Realizability

• Author : Jaap van Oosten
• Publisher : Elsevier
• Release : 10 April 2008

Aimed at starting researchers in the field, Realizability gives a rigorous, yet reasonable introduction to the basic concepts of a field which has passed several successive phases of abstraction. Material from previously unpublished sources such as Ph.D. theses, unpublished papers, etc. has been molded into one comprehensive presentation of the subject area. - The first book to date on this subject area - Provides an clear introduction to Realizability with a comprehensive bibliography - Easy to read and mathematically

• Author : T.V. Gopal,Gerhard Jäger,Silvia Steila
• Publisher : Springer
• Release : 13 April 2017

This book constitutes the refereed proceedings of the 14th Annual Conference on Theory and Applications of Models of Computation, TAMC 2017, held in Bern, Switzerland, in April 2017. The 45 revised full papers presented together with 4 invited papers were carefully reviewed and selected from 103 submissions. The main themes of TAMC 2017 have been computability, computer science logic, complexity, algorithms, and models of computation and systems theory.

• Author : Claudia Casadio,Philip J. Scott
• Publisher : Springer Nature
• Release : 21 April 2021

This book is dedicated to the life and work of the mathematician Joachim Lambek (1922–2014). The editors gather together noted experts to discuss the state of the art of various of Lambek’s works in logic, category theory, and linguistics and to celebrate his contributions to those areas over the course of his multifaceted career. After early work in combinatorics and elementary number theory, Lambek became a distinguished algebraist (notably in ring theory). In the 1960s, he began to work in

• Author : Gianluigi Oliveri,Claudio Ternullo,Stefano Boscolo
• Publisher : Springer Nature
• Release : 08 March 2022

This edited collection casts light on central issues within contemporary philosophy of mathematics such as the realism/anti-realism dispute; the relationship between logic and metaphysics; and the question of whether mathematics is a science of objects or structures. The discussions offered in the papers involve an in-depth investigation of, among other things, the notions of mathematical truth, proof, and grounding; and, often, a special emphasis is placed on considerations relating to mathematical practice. A distinguishing feature of the book is

• Author : Dieter Probst,Peter Schuster
• Publisher : Walter de Gruyter GmbH & Co KG
• Release : 25 July 2016

A proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive science. Proofs thus are utterly relevant for research, teaching and communication in mathematics and of particular interest for the philosophy of mathematics. In computer science, moreover, proofs have proved to

• Author : Hector Zenil
• Publisher : World Scientific
• Release : 30 May 2023

This volume, with a foreword by Sir Roger Penrose, discusses the foundations of computation in relation to nature.It focuses on two main questions: What is computation? How does nature compute?The contributors are world-renowned experts who have helped shape a cutting-edge computational understanding of the universe. They discuss computation in the world from a variety of perspectives, ranging from foundational concepts to pragmatic models to ontological conceptions and philosophical implications.The volume provides a state-of-the-art collection of technical papers

• Author : Hector Zenil
• Publisher : World Scientific
• Release : 30 October 2012

This volume, with a Foreword writer Sir Roger Penrose, discusses the foundations of computation in relation to nature. It focuses on two main questions: What is computation?How does nature compute? The contributors are world-renowned experts who have helped shape a cutting-edge computational understanding of the universe. They discuss computation in the world from a variety of perspectives, ranging from foundational concepts to pragmatic models to ontological conceptions and philosophical implications. The volume provides a state-of-the-art collection of technical papers

• Author : Douglas Bridges,Hajime Ishihara,Michael Rathjen,Helmut Schwichtenberg
• Publisher : Cambridge University Press
• Release : 31 March 2023

Gives a complete overview of modern constructive mathematics and its applications through surveys by leading experts.

• Author : Cyrus F. Nourani
• Publisher : CRC Press
• Release : 24 February 2016

This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples for languages. Functorial models for Peano arithmetic are described toward important computational complexity areas on a Hilbert program, leading to computability with initial models. Infinite language categories are also introduced to explain descriptive complexity

• Author : Ulrich Berger,Johanna N. Y. Franklin,Florin Manea,Arno Pauly
• Publisher : Springer Nature
• Release : 25 June 2022

This book constitutes the proceedings of the 18th Conference on Computability in Europe, CiE 2022, in Swansea, UK, in July 2022. The 19 full papers together with 7 invited papers presented in this volume were carefully reviewed and selected from 41 submissions. The motto of CiE 2022 was “Revolutions and revelations in computability”. This alludes to the revolutionary developments we have seen in computability theory, starting with Turing's and Gödel's discoveries of the uncomputable and the unprovable and continuing to the present day with the

• Author : T-H. Hubert Chan,Lap Chi Lau,Luca Trevisan
• Publisher : Springer
• Release : 15 April 2013

This book constitutes the refereed proceedings of the 10th International Conference on Theory and Applications of Models of Computation, TAMC 2013, held in Hong Kong, China, in May 2013. The 31 revised full papers presented were carefully reviewed and selected from 70 submissions. Bringing together a wide range of researchers with interests in computational theory and applications, the papers address the three main themes of the conference which were computability, complexity, and algorithms and present current research in these fields with aspects to theoretical

• Author : Alexandra Silva,Renata Wassermann,Ruy de Queiroz
• Publisher : Springer Nature
• Release : 05 October 2021

Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 27th Workshop on Logic, Language, Information and Communication, WoLLIC 2021, Virtual Event, in October 2021. The 25 full papers presented included 6 invited lectures were fully reviewed and selected from 50 submissions. The idea is to have a forum which is large enough in the number of possible interactions between logic and the sciences related to information and computation.

• Author : Javier Esparza,Andrzej S. Murawski
• Publisher : Springer
• Release : 15 March 2017

This book constitutes the proceedings of the 20th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2017, which took place in Uppsala, Sweden in April 2017, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017. The 32 papers presented in this volume were carefully reviewed and selected from 101 submissions. They were organized in topical sections named: coherence spaces and higher-order computation; algebra and coalgebra; games and automata; automata, logic and formal languages; proof theory;

• Author : John Longley,Dag Normann
• Publisher : Springer
• Release : 06 November 2015

This book offers a self-contained exposition of the theory of computability in a higher-order context, where 'computable operations' may themselves be passed as arguments to other computable operations. The subject originated in the 1950s with the work of Kleene, Kreisel and others, and has since expanded in many different directions under the influence of workers from both mathematical logic and computer science. The ideas of higher-order computability have proved valuable both for elucidating the constructive content of logical systems, and

• Author : Sergei Artemov,Anil Nerode
• Publisher : Springer
• Release : 22 December 2017

This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2018, held in Deerfield Beach, FL, USA, in January 2018. The 22 revised full papers were carefully reviewed and selected from 22 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive