Martin Davis on Computability, Computational Logic, and Mathematical Foundations

✍ Scribed by Eugenio G. Omodeo, Alberto Policriti (eds.)

• Publisher: Springer International Publishing
• Year: 2016
• Tongue: English
• Leaves: 454
• Series: Outstanding Contributions to Logic 10
• Edition: 1
• Category: Library

✦ Synopsis

This book presents a set of historical recollections on the work of Martin Davis and his role in advancing our understanding of the connections between logic, computing, and unsolvability. The individual contributions touch on most of the core aspects of Davis’ work and set it in a contemporary context. They analyse, discuss and develop many of the ideas and concepts that Davis put forward, including such issues as contemporary satisfiability solvers, essential unification, quantum computing and generalisations of Hilbert’s tenth problem.

The book starts out with a scientific autobiography by Davis, and ends with his responses to comments included in the contributions. In addition, it includes two previously unpublished original historical papers in which Davis and Putnam investigate the decidable and the undecidable side of Logic, as well as a full bibliography of Davis’ work. As a whole, this book shows how Davis’ scientific work lies at the intersection of computability, theoretical computer science, foundations of mathematics, and philosophy, and draws its unifying vision from his deep involvement in Logic.

✦ Table of Contents

Front Matter....Pages i-xxvii
My Life as a Logician....Pages 1-33
Martin Davis and Hilbert’s Tenth Problem....Pages 35-54
Extensions of Hilbert’s Tenth Problem: Definability and Decidability in Number Theory....Pages 55-92
A Story of Hilbert’s Tenth Problem....Pages 93-105
Hyperarithmetical Sets....Pages 107-149
Honest Computability and Complexity....Pages 151-173
Why Post Did [Not] Have Turing’s Thesis....Pages 175-208
On Quantum Computation, Anyons, and Categories....Pages 209-241
Taking Physical Infinity Seriously....Pages 243-254
Banishing Ultrafilters from Our Consciousness....Pages 255-283
What Is Essential Unification?....Pages 285-314
DPLL: The Core of Modern Satisfiability Solvers....Pages 315-335
On Davis’s “Pragmatic Platonism”....Pages 337-347
Pragmatic Platonism....Pages 349-356
Concluding Comments by Martin....Pages 357-362
Martin Davis’s Bibliography 1950–2015....Pages 363-370
Back Matter....Pages 371-438

✦ Subjects

Logic;Mathematical Logic and Foundations