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Advances in Modal Logic, Volume 2

Modal Logic, originally conceived as the logic of necessity and possibility, has developed into a powerful mathematical and computational discipline. It is the main source of formal languages aimed at analyzing complex notions such as common knowledge and formal provability. Modal and modal-like languages also provide us with families of restricted description languages for relational and topological structures; they are being used in many disciplines, ranging from artificial intelligence, computer science and mathematics via natural language syntax and semantics to philosophy.

This volume presents a broad and up-to-date view of the field, with contributions covering both the foundations of modal logic itself and each of the aforementioned application areas. Complemented with an editorial introduction covering the roots of modal logic, this book is indispensable for any advanced student and researcher in non-classical logic and its applications.

Table of Contents

The Origins of Modern Modal Logic
Michael Zakharyaschev, Krister Segerberg, Maarten de Rijke, and Heinrich Wansing
1. STS: A Structural Theory of Sets
Alexandru Baltag
2. Interpolation, Definability and Fixed Points in Interpretability Logics
Carlos Areces, Eva Hoogland, and Dick de Jongh
3. Operations on Proofs that can be Specified by Means of Modal Logic
Sergei N. Artemov
4. Modal Logic in Two Gestalts
Johan van Benthem
5. Locally Tabular Extensions of MIPC
Guram Bezhanishvili and Revaz Grigolia
6. Conditional and Unconditional Obligation for Agents in Time
Mark A. Brown
7. How to Complete Some Modal Predicate Logics
Max J. Cresswell
8. Dynamics of Practical Reasoning: A Position Paper
Dov M. Gabbay
9. A Resolution-Based Decision Procedure for Extensions of K4
Harald Ganzinger, Ullrich Hustadt, Christoph Meyer, and Renate A. Schmidt
10. Modal Logic and Universal Algebra I: Modal Axiomatizations of Structures
Valentin Goranko and Dimiter Vakarelov
11. Abductive Reasoning over Temporal Specifications of Objects
Paula Gouveia and Cristina Sernadas
12. A Modal Analysis of Some Principles of the Provability Logic of Heyting Arithmetic
Rosalie Iemhoff
13. Logic and Syntax - A Personal Perspective
Marcus Kracht
14. A Co-Variety-Theorem for Modal Logic
Alexander Kurz
15. Propositions, Propositional Attitudes and Belief Revision
Rohit Parikh
16. Rasiowa-Sikorski Lemma and Kripke Completeness of Predicate and Infinitary Modal Logics
Yoshihito Tanaka and Hiroakira Ono
17. Canonical Pseudo-Correspondence
Yde Venema
18. Dynamic Description Logics
Frank Wolter and Michael Zakharyaschev
Subject Index
Author Index

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