.
The coverage of the book is extensive, from the philosophy of science to
computer science and AI, from diagnostics to the law, from historical explanation to linguistic interpretation. One of the volume's strongest contributions is its exploration of the abductive character of criminal trials, with special attention given to the standard of proof beyond a reasonable doubt.
Underlying their analysis of abductive reasoning is the authors' conception of
practical agency. In this approach, practical agency is dominantly a matter of the
comparative modesty of an agent's cognitive agendas, together with comparatively scant resources available for their advancement. Seen in these ways, abduction has a significantly practical character, precisely because it is a form of inference that satisfices rather than maximizes its response to the agent's cognitive target.
The Reach of Abduction will be necessary reading for researchers, graduate
students and senior undergraduates in logic, computer science, AI, belief dynamics, argumentation theory, cognitive psychology and neuroscience, linguistics, forensic science, legal reasoning and related areas.
Key features:
- Reach of Abduction is fully integrated with a background logic of cognitive systems.
- The most extensive coverage compared to competitive works.
- Demonstrates not only that abduction is a form of ignorance preserving
inference but that it is a mode of inference that is wholly rational.
- Demonstrates the satisficing rather than maximizing character of
abduction.
- The development of formal models of abduction is considerably more extensive than one finds in existing literature. It is an especially impressive amalgam of sophisticated
conceptual analysis and extensive logical modelling.
? Reach of Abduction is fully integrated with a background logic of cognitive systems.
? The most extensive coverage compared to competitive works
? Demonstrates not only that abduction is a form of ignorance preserving
inference but that it is a mode of inference that is wholly rational.
? Demonstrates the satisficing rather than maximizing character of
abduction.
? The development of formal models of abduction is considerably more extensive than one finds in existing literature. It is an especially impressive amalgam of sophisticated
conceptual analysis and extensive logical modelling.
The present work is a continuation of the authors' acclaimed multi-volume APractical Logic of Cognitive Systems. After having investigated the notion ofrelevance in their previous volume, Gabbay and Woods now turn to abduction. Inthis highly original approach, abduction is construed as ignorance-preservinginference, in which conjecture plays a pivotal role. Abduction is a response to acognitive target that cannot be hit on the basis of what the agent currently knows.The abducer selects a hypothesis which were it true would enable the reasoner to attain his target. He concludes from this fact that the hypothesis may be conjectured. In allowing conjecture to stand in for the knowledge he fails to have, the abducer reveals himself to be a satisficer, since an abductive solution is not a solution from knowledge. Key to the authors' analysis is the requirement that a conjectured proposition is not just what a reasoner might allow himself to assume, but a proposition he must defeasibly release as a premiss for further inferences in the domain of enquiry in which the original abduction problem has arisen.The coverage of the book is extensive, from the philosophy of science tocomputer science and AI, from diagnostics to the law, from historical explanation to linguistic interpretation. One of the volume's strongest contributions is its exploration of the abductive character of criminal trials, with special attention given to the standard of proof beyond a reasonable doubt.Underlying their analysis of abductive reasoning is the authors' conception ofpractical agency. In this approach, practical agency is dominantly a matter of thecomparative modesty of an agent's cognitive agendas, together with comparatively scant resources available for their advancement. Seen in these ways, abduction has a significantly practical character, precisely because it is a form of inference that satisfices rather than maximizes its response to the agent's cognitive target.The Reach of Abduction will be necessary reading for researchers, graduatestudents and senior undergraduates in logic, computer science, AI, belief dynamics, argumentation theory, cognitive psychology and neuroscience, linguistics, forensic science, legal reasoning and related areas.Key features:- Reach of Abduction is fully integrated with a background logic of cognitive systems.- The most extensive coverage compared to competitive works.- Demonstrates not only that abduction is a form of ignorance preservinginference but that it is a mode of inference that is wholly rational.- Demonstrates the satisficing rather than maximizing character ofabduction.- The development of formal models of abduction is considerably more extensive than one finds in existing literature. It is an especially impressive amalgam of sophisticatedconceptual analysis and extensive logical modelling.* Reach of Abduction is fully integrated with a background logic of cognitive systems.* The most extensive coverage compared to competitive works* Demonstrates not only that abduction is a form of ignorance preservinginference but that it is a mode of inference that is wholly rational.* Demonstrates the satisficing rather than maximizing character ofabduction.* The development of formal models of abduction is considerably more extensive than one finds in existing literature. It is an especially impressive amalgam of sophisticatedconceptual analysis and extensive logical modelling.
