May 2002, ISBN 1-4020-0604-7, Hardbound
Book Series: TRENDS IN LOGIC : Volume 12
Godel's modal ontological argument is the centrepiece of an extensive examination of intensional logic. First, classical type theory is presented semantically, tableau rules for it are introduced, and the Prawitz/Takahashi completeness proof is given. Then modal machinery is added, semantically and through tableau rules, to produce a modified version of Montague/Gallin intensional logic. Extensionality, rigidity, equality, identity, and definite descriptions are investigated. Finally, various ontological proofs for the existence of God are discussed informally, and the Godel argument is fully formalized. Objections to the Godel argument are examined, including one due to Howard Sobel showing Godel's assumptions are so strong that the modal logic collapses. It is shown that this argument depends critically on whether properties are understood intensionally or extensionally.
Parts of the book are mathematical, parts philosophical. A reader interested in (modal) type theory can safely skip ontological issues, just as one interested in Godel's argument can omit the more mathematical portions, such as the completeness proof for tableaus. There should be something for everybody (and perhaps everything for somebody).
Contents
Preface. Part I: Classical Logic. 1. Classical
Logic - Syntax. 2.
Classical Logic - Semantics. 3. Classical
Logic - Basic Tableaus.
4. Soundness and Completeness. 5. Equality.
6. Extensionality.
Part II: Modal Logic. 7. Modal Logic, Syntax
and Semantics. 8.
Modal Tableaus. 9. Miscellaneous Matters.
Part III: Ontological
Arguments. 10. Godel's Argument, Background.
11. Godel's
Argument, Formally. References. Index.
May 2002, ISBN 1-4020-0583-0, Hardbound
Book Series: HANDBOOK OF PHILOSOPHICAL LOGIC, *SECOND EDITION* : Volume 6
The sixth volume of the Handbook of Philosophical Logic, Second Edition contains major contributions on Relevance Logic, Quantum Logics, Combinators, Proofs and Implicational Logics and Paraconsistent Logic.
Audience: Students and researchers whose work or interests involve philosophical logic and its applications.
Contents and Contributors
Editorial Preface; D.M. Gabbay. Relevance Logic; M. Dunn, G. Restall. Quantum Logics; M.-L.D. Chiara, R. Giuntini. Combinators, Proofs and Implicational Logics; M. Bunder. Paraconsistent Logic; G. Priest. Index.
May 2002, ISBN 1-4020-0599-7, Hardbound
Book Series: HANDBOOK OF PHILOSOPHICAL LOGIC, *SECOND EDITION* : Volume 7
The seventh volume of the Second Edition contains major contributions on Basic Tense Logic, Advanced Tense Logic, Combinations of Tense and Modality, Philosophical Perspectives on Quantification in Tense and Modal Logic as well as Tense and Time.
Audience: Students and researchers whose work or interests involve philosophical logic and its applications.
Contents and Contributors
Editorial Preface; D.M. Gabbay. Basic Tense Logic; J.P. Burgess. Advanced Tense Logic; M. Finger, et al. Combinations of Tense and Modality; R.H. Thomason. Philosophical Perspectives on Quantification in Tense and Modal Logic; N.B. Cocchiarella. Tense and Time; S.T. Kuhn, P. Portner. Index.
June 2002, ISBN 1-4020-0665-9, Hardbound
Book Series: HANDBOOK OF PHILOSOPHICAL LOGIC, *SECOND EDITION* : Volume 8
The eighth volume of the Second Edition contains major contributions on the Logic of Questions, Sequent Systems for Modal Logics, Deontic Logic as well as Deontic Logic and Contrary-to-duties.
Audience: Students and researchers whose work or interests involve philosophical logic and its applications.
Contents and Contributors
Editorial Preface; D.M. Gabbay. The Logic
of Questions; D.
Harrah. Sequent Systems for Modal Logics;
H. Wansing. Deontic
Logic; L. Aqvist. Deontic Logic and Contrary-to-Dutiesl
J. Carmo,
A. Jones. Index.
September 2002, ISBN 1-4020-0699-3, Hardbound
Book Series: HANDBOOK OF PHILOSOPHICAL LOGIC, *SECOND EDITION* : Volume 9
The ninth volume of the Second Edition contains major contributions on Rewriting Logic as a Logical and Semantic Framework, Logical Frameworks, Proof Theory and Meaning, Goal Directed Deductions, Negations, Completeness and Consistency as well as Logic as General Rationality.
Audience: Students and researchers whose work or interests involve philosophical logic and its applications.
Contents and Contributors
Editorial Preface; D.M. Gabbay. Rewriting
Logic as a Logical
and Semantic Framework; N. Marti-Oliet, J.
Meseguer. Logical
Frameworks; D. Basin, S. Matthews. Proof
Theory and Meaning; G.
Sundholm. Goal Driected Deductions; D.M.
Gabbay, N. Olivetti. On
Negation, Completeness and Consistency; A.
Avron. Logic as
General Rationality: A Survey; T. Sales.
Index.
September 2002, ISBN 1-4020-0852-X, Hardbound
Book Series: KLUWER TEXTS IN THE MATHEMATICAL SCIENCES : Volume 24
Introduction to Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear programming, and nonlinear optimization are closely linked. This book offers a comprehensive introduction to the whole subject and leads the reader to the frontiers of current research. The prerequisites to use the book are very elementary. All the tools from numerical linear algebra and calculus are fully reviewed and developed. Rather than attempting to be encyclopedic, the book illustrates the important basic techniques with typical problems. The focus is on efficient algorithms with respect to practical usefulness. Algorithmic complexity theory is presented with the goal of helping the reader understand the concepts without having to become a theoretical specialist. Further theory is outlined and supplemented with pointers to the relevant literature.
The book is equally suited for self-study for a motivated beginner and for a comprehensive course on the principles of mathematical programming within an applied mathematics or computer science curriculum at advanced undergraduate or graduate level. The presentation of the material is such that smaller modules on discrete optimization, linear programming, and nonlinear optimization can easily be extracted separately and used for shorter specialized courses on these subjects.
Contents
Introduction. 1. Real Vector Spaces. 2. Linear
Equations and
Linear Inequalities. 3. Polyhedra. 4. Linear
Programs and the
Simplex Method. 5. Lagrangian Duality. 6.
An Interior Point
Algorithm for Linear Programs. 7. Network
Flows. 8. Complexity. 9.
Integer Programming. 10. Convex Sets and
Convex Functions. 11.
Unconstrained Optimization. 12. Constrained
Nonlinear
Optimization. List of frequently used Symbols.
Bibliography.
Index.