Proceedings of the 7th & 8th Asian Logic Conferences : Hsi-Tou, Taiwan, 6-10 June 1999, Chongqing, China, 29 August-2 September 2002 / editors Rod Downey ... [et al.].

Format:

Book

Conference/Event

Contributor:

Downey, R. G. (Rod G.)

Conference Name:

Asian Logic Conference (7th : 1999 : Hsi-Tou, Taiwan)

Asian Logic Conference (8th : 2002 : Chongqing, China)

Language:

English

Subjects (All):

Logic, Symbolic and mathematical--Congresses.

Logic, Symbolic and mathematical.

Mathematics--Congresses.

Mathematics.

Physical Description:

1 online resource (481 p.)

Place of Publication:

River Edge ; London : World Scientific, c2003.

Language Note:

English

Summary:

The 7th and the 8th Asian Logic Conferences belong to the series of logic conferences inaugurated in Singapore in 1981. This meeting is held once every three years and rotates among countries in the Asia-Pacific region, with interests in the broad area of logic, including theoretical computer science. It is now considered a major conference in this field and is regularly sponsored by the Association for Symbolic Logic.This book contains papers - many of them surveys by leading experts - of both the 7th meeting (in Hsi-Tou, Taiwan) and the 8th (in Chongqing, China). The volume planned for the 7

Contents:

CONTENTS; Elementary Properties of Rogers Semilattices of Arithmetical Numberings S. A . Badaev, S. S. Goncharov and A. Sorbi; 1. Preliminaries and Background; 1.1. Cardinality, Lattice Properties, Undecidability; 1.2. Extremal Elements; 1.3. The Weak Distributivity Property; 2. The Main Result; References; Five Puzzles about Mathematics in Search of Solutions C. S. Chihara; I. The Five Puzzles; [l] A puzzle about geometry; [2] The inertness of mathematical objects; [3] Consistency and mathematical existence

[4] Different attitudes of practicing mathematicians regarding the ontology of mathematics[5] The van Inwagen Puzzle; II. Analysis and Explanation; The van Inwagen puzzle; Structures; The fourth puzzle; The third puzzle; An example; The second puzzle; The first puzzle; Bibliography; Complexity Classes over the Reals: A Logician's Viewpoint F. Cucker; 1. Introduction; 2. Machines and complexity classes over the reals; 3. Descriptive complexity over R; 3.1. Logics on lR-structures; 3.2. First-order logic; 3.3. Fixed point first-order logic; 3.4. Complexity classes beyond PR

3.5. A fixed point rule for DSOm4. Implicit Complexity over R; 4.1. Safe recursive functions; 4.2. Safe recursion with substitution; References; Computability, Definability and Algebraic Structures R. Downey; 1. Introduction; 2. Presentations; 3. Degrees of Isomorphism Types; 4. Jump Degrees and a Question on Torsion Free Groups; 5. Every Set Has a Least Jump Enumeration; 6. Computably Enumerable Reals; 7. Epilog: What are good questions in computable mat hemat ics?; References; Trivial Reals R. G. Downey, D. R. Hirschfeldt, A. Nies and F. Stephan; 1. Introduction; 2. Basic Definitions

3. A short proof of Solovay's theorem4. Turing degrees of H-trivials; 5. Listing the H-trivials; 6. Theorems of Chaitin and of Zambella; 7. Triviality and wtt-reducibility; Acknowledgments; References; Popper and Miller, and Induction and Deduction E. Eells; 1. The Popper-Miller Argument; 2. "Parts" of h; 3. "Components" of Support; 4. Inductive Assessments; 5. Conclusion; REFERENCES; Enlargements of Polynomial Coalgebras R. Goldblatt; 1. Introduction and Overview; 2. Essential Background; 2.1. Polynomial Functors and Coalgebras; 2.2. Paths and Bisinzulations; 2.3. Types, Terms, and Formulas

2.4. Semantics of Terms and Formulas2.5. The Role of Observable Formulas; 2.6. Defining Path Action and Bisimilarity; 3. Ultrafilter Enlargements; 4. The Proof of Theorem 3.2; 5. Definable Enlargements; 6. Monads From Enlargements; The Definable Case; References; A Layered Approach to Extracting Programs from Proofs with an Application in Graph Theory J. Jeavons, B. Basit, I. Poernomo and J. N. Crossley; Abstract; 1. Introduction; 2. The Logical Type Theory (LTT); 2.1. New induction rules; 2.2. New predicates and functions; 3. The Computational Type Theory (CTT)

3.1. Protocol between the CTT and the LTT

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

1-281-90881-9

9786611908812

981-270-581-3