Advances in Modal Logic

by Zakharyaschev, Michael; Segerberg, Krister; De Rijke, Maarten; Wansing, Heinrich

• ISBN13: 9781575862712
• ISBN10: 1575862719
• Format: Hardcover
• Copyright: 2001-03-20
• Publisher: Stanford Univ Center for the Study

Summary

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

Contributors	vii
The Origins of Modern Modal Logic	xi
Michael Zakharyaschev
Krister Segerberg
Maarten de Rijke
Heinrich Wansing
STS: A Structural Theory of Sets	1	(34)
Alexandru Baltag
Interpolation, Definability and Fixed Points in Interpretability Logics	35	(24)
Carlos Areces
Eva Hoogland
Dick de Jongh
Operations on Proofs that can be Specified by Means of Modal Logic	59	(14)
Sergei N. Artemov
Modal Logic in Two Gestalts	73	(28)
Johan van Benthem
Locally Tabular Extensions of MIPC	101	(20)
Guram Bezhanishvili
Revaz Grigolia
Conditional and Unconditional Obligation for Agents in Time	121	(34)
Mark A. Brown
How to Complete Some Modal Predicate Logics	155	(24)
Max J. Cresswell
Dynamics of Practical Reasoning: A Position Paper	179	(46)
Dov M. Gabbay
A Resolution-Based Decision Procedure for Extensions of K4	225	(22)
Harald Ganzinger
Ullrich Hustadt
Christoph Meyer
Renate A. Schmidt
Modal Logic and Universal Algebra I: Modal Axiomatizations of Structures	247	(28)
Valentin Goranko
Dimiter Vakarelov
Abductive Reasoning over Temporal Specifications of Objects	275	(26)
Paula Gouveia
Cristina Sernadas
A Modal Analysis of Some Principles of the Provability Logic of Heyting Arithmetic	301	(36)
Rosalie Iemhoff
Logic and Syntax---A Personal Perspective	337	(30)
Marcus Kracht
A Co-Variety-Theorem for Modal Logic	367	(14)
Alexander Kurz
Propositions, Propositional Attitudes and Belief Revision	381	(20)
Rohit Parikh
Rasiowa-Sikorski Lemma and Kripke Completeness of Predicate and Infinitary Modal Logics	401	(20)
Yoshihito Tanaka
Hiroakira Ono
Canonical Pseudo-Correspondence	421	(10)
Yde Venema
Dynamic Description Logics	431	(16)
Frank Wolter
Michael Zakharyaschev
Subject Index	447	(8)
Author Index	455