front cover 1
copyright 5
table of contents 8
front matter 14
body 20
Cover 2
Contents 8
Acknowledgements 14
Preface 18
A Practical Logic of Cognitive Systems 20
Introduction 22
Practical Logic 30
First Thoughts on a Practical Logic 30
A Hierarchy of Agency Types 31
Peculiarities of Institutional Agents 36
Normativity 39
Mathematical Models 43
Slight-resource Adjustment Strategies 45
Hasty Generalization 45
Generic Inference 45
Natural Kinds 46
Defaults 47
Discourse Economies 47
Consciousness 48
Practical Logic 51
Connectionist Logic 53
Fallacies 54
Conceptual Models of Abduction 58
The Structure of Abduction 60
Introductory Remark on Abduction 60
The Elementary Structure of Abductive Logic 61
Expanding the Schema 63
Frames 65
Generalizing I P s 66
Avoiding a Confusion 66
Locating Abduction on the Logical Map 67
Abductive Schematics 68
Consequentialist Abduction 68
The Good that AKM Does 74
The Reach of Abduction 75
Simplicity 77
The Cut Down Problem 77
Abduction as Practical 79
Proof-theoretic Abduction 79
The Adaptive and the Epistemically Subpar 83
Knowledge-Sets 84
Filtration Structures 87
Hypothesis-Engagement 90
Grounds of Action 91
Tasks for an Abductive Logic 92
Explanationist Abduction 96
Peirce 96
Surprise 102
Testability and Economics 103
Insight and Trial 106
Rationality and Diminished Epistemic Virtue 107
Explanation ism 108
The Covering Law Model 111
The Rational Model 114
Teleological Explanation 117
The Pluralism of Explanation 120
Assessing IBE 121
Characteristicness 123
Hanson 125
Darden 130
Fodor 130
Adaptive Explanationism 131
Non-abductive Conjecture 134
Non-Plausibilistic Abduction 136
Introductory remark 136
Newton 137
Planck 142
Physical Dependencies 143
The Superstring Controversy 144
Russell and Godel 146
The Consequence Relation 150
Lakatos 155
Hintikka 159
Empirical Progress 162
Semantic Tableaux 163
Assessing Semantic Tableau Abduction 167
Is It Abduction? 168
Inconsistency Again 169
Bayesian Inference 171
Diagnostic Abduction in AI 176
Explanationist Diagnostics 176
Difficulties with AP 182
Another Example 184
Remarks 190
Coherentism and Probabilism 191
The Rivalry of Explanationism and Probabilism 191
Explanatory Coherence 192
Probabilistic Networks 195
Pearl Networks for ECHO 197
Neuropharmacological Intervention 201
Mechanizing Abduction 205
Abduction in Neural-Symbolic Networks 210
The Characteristic and the Plausible 216
The Open Door 216
The Element of Surprise 217
Plausibility 221
A Resolution Point 222
How to Get Determinacy Out of Indeterminacy 223
Alternatives 225
The Piccadilly Line 227
Plausibility Again 230
Historical Note on Plausibility 231
Cut-to-the Chase Abduction 233
Characteristicness 234
Common Knowledge 240
Rescher's Plausibility Logic 243
Reliability 248
Axioms for Plausibility 249
Plausibility and Presumption 253
Brief Concluding Remarks 258
Relevance and Analogy 260
Relevance 260
Relevance as Cognitive 261
Topical Relevance 264
Contextual Effects 268
Irredundancy Relevance 269
Relevance and Cutting to the Chase 271
Legal Relevance 275
Ideology 277
Legal Presumption 279
Types of Presumption 281
The Reasonable Person 285
Reasonable Doubt 286
Hypothesis-Discharge 289
The Probativity Question 290
Revision Structures 291
Proof Standards 293
Analogy 295
The Meta Approach 297
Similarity 302
Analogy in Law 303
Precedent 305
Analogue Modelling 307
Interpretation Abduction 310
Hermeneutics 310
Enthymemes 312
Fermat's Last Theorem 315
Enthymeme Resolution as Abductive 317
The Attack on Analyticity 319
Inarticulacy as Economics 321
Some Virtual Guidelines 323
Background Knowledge 324
