 |
|
| TOOLS AND TECHNIQUES IN MODAL LOGIC, 142
| |
| | |
|
|
 To order this title, and for more information, click here
By
M. Kracht, Freie Universität Berlin, II. Mathematisches Institut, Berlin, Germany
Included in series
Studies in Logic and the Foundations of Mathematics, 142
Description
This book treats modal logic as a theory, with several subtheories, such as completeness theory, correspondence theory, duality theory
and transfer theory and is intended as a course in modal logic for students who have had prior contact with modal logic and who wish
to study it more deeply. It presupposes training in mathematical or logic. Very little specific knowledge is presupposed, most results
which are needed are proved in this book.
Contents
About this Book. Overview.
Part 1. The Fundamentals.
Chapter 1. Algebra, Logic and Deduction. Basic facts and structures. Propositional
languages. Algebraic constructions. General logic. Completeness of matrix semantics. Properties of logics. Boolean logic. Some notes
on computation and complexity. Chapter 2. Fundamentals of Modal Logic I. Syntax of modal logics. Modal algebras. Kripke-Frames and frames.
Frame constructions I. Some important modal logics. Decidability and finite modal property. Normal forms. The Lindenbaum-Tarski construction.
The lattices of normal and quasi-normal logics. Chapter 3. Fundamentals of Modal Logic II. Local and global consequense relations. Completeness,
correspondence and persistence. Frame constructions II. Weakly transitive logics I. Subframe logics. Constructive reduction. Interpolation
and beth theorems. Tableau calculi and interpolation. Modal consequence relations.
Part 2. The General Theory of Modal Logic.
Chapter 4. Universal Algebra and Duality Theory. More on products. Varieties, logics and equationally definable classes. Weakly transitive
logics II. Stone representation and duality. Adjoint functors and natural transformations. Generalized frames and modal duality theory.
Frame constructions III. Free algebras, canonical frames and descriptive frames. Algebraic characterizations of interpolation. Chater
5. Definability and Correspondence. Motivation. The languages of description. Frame correspondence - an example. The basic calculus of
internal descriptions. Sahlqvist's theorem. Elementary Sahlqvist conditions. Preservation classes. Some results from model theory. Chapter
6. Reducing Polymodal Logic to Monomodal Logic. Interpretations and simulations. Some preliminary results. The fundamental construction.
A general theorem for consistency reduction. More preservation results. Thomason simulations. Properties of the simulation. Simulation
and transfer - some generalizations. Chapter 7. Lattices of Modal Logics. The relevance of studying lattices of logics. Splittings and
other lattice concepts. Irreducible and prime logics. Duality theory for upper continuous lattices. Some consequences of the duality
theory. Properties of logical calculi and related lattice properties. Splittings of the lattices of modal logics and completeness. Blok's
alternative. The lattice of tense logics.
Part 3. Case Studies.
Chapter 8. Extensions of
K4.
The global structure of ΞΎ
K4.
The structure of finitely generated
K4
-frames. The selection procedure. Refutation patterns. Embeddability patterns and the elementarity
of logics. Logics of finite width I. Logics of finite width II. Bounded properties and precomplete logics above
S4.
Logics of
finite tightness. Chapter 9. Logics of Bounded Alternativity. The logics containing
K.alt
1. Polymodal logics with quasi-functional
operators. Colourings and decolourings. Decidability of logics. Decidability of properties of logics I. Decidability of properties of
logics II. Chapter 10. Dynamic Logic.
PDL
- A calculus of compound modalities. Axiomatizing
PDL
The finite model property.
Regular languages. An evaluation procedure. The unanswered question. The logic of finite computations. Index. Bibliography.
| Bibliographic details |
Hardbound, publication date: JUN-1999
ISBN-13: 978-0-444-50055-7
ISBN-10: 0-444-50055-3
Imprint: NORTH-HOLLAND
|
| Price and Ordering |
Price:
USD 155
EUR 137
GBP 91
|  |
Books and book related electronic products are priced in US dollars (USD), euro (EUR), and Great Britain Pounds (GBP). USD prices apply to the Americas and Asia Pacific. EUR prices apply in Europe and the Middle East. GBP prices apply to the UK and all other countries.
|
See also information about conditions of sale & ordering procedures, and links to our regional sales offices.
|
050/500
Last update: 26 Sep 2008
|
|
| |
| | |
|
|
| |
