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Mathematical Problems from Applied Logic I Dov M. Gabbay

Mathematical Problems from Applied Logic I By Dov M. Gabbay

Mathematical Problems from Applied Logic I by Dov M. Gabbay


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Summary

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.

Mathematical Problems from Applied Logic I Summary

Mathematical Problems from Applied Logic I: Logics for the XXIst Century by Dov M. Gabbay

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.

Mathematical Problems from Applied Logic I Reviews

From the reviews:

It may be one of the best books I ever read ... . The book is best described as a drawerful of ambitious, thought-provoking research questions. Some will inspire you to go search for more literature, and some might even get you started on new research topics. ... this collection is a fascinating bouquet of research questions to pursue or suggest to your students. ... I am convinced that this collection will nurture future research and be a great source of inspiration for young researchers. (Anders Sogaard, Studia Logica, Vol. 87 (361-365), 2007)

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.

Additional information

NLS9781441921109
9781441921109
1441921109
Mathematical Problems from Applied Logic I: Logics for the XXIst Century by Dov M. Gabbay
New
Paperback
Springer-Verlag New York Inc.
2010-11-25
348
N/A
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