Cognitive reasoning : a formal approach

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.

1 Introduction	p. 1
1.1 What is Cognition?	p. 1
1.2 Cognizing Agents	p. 4
1.3 Cognitive Reasoning	p. 6
1.4 Logic and Cognitive Reasoning	p. 10
1.5 Requirements for a Formal Cognitive Reasoning Theory	p. 11
1.6 Objectives	p. 13
1.7 The Formal Approach to Be Developed	p. 14
1.8 Overview	p. 15
Part I Conceptual Theory of Cognitive Reasoning
2 Introductory Explanation	p. 25
3 Basic System of Concepts	p. 29
3.1 Facts and Knowledge	p. 29
3.2 Truth Values: Informal Discussion	p. 32
3.3 Reasoning	p. 35
4 Constructing a Model of a Cognizing Agent	p. 41
4.1 The Structure and Functioning of the Cognizing Agent	p. 43
5 Cognitive Reasoning Framework	p. 51
5.1 Theories of the CR Framework	p. 52
5.2 Modelling Cognitive Reasoning in the CR Framework	p. 60
Part II Logic Foundation
6 Introductory Explanation	p. 71
7 Propositional Logic	p. 73
7.1 Notation	p. 74
7.2 Classical Propositional Logic (Syntax and Semantics)	p. 75
7.3 Classical Propositional Logic (Calculus)	p. 77
7.4 Propositional PJ Logics (Syntax and Semantics)	p. 78
7.5 PJ Logics (Calculus)	p. 83
8 First-Order Logics	p. 93
8.1 Terms and Notation	p. 93
8.2 Classical First-Order Logic (Syntax and Semantics)	p. 105
8.3 Classical First-Order Logic (Calculus)	p. 108
8.4 First-Order PJ Logics (Syntax and Semantics)	p. 110
8.5 First-Order PJ Logic (Calculus)	p. 114
Part III Formal CR Framework
9 Introductory Explanation	p. 127
10 Modification Calculi	p. 131
10.1 State Descriptions over Sets of Constants	p. 132
10.2 Inference	p. 141
11 Derivability in Modification Calculi and L1	p. 159
11.1 Cuts of Record Strings: the General Case	p. 159
11.2 (m, s)-Cuts	p. 168
11.3 Deductive Cuts and Their Applications	p. 179
11.4 Deductive Correctness	p. 185
12 Semantics	p. 195
12.1 Sequences of L-Structures	p. 195
12.2 Structure Generators	p. 198
13 Iterative Representation of Structure Generators	p. 209
13.1 Immersions and Snaps	p. 209
13.2 Implementations and Extensions	p. 213
13.3 Iterative Images	p. 220
14 Modification Theories	p. 237
14.1 Validity and Derivability	p. 237
14.2 Modification Theories	p. 244
15 Conformability	p. 259
15.1 Locality	p. 259
15.2 Atomic Sorts	p. 268
Part IV Handling Complex Structures
16 Introductory Explanation	p. 277
16.1 Atomic Sorts	p. 277
16.2 Set Sorts	p. 278
16.3 Some Properties of the Set Sorts	p. 281
16.4 Modification Rules and Modification Calculi for Set Sorts	p. 282
16.5 Example	p. 284
17 Set-Admitting Structures	p. 291
17.1 Atoms	p. 291
17.2 Set Axioms	p. 295
18 Set Sorts in Modification Calculi	p. 301
18.1 Positive and Negative Connection w.r.t. Set Sorts	p. 301
18.2 Generating Rules for Modification Rule Systems with Set Sorts	p. 305
19 Perfect Modification Calculi (PMC)	p. 313
19.1 Coherent Inferences in Perfect Modification Calculi (General Properties)	p. 313
19.2 Modification Rules Within Coherent Inferences (Positive Case)	p. 322
19.3 Modification Rules Within Coherent Inferences (Negative Case)	p. 330
19.4 Conformability (Set Case)	p. 337
Part V JSM Theories
20 Introductory Explanation	p. 343
21 Simple JSM Theories	p. 345
21.1 Basic JSM theories	p. 345
21.2 Simple JSM Theories	p. 346
21.3 Causal and Prediction Rules	p. 349
21.4 Defining Axioms for the Simple JSM Theories	p. 350
21.5 Simple JSM Theories with Exclusion of Counterexamples	p. 352
22 Advanced JSM Theories	p. 355
22.1 Generalised JSM Theories	p. 355
22.2 Defining Axioms for the Generalised JSM Theories	p. 359
22.3 Non-symmetric JSM Theories	p. 361
23 Similarity Representation	p. 365
23.1 Basic Concepts	p. 365
23.2 Distinguishability Condition and Similarity Representation	p. 367
24 JSM Theories for Complex Structures	p. 371
24.1 JSM Theories with Set Sorts	p. 371
24.2 Simple JSM Theories with Property Sets	p. 373
24.3 Defining Axioms for the Simple JSM Theories with Property Sets	p. 377
Part VI Looking Back and Ahead
25 Introductory Overview	p. 383
26 Towards the Realisation	p. 387
26.1 Object Model Description	p. 387
26.2 Object Model Application	p. 397
27 CR Framework	p. 399
27.1 Conceptual CR Framework	p. 399
27.2 Formal CR Framework	p. 401
28 Open Problems	p. 407
29 Philosophical-Methodological Implications of the Proposed CR Framework	p. 411
29.1 Epistemology	p. 411
29.2 Ontology	p. 414
29.3 Methodology	p. 416
References	p. 421
Glossary	p. 425
Index	p. 431

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