Tools and Techniques in Modal Logic: Kracht: 9780444500557: Book: Technology: eCampus.com

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.

Intended as a course in modal logic for students who have had prior contact with modal logic and desire to study it more deeply.

About this Book

(2)

Overview

vii

Part 1. The Fundamentals

(164)

Chapter 1. Algebra, Logic and Deduction

(44)

1.1. Basic Facts and Structures

(5)

1.2. Propositional Languages

(6)

1.3. Algebraic Constructions

(4)

1.4. General Logic

(5)

1.5. Completeness of Matrix Semantics

(3)

1.6. Properties of Logics

(5)

1.7. Boolean Logic

(7)

1.8. Some Notes on Computation and Complexity

(9)

Chapter 2. Fundamentals of Modal Logic I

(56)

2.1. Syntax of Modal Logics

(8)

2.2. Modal Algebras

(5)

2.3. Kripke-Frames and Frames

(5)

2.4. Frame Constructions I

(6)

2.5. Some Important Modal Logics

(4)

2.6. Decidability and Finite Model Property

(7)

2.7. Normal Forms

(8)

2.8. The Lindenbaum-Tarski Construction

(6)

2.9. The Lattices of Normal and Quasi-Normal Logics

(7)

Chapter 3. Fundamentals of Modal Logic II

103

(62)

3.1. Local and Global Consequence Relations

103

(6)

3.2. Completeness, Correspondence and Persistence

109

(7)

3.3. Frame Constructions II

116

(6)

3.4. Weakly Transitive Logics I

122

(2)

3.5. Subframe Logics

124

(7)

3.6. Constructive Reduction

131

(7)

3.7. Interpolation and Beth Theorems

138

(8)

3.8. Tableau Calculi and Interpolation

146

(10)

3.9. Modal Consequence Relations

156

(9)

Part 2. The General Theory of Modal Logic

165

(230)

Chapter 4. Universal Algebra and Duality Theory

167

(64)

4.1. More on Products

167

(8)

4.2. Varieties, Logics and Equationally Definable Classes

175

(6)

4.3. Weakly Transitive Logics II

181

(9)

4.4. Stone Representation and Duality

190

(8)

4.5. Adjoint Functors and Natural Transformations

198

(7)

4.6. Generalized Frames and Modal Duality Theory

205

(9)

4.7. Frame Constructions III

214

(6)

4.8. Free Algebras, Canonical Frames and Descriptive Frames

220

(5)

4.9. Algebraic Characterizations of Interpolation

225

(6)

Chapter 5. Definability and Correspondence

231

(44)

5.1. Motivation

231

(1)

5.2. The Languages of Description

232

(4)

5.3. Frame Correspondence -- An Example

236

(3)

5.4. The Basic Calculus of Internal Descriptions

239

(7)

5.5. Sahlqvist's Theorem

246

(6)

5.6. Elementary Sahlqvist Conditions

252

(6)

5.7. Preservation Classes

258

(8)

5.8. Some Results from Model Theory

266

(9)

Chapter 6. Reducing Polymodal Logic to Monomodal Logic

275

(56)

6.1. Interpretations and Simulations

275

(3)

6.2. Some Preliminary Results

278

(3)

6.3. The Fundamental Construction

281

(10)

6.4. A General Theorem for Consistency Reduction

291

(5)

6.5. More Preservation Results

296

(4)

6.6. Thomason Simulations

300

(10)

6.7. Properties of the Simulation

310

(12)

6.8. Simulation and Transfer -- Some Generalizations

322

(9)

Chapter 7. Lattices of Modal Logics

331

(64)

7.1. The Relevance of Studying Lattices of Logics

331

(2)

7.2. Splittings and other Lattice Concepts

333

(7)

7.3. Irreducible and Prime Logics

340

(7)

7.4. Duality Theory for Upper Continuous Lattices

347

(6)

7.5. Some Consequences of the Duality Theory

353

(9)

7.6. Properties of Logical Calculi and Related Lattice Properties

362

(6)

7.7. Splittings of the Lattices of Modal Logics and Completeness

368

(10)

7.8. Blok's Alternative

378

(6)

7.9. The Lattice of Tense Logics

384

(11)

Part 3. Case Studies

395

(140)

Chapter 8. Extensions of K4

397

(66)

8.1. The Global Structure of (Epsilon)K4

397

(5)

8.2. The Structure of Finitely Generated K4-Frames

402

(9)

8.3. The Selection Procedure

411

(4)

8.4. Refutation Patterns

415

(9)

8.5. Embeddability Patterns and the Elementarity of Logics

424

(6)

8.6. Logics of Finite Width I

430

(9)

8.7. Logics of Finite Width II

439

(11)

8.8. Bounded Properties and Precomplete Logics above S4

450

(6)

8.9. Logics of Finite Tightness

456

(7)

Chapter 9. Logics of Bounded Alternativity

463

(34)

9.1. The Logics Containing K.alt(1)

463

(5)

9.2. Polymodal Logics with Quasi-Functional Operators

468

(7)

9.3. Colourings and Decolourings

475

(7)

9.4. Decidability of Logics

482

(3)

9.5. Decidability of Properties of Logics I

485

(5)

9.6. Decidability of Properties of Logics II

490

(7)

Chapter 10. Dynamic Logic

497

(38)

10.1. PDL -- A Calculus of Compound Modalities

497

(2)

10.2. Axiomatizing PDL

499

(6)

10.3. The Finite Model Property

505

(3)

10.4. Regular Languages

508

(6)

10.5. An Evaluation Procedure

514

(9)

10.6. The Unanswered Question

523

(6)

10.7. The Logic of Finite Computations

529

(6)

Index

535

(14)

Bibliography

549


	Buy Textbooks Sell Textbooks College Apparel Shop by School Virtual Bookstores	Order Status Shipping Rates Return Policy Marketplace Info F.A.S.T.	Contact Us Privacy Policy Legal Notices Site Security Employment	Help Desk eCampus Blog Affiliate Program Bulk Orders College Marketing

Need Help? eService@ecampus.com Copyright© 1999-2008
.