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Author: M.J. Beeson
Publisher: Springer Science & Business Media
ISBN: 3642689523
Category : Mathematics
Languages : en
Pages : 484
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Book Description
This book is about some recent work in a subject usually considered part of "logic" and the" foundations of mathematics", but also having close connec tions with philosophy and computer science. Namely, the creation and study of "formal systems for constructive mathematics". The general organization of the book is described in the" User's Manual" which follows this introduction, and the contents of the book are described in more detail in the introductions to Part One, Part Two, Part Three, and Part Four. This introduction has a different purpose; it is intended to provide the reader with a general view of the subject. This requires, to begin with, an elucidation of both the concepts mentioned in the phrase, "formal systems for constructive mathematics". "Con structive mathematics" refers to mathematics in which, when you prove that l a thing exists (having certain desired properties) you show how to find it. Proof by contradiction is the most common way of proving something exists without showing how to find it - one assumes that nothing exists with the desired properties, and derives a contradiction. It was only in the last two decades of the nineteenth century that mathematicians began to exploit this method of proof in ways that nobody had previously done; that was partly made possible by the creation and development of set theory by Georg Cantor and Richard Dedekind.
Author: M.J. Beeson
Publisher: Springer Science & Business Media
ISBN: 3642689523
Category : Mathematics
Languages : en
Pages : 484
Get Book Here
Book Description
This book is about some recent work in a subject usually considered part of "logic" and the" foundations of mathematics", but also having close connec tions with philosophy and computer science. Namely, the creation and study of "formal systems for constructive mathematics". The general organization of the book is described in the" User's Manual" which follows this introduction, and the contents of the book are described in more detail in the introductions to Part One, Part Two, Part Three, and Part Four. This introduction has a different purpose; it is intended to provide the reader with a general view of the subject. This requires, to begin with, an elucidation of both the concepts mentioned in the phrase, "formal systems for constructive mathematics". "Con structive mathematics" refers to mathematics in which, when you prove that l a thing exists (having certain desired properties) you show how to find it. Proof by contradiction is the most common way of proving something exists without showing how to find it - one assumes that nothing exists with the desired properties, and derives a contradiction. It was only in the last two decades of the nineteenth century that mathematicians began to exploit this method of proof in ways that nobody had previously done; that was partly made possible by the creation and development of set theory by Georg Cantor and Richard Dedekind.
Author:
Publisher: Springer Nature
ISBN: 1461585880
Category :
Languages : en
Pages : 133
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Book Description
Author: V. M. Kalinin
Publisher: Springer Science & Business Media
ISBN: 1468482114
Category : Science
Languages : en
Pages : 149
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Book Description
Author: A. O. Slisenko
Publisher: Springer
ISBN: 9781489953292
Category : Science
Languages : en
Pages : 136
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Book Description
Author: Steven Rudich, Avi Wigderson
Publisher: American Mathematical Soc.
ISBN: 9780821886922
Category : Computational complexity
Languages : en
Pages : 410
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Book Description
Computational Complexity Theory is the study of how much of a given resource is required to perform the computations that interest us the most. Four decades of fruitful research have produced a rich and subtle theory of the relationship between different resource measures and problems. At the core of the theory are some of the most alluring open problems in mathematics. This book presents three weeks of lectures from the IAS/Park City Mathematics Institute Summer School on computational complexity. The first week gives a general introduction to the field, including descriptions of the basic mo.
