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Mathematical Problems from Applied Logic I Logics for the XXIst Century

:	Dov M. Gabbay, Sergei S. Goncharov, Michael Zakharyaschev
:	Dov M. Gabbay, Sergey Goncharov, Michael Zakharyaschev
:	Mathematical Problems from Applied Logic I Logics for the XXIst Century
:	Springer-Verlag
:	9780387310725
:	1
:	CHF 132.70
:

:	Grundlagen
:	English

:	348
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

This is an overview of the current state of knowledge along with open problems and perspectives, clarified in such fields as non-standard inferences in description logics, logic of provability, logical dynamics and computability theory. The book includes contributions concerning the role of logic today, including unexpected aspects of contemporary logic and the application of logic. This book will be of interest to logicians and mathematicians in general.

CHAPTER 15
Interaction in Small Groups (p. 363-364)

PETER J. BURKE

INTRODUCTION

In the early 1970s, the question"

	Authors	21
	Main Topics	9
	Editors	10
	Dov M Gabbay	11
	Sergei S Goncharov	12
	Michael Zakharyaschev	13
	Authors	14
	Franz Baader	17
	Lev Beklemishev	17
	Johan van Benthem	18
	S Barry Cooper	19
	John N Crossley	19
	Wilfrid A Hodges	20
	Ralf Küsters	20
	Lawrence S Moss	21
	Albert Visser	21
	Content	23
	Nonstandard Inferences in Description Logics: The Story So Far	29
	1. Introduction	30
	2. Description Logics and Standard Inferences	34
	3. Nonstandard Inferences—Motivation and Definitions	39
	4. A Structural Characterization of Subsumption	51
	5. The Least Common Subsumer	60
	6. The Most Specific Concept	64
	7. Rewriting	72
	8. Matching	81
	9. Conclusion and Future Perspectives	92
	References	94
	Problems in the Logic of Provability	104
	1. Introduction	105
	2. Informal Concepts of Proof	108
	3. Basics of Provability Logic	118
	4. Provability Logic for Intuitionistic Arithmetic	120
	5. Provability Logic and Bounded Arithmetic	129
	6. Classification of Bimodal Provability Logics	133
	7. Magari Algebras	136
	8. Interpretability Logic	141
	9. Graded Provability Algebras	147
	10. List of Problems	152
	References	156
	Open Problems in Logical Dynamics	164
	1. Logical Dynamics	164
	2. Standard Epistemic Logic	166
	3. Public Announcement: Epistemic Logic Dynamfied	171
	4. Dynamic Epistemic Logic	184
	5. Background in Standard Logics	191
	6. From Information Update to Belief Revision	197
	7. Temporal Epistemic Logic	205
	8. Game Logics and Game Theory	211
	9. Conclusion	212
	References	213
	Computability and Emergence	220
	1. An Emergent World around Us	221
	2. Descriptions, Algorithms, and the Breakdown of Inductive Structure	222
	3. Ontology and Mathematical Structure	229
	4. Where Does It All Start?	231
	5. Towards a Model Based on Algorithmic Content	236
	6. Levels of Reality	241
	7. Algorithmic Content Revisited	248
	8. What Is to Be Done?	251
	References	255
	Samsara†	259
	1. Introduction	260
	2. An Example of a Process	261
	3. What Logics Do We Need?	262
	4. What Are Logical Systems	284
	and What Should They Be?	284
	5. The Nature of Proof	288
	6. Final Remarks	295
	References	296
	Two Doors to Open	303
	1. Logic and Cognitive Science	305
	2. Medieval Arabic Semantics	326
	References	339
	Applied Logic: A Manifesto	343
	1. What is Applied Logic?	343
	2. Mathematics and Logic, but Different from Mathematical Logic	345
	3. Applied Philosophical Logic	352
	4. What Does Computer Science Have to Do with It?	354
	5. Other Case Studies	358
	6. Being as catholic as Possible	367
	References	369
	Index	370