Charity 326
Indeterminacy of Translation 328
Is it Abduction (Again)? 333
Constitutional Inarticulacies 334
Inarticulate Understanding 334
Visual Abduction 338
Empathy 340
Discourse Empathies 342
Semantic Space Interpretation of Texts 344
The Raynaud-Fish Oil Abduction 349
Formal Models of Abduction 354
Glimpse of Formality 356
Introduction 356
The AKM model 357
The GW Model 363
Some Schematic Remarks 365
Case Study: Defeasible Logic 372
A General Theory of Logical Systems 378
Introduction 378
Logical Systems 381
Refining the Notion of a Logical System 393
Structured consequence 393
Algorithmic structured consequence relation 394
Mechanisms 397
Modes of Evaluation 399
TAR-Logics 401
Relevance 403
Discussion and Further Reading 403
A Base Logic 404
Formal Abduction: An Overview 404
Introducing LDS 409
Examples of Resource LDS 412
The Algorithm 419
Examples 421
Intuitive Theory of Labelled Abduction 423
Abduction in Knowledge Bases 424
Abduction in Planning and Natural Language 430
Abduction in Logic Programming 432
A Conversation Between Two Intelligent Databases 439
An Abductive Mechanism for the Base Logic 444
Introduction 444
Case Study: Abduction for Intuitionistic Implications 453
Case Study: Abduction for Relevance Logic 458
Conclusion 462
Bibliography 464
Index 494
Part I A Practical Logic of Cognitive Systems 20
1 Introduction 22
2 Practical Logic 30
2.1 First Thoughts on a Practical Logic 30
2.1.1 A Hierarchy of Agency Types 31
2.1.2 Peculiarities of Institutional Agents 36
2.1.3 Normativity 39
2.1.4 Mathematical Models 43
2.1.5 Slight-resource Adjustment Strategies 45
2.1.6 Hasty Generalization 45
2.1.7 Generic Inference 45
2.1.8 Natural Kinds 46
2.1.9 Defaults 47
2.1.10 Discourse Economies 47
2.1.11 Consciousness 48
2.2 Practical Logic 51
2.3 Connectionist Logic 53
2.3.1 Fallacies 54
Part II Conceptual Models of Abduction 58
3 The Structure of Abduction 60
3.1 Introductory Remark on Abduction 60
3.2 The Elementary Structure of Abductive Logic 61
3.3 Expanding the Schema 63
3.4 Frames 65
3.5 Generalizing 66
3.6 Avoiding a Confusion 66
3.7 Locating Abduction on the Logical Map 67
3.8 Abductive Schematics 68
3.8.1 Consequentialist Abduction 68
3.8.2 The Good that A K M Does 74
3.8.3 The Reach of Abduction 75
3.8.4 Simplicity 77
3.9 The Cut Down Problem 77
3.9.1 Abduction as Practical 79
3.9.2 Proof-theoretic Abduction 79
3.10 The Adaptive and the Epistemically Subpar 83
3.11 Knowledge-Sets 84
3.12 Filtration Structures 87
3.13 Hypothesis-Engagement 90
3.14 Grounds of Action 91
3.15 Tasks for an Abductive Logic 92
4 Explanationist Abduction 96
4.1 Peirce 96
4.1.1 Surprise 102
4.1.2 Testability and Economics 103
4.1.3 Insight and Trial 106
4.2 Rationality and Diminished Epistemic Virtue 107
4.3 Explanationism 108
4.3.1 The Covering Law Model 111
4.3.2 The Rational Model 114
4.3.3 Teleological Explanation 117
4.3.4 The Pluralism of Explanation 120
4.4 Assessing 121
4.5 Characteristicness 123
4.6 Hanson 125
4.7 Darden 130
4.8 Fodor 130
4.9 Adaptive Explanationism 131
4.10 Non-abductive Conjecture 134
5 Non-Plausibilistic Abduction 136
5.1 Introductory remark 136
5.2 Newton 137
5.3 Planck 142
5.4 Physical Dependencies 143
5.5 The Superstring Controversy 144
5.6 Russell and Godel 146
5.7 The Consequence Relation 150
5.8 Lakatos 155
5.9 Hintikka 159
5.10 Empirical Progress 162
5.11 Semantic Tableaux 163
5.11.1 Assessing Semantic Tableau Abduction 167
5.11.2 Is It Abduction? 168
5.12 Inconsistency Again 169
5.12.1 Bayesian Inference 171
6 Diagnostic Abduction in AI 176
6.1 Explanationist Diagnostics 176
6.1.1 Difficulties with AP 182
