Mathematical Problems from Applied Logic II

by Gabbay, Dov M.; Goncharov, Sergei S.; Zakharyaschev, Michael

• ISBN13: 9780387692449
• ISBN10: 0387692444
• Format: Hardcover
• Copyright: 2007-03-30
• Publisher: Springer Verlag

Summary

"Mathematical Problems from Applied Logic II" presents chapters from selected, world renowned, logicians. Important topics of logic are discussed from the point of view of their further development in light of requirements arising from their successful application in areas such as Computer Science and AI language. Fields covered include: logic of provability, applications of computability theory to biology, psychology, physics, chemistry, economics, and other basic sciences; computability theory and computable models; logic and space-time geometry; hybrid systems; logic and region-based theory of space. Contributors include: Sergei Artemov, USA; John Case, USA; Sergei Goncharov, Russia, Judit X. Madaràsz, Istvàn Nèmeti, and Gergely, Szèkely, Hungary, Anil Nerode, USA and Dimiter Vakarelov, Bulgaria.

Table of Contents

On Two Models of Provability

Provability Logic, Logic of Proofs

Directions for Computability Theory Beyond Pure Mathematical

Motivations, Directions, Progress So Far

And How One Might Go From Here

Computability and Computable Models

Preliminaries

Bounds for Computable Models

Structure Complexity of Computable Models

Isomorphism Problem, Classes of Computable Models and Index Sets

First-order Logic Foundation of Relativity Theories

Introduction (Logic and Spacetime Geometry)

More Concrete Introduction (Foundation of Spacetime)

Intriguing Features of GR Spacetimes (Challenges for the Logician)

A FOL Axiom System of SR Extended with Accelerated Observers

One Step toward GR (Effect of Gravitation on Clocks)

Questions, Suggestions for Future Research

Beyond Hybrid Systems

Digital Programs

Continuous Plants and Controllers

Hybrid Systems

Discretization

Continualization

Methodology

Region-Based Theory of Space

Algebras of Regions

Representation Theory, and Logics

Historical Excursion in the Region-Based Theory of Space

Algebras of Regions

Models, and Representation Theory

Region-Based Propositional Modal Logics of Space

Table of Contents provided by Publisher. All Rights Reserved.