Cognitive Reasoning (eBook)
X, 437 Seiten
Springer Berlin (Verlag)
978-3-540-68875-4 (ISBN)
Dealing with uncertainty, moving from ignorance to knowledge, is the focus of cognitive processes. Understanding these processes and modelling, designing, and building artificial cognitive systems have long been challenging research problems.
This book describes the theory and methodology of a new, scientifically well-founded general approach, and its realization in the form of intelligent systems applicable in disciplines ranging from social sciences, such as cognitive science and sociology, through natural sciences, such as life sciences and chemistry, to applied sciences, such as medicine, education, and engineering.
The main subject developed in the book is cognitive reasoning investigated at three levels of abstraction: conceptual, formal, and realizational. The authors offer a model of a cognizing agent for the conceptual theory of cognitive reasoning, and they also present a logically well-founded formal cognitive reasoning framework to handle the various plausible reasoning methods. They conclude with an object model of a cognitive engine.
The book is suitable for researchers, scientists, and graduate students working in the areas of artificial intelligence, mathematical logic, and philosophy.
Preface 5
Contents 7
Introduction 11
What Is Cognition? 11
Cognizing Agents 14
Cognitive Reasoning 16
Logic and Cognitive Reasoning 20
Requirements for a Formal Cognitive Reasoning Theory 21
Objectives 23
The Formal Approach to Be Developed 24
Overview 25
Part I Conceptual Theory of Cognitive Reasoning 32
Introductory Explanation 33
Basic System of Concepts 36
Facts and Knowledge 36
Truth Values: Informal Discussion 39
Reasoning 42
Constructing a Model of a Cognizing Agent 48
The Structure and Functioning of the Cognizing Agent 50
Cognitive Reasoning Framework 57
Theories of the CR Framework 58
Modelling Cognitive Reasoning in the CR Framework 66
Part II Logic Foundation 75
Introductory Explanation 76
Propositional Logic 78
Notation 79
Classical Propositional Logic (Syntax and Semantics) 80
Classical Propositional Logic (Calculus) 82
Propositional PJ Logics (Syntax and Semantics) 83
PJ Logics (Calculus) 88
First-Order Logics 98
Terms and Notation 98
Classical First-Order Logic (Syntax and Semantics) 110
Classical First-Order Logic (Calculus) 113
First-Order PJ Logics (Syntax and Semantics) 115
First-Order PJ Logic (Calculus) 119
Part III Formal CR Framework 129
Introductory Explanation 130
Modification Calculi 133
State Descriptions over Sets of Constants 134
Inference 143
Derivability in Modification Calculi and L1 160
Cuts of Record Strings: the General Case 160
(m,s)-Cuts 169
Deductive Cuts and Their Applications 180
Deductive Correctness 186
Semantics 195
Sequences of L-Structures 195
Structure Generators 198
Iterative Representation of Structure Generators 209
Immersions and Snaps 209
Implementations and Extensions 213
Iterative Images 220
Modification Theories 236
Validity and Derivability 236
Modification Theories 243
Conformability 258
Locality 258
Atomic Sorts 267
Part IV Handling Complex Structures 274
Introductory Explanation 275
Atomic Sorts 275
Set Sorts 276
Some Properties of the Set Sorts 279
Modification Rules and Modification Calculi for Set Sorts 280
Example 282
Set-Admitting Structures 289
Atoms 289
Set Axioms 293
Set Sorts in Modification Calculi 298
Positive and Negative Connection w.r.t. Set Sorts 298
Generating Rules for Modification Rule Systems with Set Sorts 302
Perfect Modification Calculi (PMC) 309
Coherent Inferences in Perfect Modification Calculi (General Properties) 309
Modification Rules Within Coherent Inferences (Positive Case) 318
Modification Rules Within Coherent Inferences (Negative Case) 326
Conformability (Set Case) 333
Part V JSM Theories 336
Introductory Explanation 337
Simple JSM Theories 339
Basic JSM theories 339
Simple JSM Theories 340
Causal and Prediction Rules 343
Defining Axioms for the Simple JSM Theories 344
Simple JSM Theories with Exclusion of Counterexamples 346
Advanced JSM Theories 349
Generalised JSM Theories 349
Defining Axioms for the Generalised JSM Theories 353
Non-symmetric JSM Theories 355
Similarity Representation 358
Basic Concepts 358
Distinguishability Condition and Similarity Representation 360
JSM Theories for Complex Structures 364
JSM Theories with Set Sorts 364
Simple JSM Theories with Property Sets 366
Defining Axioms for the Simple JSM Theories with Property Sets 370
Part VI Looking Back and Ahead 373
Introductory Overview 374
Towards the Realisation 377
Object Model Description 377
Object Model Application 387
CR Framework 389
Conceptual CR Framework 389
Formal CR Framework 391
Open Problems 397
Philosophical--Methodological Implications of the Proposed CR Framework 400
Epistemology 400
Ontology 403
Methodology 405
References 409
Glossary 413
Index 418
| Erscheint lt. Verlag | 11.3.2010 |
|---|---|
| Reihe/Serie | Cognitive Technologies |
| Zusatzinfo | X, 437 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Themenwelt | Geisteswissenschaften ► Philosophie ► Logik |
| Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik | |
| Mathematik / Informatik ► Mathematik | |
| Medizin / Pharmazie | |
| Technik | |
| Schlagworte | Abduction • Analogy • Artificial Intelligence • cognitive science • Common-sense reasoning • Formal inference • Formal philosophy • Formal Reasoning • Fuzzy Logic • information systems • Knowledge • Logic • Many-valued Logic • Mathematical Logic • Modeling • Non-Classical Logic • Problem Solving |
| ISBN-10 | 3-540-68875-7 / 3540688757 |
| ISBN-13 | 978-3-540-68875-4 / 9783540688754 |
| Haben Sie eine Frage zum Produkt? |
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