6.2 Another Example 184
6.2.1 Remarks 190
6.3 Coherentism and Probabilism 191
6.3.1 The Rivalry of Explanationism and Probabilism 191
6.4 Explanatory Coherence 192
6.4.1 Probabilistic Networks 195
6.5 Pearl Networks for ECHO 197
6.6 Neuropharmacological Intervention 201
6.7 Mechanizing Abduction 205
6.8 Abduction in Neural-Symbolic Networks 210
7 The Characteristic and the Plausible 216
7.1 The Open Door 216
7.1.1 The Element of Surprise 217
7.1.2 Plausibility 221
7.1.3 A Resolution Point 222
7.1.4 How to Get Determinacy Out of Indeterminacy 223
7.1.5 Alternatives 225
7.2 The Piccadilly Line 227
7.3 Plausibility Again 230
7.3.1 Historical Note on Plausibility 231
7.3.2 Cut-to-the Chase Abduction 233
7.4 Characteristicness 234
7.5 Common Knowledge 240
7.6 Rescher's Plausibility Logic 243
7.6.1 Reliability 248
7.6.2 Axioms for Plausibility 249
7.7 Plausibility and Presumption 253
7.8 Brief Concluding Remarks 258
8 Relevance and Analogy 260
8.1 Relevance 260
8.1.1 Relevance as Cognitive 261
8.1.2 Topical Relevance 264
8.1.3 Contextual Effects 268
8.2 Irredundancy Relevance 269
8.3 Relevance and Cutting to the Chase 271
8.4 Legal Relevance 275
8.4.1 Ideology 277
8.5 Legal Presumption 279
8.5.1 Types of Presumption 281
8.5.2 The Reasonable Person 285
8.5.3 Reasonable Doubt 286
8.6 Hypothesis-Discharge 289
8.7 The Probativity Question 290
8.8 Revision Structures 291
8.8.1 Proof Standards 293
8.8.2 Analogy 295
8.8.3 The Meta Approach 297
8.8.4 Similarity 302
8.9 Analogy in Law 303
8.9.1 Precedent 305
8.10 Analogue Modelling 307
9 Interpretation Abduction 310
9.1 Hermeneutics 310
9.1.1 Enthymemes 312
9.1.2 Fermat's Last Theorem 315
9.2 Enthymeme Resolution as Abductive 317
9.2.1 The Attack on Analyticity 319
9.2.2 Inarticulacy as Economics 321
9.2.3 Some Virtual Guidelines 323
9.2.4 Background Knowledge 324
9.3 Charity 326
9.3.1 Indeterminacy of Translation 328
9.4 Is it Abduction (Again)? 333
9.5 Constitutional Inarticulacies 334
9.5.1 Inarticulate Understanding 334
9.6 Visual Abduction 338
9.7 Empathy 340
9.7.1 Discourse Empathies 342
9.8 Semantic Space Interpretation of Texts 344
9.8.1 The Raynaud-Fish Oil Abduction 349
Part III Formal Models of Abduction 354
10 A Glimpse of Formality 356
10.1 Introduction 356
10.1.1 The AKM model 357
10.1.2 The GW Model 363
10.2 Some Schematic Remarks 365
10.3 Case Study: Defeasible Logic 372
11 A General Theory of Logical Systems 378
11.1 Introduction 378
11.2 Logical Systems 381
11.3 Refining the Notion of a Logical System 393
11.3.1 Structured consequence 393
11.3.2 Algorithmic structured consequence relation 394
11.3.3 Mechanisms 397
11.3.4 Modes of Evaluation 399
11.3.5 TAR-Logics 401
11.3.6 Relevance 403
11.4 Discussion and Further Reading 403
12 A Base Logic 404
12.1 Formal Abduction: An Overview 404
12.2 Introducing LDS 409
12.2.2 Examples of Resource LDS 412
12.3 Goal Directed Algorithm for => •
12.3.1 The Algorithm 419
12.3.2 Examples 421
12.4 Intuitive Theory of Labelled Abduction 423
12.4.1 Abduction in Knowledge Bases 424
Possible Principles of Abduction 425
12.4.2 Abduction in Planning and Natural Language 430
12.4.3 Abduction in Logic Programming 432
12.4.4 A Conversation Between Two Intelligent Databases 439
13 An Abductive Mechanism for the Base Logic 444
13.1 Introduction 444
13.3 Case Study: Abduction for Intuitionistic Impli-cations 453
13.4 Case Study: Abduction for Relevance Logic 458
13.5 Conclusion 462
back matter 464
Bibliography 464
index 494
Practical Logic
Dav M. Gabbay Department of Computer Science King's College London Strand, London, WC2R 2LS, U.K.