Author: Ivo Düntsch
Publisher: Springer Nature
ISBN: 3030714306
Category : Philosophy
Languages : en
Pages : 591
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Book Description
This book is dedicated to the work of Alasdair Urquhart. The book starts out with an introduction to and an overview of Urquhart’s work, and an autobiographical essay by Urquhart. This introductory section is followed by papers on algebraic logic and lattice theory, papers on the complexity of proofs, and papers on philosophical logic and history of logic. The final section of the book contains a response to the papers by Urquhart. Alasdair Urquhart has made extremely important contributions to a variety of fields in logic. He produced some of the earliest work on the semantics of relevant logic. He provided the undecidability of the logics R (of relevant implication) and E (of relevant entailment), as well as some of their close neighbors. He proved that interpolation fails in some of those systems. Urquhart has done very important work in complexity theory, both about the complexity of proofs in classical and some nonclassical logics. In pure algebra, he has produced a representation theorem for lattices and some rather beautiful duality theorems. In addition, he has done important work in the history of logic, especially on Bertrand Russell, including editing Volume four of Russell’s Collected Papers.
Author: Ian Gent
Publisher:
ISBN: 9784274903632
Category : Computer algorithms
Languages : en
Pages : 568
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Book Description
Author: Ricardo Reis
Publisher: Springer Science & Business Media
ISBN: 0387895574
Category : Computers
Languages : en
Pages : 315
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Book Description
This book contains extended and revised versions of the best papers that were presented during the fifteenth edition of the IFIP/IEEE WG10.5 International Conference on Very Large Scale Integration, a global System-on-a-Chip Design & CAD conference. The 15th conference was held at the Georgia Institute of Technology, Atlanta, USA (October 15-17, 2007). Previous conferences have taken place in Edinburgh, Trondheim, Vancouver, Munich, Grenoble, Tokyo, Gramado, Lisbon, Montpellier, Darmstadt, Perth and Nice. The purpose of this conference, sponsored by IFIP TC 10 Working Group 10.5 and by the IEEE Council on Electronic Design Automation (CEDA), is to provide a forum to exchange ideas and show industrial and academic research results in the field of microelectronics design. The current trend toward increasing chip integration and technology process advancements brings about stimulating new challenges both at the physical and system-design levels, as well in the test of these systems. VLSI-SoC conferences aim to address these exciting new issues.
Author: Hartmut Ehrig
Publisher: Springer
ISBN: 3642159281
Category : Computers
Languages : en
Pages : 431
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Book Description
Graphs are among the simplest and most universal models for a variety of s- tems, not just in computer science, but throughout engineering and the life sciences. When systems evolve we are interested in the way they change, to p- dict, support, or react to their evolution. Graph transformation combines the idea of graphs as a universal modelling paradigm with a rule-based approach to specify their evolution. The area is concerned with both the theory of graph transformation and their application to a variety of domains. The biannual International Conferences on Graph Transformation aim at bringingtogetherresearchersandpractitionersinterestedin the foundations and applicationsof graphtransformation.The ?fth conference,ICGT 2010,was held at the University of Twente (The Netherlands) in September/October 2010, alongwith severalsatellite events.It continuedthe line ofconferences previously held in Barcelona (Spain) in 2002, Rome (Italy) 2004, Natal (Brazil) in 2006 and Leicester (UK) in 2008, as well as a series of six International Workshops on Graph Transformation with Applications in Computer Science from 1978 to 1998. Also, ICGT alternates with the workshop series on Application of Graph Transformation with Industrial Relevance (AGTIVE). The conference was held under the auspices of EATCS and EASST.
Author: Dhiraj K. Pradhan
Publisher: Cambridge University Press
ISBN: 1139478303
Category : Computers
Languages : en
Pages : 277
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Book Description
Improve design efficiency and reduce costs with this practical guide to formal and simulation-based functional verification. Giving you a theoretical and practical understanding of the key issues involved, expert authors including Wayne Wolf and Dan Gajski explain both formal techniques (model checking, equivalence checking) and simulation-based techniques (coverage metrics, test generation). You get insights into practical issues including hardware verification languages (HVLs) and system-level debugging. The foundations of formal and simulation-based techniques are covered too, as are more recent research advances including transaction-level modeling and assertion-based verification, plus the theoretical underpinnings of verification, including the use of decision diagrams and Boolean satisfiability (SAT).
