Mathematical problems from applied logic : logics for the XXIst century
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Bibliographic Information
Mathematical problems from applied logic : logics for the XXIst century
（International mathematical series, 4,
Springer, c2006-2007
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- Other Title
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Mathematical problems from applied logic : new logics for the XXIst century
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Description and Table of Contents
- Volume
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1 ISBN 9780387286884
Description
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.
Table of Contents
Nonstandard Inferences in Description Logics: The Story So Far, Franz Baader and Ralf Kusters: Introduction.- Description Logics and Standard Inferences.- Nonstandard Inferences-Motivation and Definitions.- A Structural Characterization of Subsumption.- The Least Common Subsumer.- The Most Specific Concept.- Rewriting.- Matching.- Conclusion and Future Perspectives.- Problems in the Logic of Provability, Lev Beklemishev and Albert Visser: Introduction.- Informal Concepts of Proof.- Basics of Provability Logic.- Provability Logic for Intuitionistic Arithmetic.- Provability Logic and Bounded Arithmetic.- Classification of Bimodal Provability Logics.- Magari Algebras.- Interpretability Logic.- Graded Provability Algebras.- List of Problems.- Open Problems in Logical Dynamics, Johan van Benthem: Logical Dynamics.- Standard Epistemic Logic.- Public Announcement: Epistemic Logic Dynamified.- Dynamic Epistemic Logic.- Background in Standard Logics.- From Information Update to Belief Revision.- Temporal Epistemic logic.- Game Logics and Game Theory.- Conclusion.- Computability and Emergence, S Barry Cooper: An Emergent World around Us.- Descriptions, Algorithms, and the Breakdown of Inductive Structure.- Ontology and Mathematical Structure.- Where does It All Start? -Towards a Model Based on Algorithmic Content.- Levels of Reality.- Algorithmic Content Revisited.- What Is to Be Done?- Samsara, [The endless cycle of death and rebirth to which life in the material world is bound. (OED)], John N Crossley: Introduction.- An Example of a Process.- What Logics Do We Need?- What are Logical Systems and What Should They Be?- The Nature of Proof.- Final Remarks.- Two Doors to Open, Wilfrid Hodges: Logic and Cognitive Science.- Medieval Arabic Semantics.- Applied Logic: A Manifesto, Lawrence SMoss: What is Applied Logic?- Mathematics and Logic, but Different from Mathematical Logic.- Applied Philosophical Logic.- What Does Computer Science Have to Do with It?- Other Case Studies.- Being as catholic as Possible.- Subject Index.
- Volume
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2 ISBN 9780387692449
Description
This book presents contributions from world-renowned logicians, discussing important topics of logic from the point of view of their further development in light of requirements arising from successful application in Computer Science and AI language. Coverage includes: the logic of provability, computability theory applied to biology, psychology, physics, chemistry, economics, and other basic sciences; computability theory and computable models; logic and space-time geometry; hybrid systems; logic and region-based theory of space.
Table of Contents
On Two Models of Provability.- Directions for Computability Theory Beyond Pure Mathematical.- Computability and Computable Models.- First-Order Logic Foundation of Relativity Theories.- Beyond Hybrid Systems.- Region-Based Theory of Space: Algebras of Regions, Representation Theory, and Logics.
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