John Woods Philosophy Department University of British Columbia, Vancouver, BC Canada, V6T 1Z1
Department of Computer Science King's College London Strand, London, WC2R 2LS, U.K.
… for all the proclaimed rationality of modem humans and their institutions, logic touches comparatively little of human practice.
Richard Sylvan
[T]he limit on human intelligence up to now has been set by the size of the brain that will pass through the birth canal …. But within the next few years, I expect we will be able to grow babies outside the human body, so this limitation will be removed. Ultimately, however, increases in the size of the human brain through genetic engineering will come up against the problem that the body’s chemical messengers responsible for our mental activity are relatively slow-moving. This means that further increases in the complexity of the brain will be at the expense of speed. We can be quick-witted or very intelligent, but not both.
Stephen Hawking
2.1 First Thoughts on a Practical Logic
The theory of abduction that we develop in this volume is set up to meet two conditions. One is that it show how abduction plays within a practical logic of cognitive systems. The other is that, to the extent possible, it serve as an adequate standalone characterization of abduction itself. In the first instance we try to get the logic of cognitive systems right, though with specific attention to the operation of abduction. In the second instance, we try to get abduction right; and we postulate that our chances of so doing improve when the logic of abduction is lodged in this more comprehensive practical logic.
We open this chapter with a brief discussion of what we take such a logic to be. Readers who wish a detailed discussion can consult chapters 2 and 3 of the companion volume, Agenda Relevance: A Study in Formal Pragmatics. Other readers, who may be eager to get on with abduction without these prefatory remarks, can go directly to section 3.1.
In the prequel to this book we adopted a convention for flagging the more important of the claims and ideas advanced by our conceptual model of the relevance relation. Key claims that we were prepared to assert with some confidence we flagged as (numbered) definitions or propositions. Ideas that called for a greater tentativeness we flagged as (numbered) propositions prefixed with the symbol . We here follow that same practice for abduction.
2.1.1 A Hierarchy of Agency Types
We take the position that reasoning is an aid to cognition, a logic, when conceived of as a theory of reasoning, must take this cognitive orientation deeply into account. Accordingly, we will say that a cognitive system is a triple of a cognitive agent, cognitive resources, and cognitive target performed in real time. (See here [Norman, 1993; Hutchins, 1995].) Correspondingly, a logic of a cognitive system is a principled description of conditions under which agents deploy resources in order to perform cognitive tasks. Such is a practical logic when the agent it describes is a practical agent. So, then,
Definition 2.1
Cognitive systems
A cognitive system CS is a triple X, R, A of a cognitive agent X, cognitive resources R, and a cognitive agenda A executed in real time.
Definition 2.2
Practical logics, a first pass
A practical logic is a systematic account of aspects of the behaviour of a cognitive system in which X is a practical agent.
A practical logic is but an instance of a more general conception of logic. The more general notion is reasoning that is target-motivated and resource-dependent. Correspondingly, a logic that deals with such reasoning is a Resource-Target Logic (RT-logic). In our use of the term, a practical logic is a RT-logic relativized to practical agents.
How agents perform is constrained in three crucial ways: in what they are disposed towards doing or have it in mind to do (i.e., their agendas); in what they are capable of doing (i.e., their competence); and in the means they have for converting competence into performance (i.e., their resources). Loosely speaking, agendas are programmes of action, exemplified by belief-revision and belief-update, decision-making and various kinds of case-making and criticism transacted by argument. For ease of exposition we classify this motley of practices under the generic heading “cognitive”, and we extend the term to those agents whose practices these are.1
An account of cognitive practice should include an account of the type of cognitive agent involved. Agency-type is set by two complementary factors. One is the degree of command of resources an agent needs to advance or close his (or its) agendas. For cognitive agendas, three types of resources are especially important. They are (1) information, (2) time, and (3) computational capacity. The other factor is the height of the cognitive bar that the agent has set for himself. Seen this way, agency-types form a hierarchy H partially ordered by the relation C of commanding-greater-resources-in-support-of-higher-goals-than. H is a poset (a partially ordered set) fixed by the ordered pair 〈C, X〉 of the relation C on the set of agents X.
Human agency ranks low in H. If we impose a decision not to consider the question of membership in H of non-human primates, we could say that in the H-space humans are the lowest of the low. In the general case the cognitive resources of information, time and computational capacity are for human agents comparatively less abundant than for agents of higher type, and their cognitive goals are comparatively more modest. For large classes of cases, humans perform their cognitive tasks on the basis of less information and less time than they might otherwise like to have, and under limitations on the processing and manipulating of complexity. Even so, paucity must not be confused with scarcity.2 There are cases galore in which an individual’s resources are adequate for the attainment of the attendant goal. In a rough and ready way, we can say that the comparative modesty of an agent’s cognitive goals inoculates him against cognitive-resource scarcity. But there are exceptions, of course.
Institutional entities contrast with human agents in all these respects. A research group usually has more information to work with than any individual, and more time at its disposal; and if the team has access to the appropriate computer networks, more fire-power than most individuals even with good PCs. The same is true, only more so, for agents placed higher in the hierarchy — for corporate actors such as NASA, and collective endeavours such as quantum physics since 1970. Similarly, the cognitive agendas that are typical of institutional agents are by and large stricter than the run-of-the-mill goals that motivate individual agents. In most things, NASA aims at stable levels of scientific confirmation, but, for individuals the defeasibly plausible often suffices for local circumstances.
These are vital differences. Agencies of higher rank can afford to give maximization more of a shot. They can wait long enough to make a try for total information, and they can run the calculations that close their agendas both powerfully and precisely. Individual agents stand conspicuously apart. For most tasks, the human cognitive agent is a satisficer. He must do his business with the information at hand, and, much of the time, sooner rather than later. Making do in a timely way with what he knows now is not just the only chance of achieving whatever degree of cognitive success is open to him as regards the agenda at hand; it may also be what is needed in order to avert unwelcome disutilities, or even death. (We do not, when seized by an onrushing tiger experience, wait before fleeing for a refutation of skepticism about the external world or a demonstration that the approaching beast is not an hallucination.)
Given the comparative humbleness of his place in H, the human individual is frequently faced with the need to practise cognitive economies. This is certainly so when either the loftiness of his goal or the supply of drawable resources create a cognitive strain. In such cases, he must turn scantiness to advantage. That is, he must (1) deal with his resource-limits and in so doing (2) must do his best not to kill himself. There is a tension in this dyad. The paucities with which the individual is chronically faced are often the natural enemy of getting things right, of producing accurate and justified answers to the questions posed by his agenda. And yet not only do human beings contrive to get most of what they do right enough not to be killed by it, they also in varying degrees prosper and flourish.
This being so, we postulate for the individual agent slight-resource adjustment strategies (SRAS), which he uses to advantage in dealing with the cognitive limitations that inhere in the paucities presently in view. We make this assumption in the spirit of Simon...
| Erscheint lt. Verlag | 2.5.2005 |
|---|---|
| Sprache | englisch |
| Themenwelt | Geisteswissenschaften ► Philosophie ► Allgemeines / Lexika |
| Geisteswissenschaften ► Psychologie ► Allgemeine Psychologie | |
| Geisteswissenschaften ► Psychologie ► Verhaltenstherapie | |
| Mathematik / Informatik ► Informatik ► Netzwerke | |
| Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik | |
| Mathematik / Informatik ► Mathematik ► Algebra | |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| Technik | |
| ISBN-10 | 0-08-046092-5 / 0080460925 |
| ISBN-13 | 978-0-08-046092-5 / 9780080460925 |
| Haben Sie eine Frage zum Produkt? |
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