Concepts of proof in mathematics, philosophy, and computer science

In the last decades, mathematical logic has developed into a technically quite sophisticated area of mathematics. Nevertheless, inspirations from philosophy and computer science continue to be important and noticeable. The series publishes conference proceedings as well as monographs written by lead...

Full description

Saved in:
Bibliographic Details
Main Authors Probst, Dieter, Schuster, Peter
Format eBook Book
LanguageEnglish
Published Berlin De Gruyter 2016
Walter de Gruyter GmbH
Edition1
SeriesOntos Mathematical Logic
Subjects
Logic, Symbolic and mathematical
Mathematical Logic
Mathematics
Mathematische Logik
Philosophie der Mathematik
PHILOSOPHY / Epistemology
Philosophy of Mathematics
Proof theory
Theoretical Computer Science
Theoretische Informatik
Theoretical Computer Science
Mathematical Logic
Philosophy of Mathematics
Online AccessGet full text

Cover

Abstract In the last decades, mathematical logic has developed into a technically quite sophisticated area of mathematics. Nevertheless, inspirations from philosophy and computer science continue to be important and noticeable. The series publishes conference proceedings as well as monographs written by leading researchers in mathematical logic.
AbstractList This book provides the reader with research arising from the Humboldt-Kolleg 'Proof' held in Bern in fall 2013, which gathered more than sixty leading experts actively involved with the concept 'proof' in philosophy, mathematics and computer science. This volume aims to do justice to the breadth and depth of the subject and presents relevant current conceptions and technical advances featuring 'proof' in the fields mentioned above.
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 be a rich source for already certified algorithms. This book provides the reader with a collection of articles covering relevant current research topics circled around the concept 'proof'. It tries to give due consideration to the depth and breadth of the subject by discussing its philosophical and methodological aspects, addressing foundational issues induced by Hilbert's Programme and the benefits of the arising formal notions of proof, without neglecting reasoning in natural language proofs and applications in computer science such as program extraction.
In the last decades, mathematical logic has developed into a technically quite sophisticated area of mathematics. Nevertheless, inspirations from philosophy and computer science continue to be important and noticeable. The series publishes conference proceedings as well as monographs written by leading researchers in mathematical logic.
Author Probst, Dieter
Schuster, Peter
Author_xml – sequence: 1
  fullname: Probst, Dieter
– sequence: 2
  fullname: Schuster, Peter
BackLink https://cir.nii.ac.jp/crid/1130282271154978176$$DView record in CiNii
BookMark eNqNkd9LwzAQxyM6cZt79L0PgghOc2nSpI-uzB8w8EV8LWl6dXVdU5vOsf_ebBNUfBHCNznyuW_uLgNyVNsaCTkDeg0CxE0sFQjqF4sYPSCjX_EhGewCoIrSHhkwChENKZPRMenHQgGjgosTMnLujVIK0l8q0SeTxNYGm84Ftgia1not62Cpuzl6KY27Cpp5WVlnm_nmKtB1Hhi7bFYdtoEzJfrkU9IrdOVw9LUPycvd9Dl5GM-e7h-T29lYcxHyeFyoLBcoochykHEORjEDseA5moxFMYaa6zADqg0yjSxTqCQqWmiIRMTjPBySy72xdgtcu7mtOpd-VJhZu3Dpj3Fw_n-W0W92rSvfV46v7WrjD-lSt-YPe7Fn_azeV-i6dGdpsO5aXaXTScL980JtKzjfk3VZpqbcKoD_EcWYBBB86yuj8BMW5IdL
ContentType eBook
Book
Contributor Plato, Jan von
Ishihara, Hajime
Afshari, Bahareh
Pohlers, Wolfram
Rathjen, Michael
Coquand, Thierry
Strahm, Thomas
Nemoto, Takako
Leigh, Graham E
Kuznets, Roman
Rosolini, Giuseppe
Studer, Thomas
Lombardi, Henri
Negri, Sara
Benini, Marco
Maietti, Maria Emilia
Buchholtz, Ulrik
Lapenta, Serafina
Došen, Kosta
Berger, Ulrich
Schuster, Peter
Miyamoto, Kenji
Hetzl, Stefan
Kokkinis, Ioannis
Murawski, Roman
Tsuiki, Hideki
Bridges, Douglas S
Jäger, Gerhard
Probst, Dieter
Schwichtenberg, Helmut
Leuştean, Ioana
Contributor_xml – sequence: 1
  fullname: Afshari, Bahareh
– sequence: 2
  fullname: Benini, Marco
– sequence: 3
  fullname: Berger, Ulrich
– sequence: 4
  fullname: Bridges, Douglas S
– sequence: 5
  fullname: Buchholtz, Ulrik
– sequence: 6
  fullname: Coquand, Thierry
– sequence: 7
  fullname: Došen, Kosta
– sequence: 8
  fullname: Hetzl, Stefan
– sequence: 9
  fullname: Ishihara, Hajime
– sequence: 10
  fullname: Jäger, Gerhard
– sequence: 11
  fullname: Kokkinis, Ioannis
– sequence: 12
  fullname: Kuznets, Roman
– sequence: 13
  fullname: Lapenta, Serafina
– sequence: 14
  fullname: Leigh, Graham E
– sequence: 15
  fullname: Leuştean, Ioana
– sequence: 16
  fullname: Lombardi, Henri
– sequence: 17
  fullname: Maietti, Maria Emilia
– sequence: 18
  fullname: Miyamoto, Kenji
– sequence: 19
  fullname: Murawski, Roman
– sequence: 20
  fullname: Negri, Sara
– sequence: 21
  fullname: Nemoto, Takako
– sequence: 22
  fullname: Plato, Jan von
– sequence: 23
  fullname: Pohlers, Wolfram
– sequence: 24
  fullname: Probst, Dieter
– sequence: 25
  fullname: Rathjen, Michael
– sequence: 26
  fullname: Rosolini, Giuseppe
– sequence: 27
  fullname: Schuster, Peter
– sequence: 28
  fullname: Schwichtenberg, Helmut
– sequence: 29
  fullname: Strahm, Thomas
– sequence: 30
  fullname: Studer, Thomas
– sequence: 31
  fullname: Tsuiki, Hideki
DBID RYH
DEWEY 511.36
DOI 10.1515/9781501502620
DatabaseName CiNii Complete
DatabaseTitleList



DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISBN 9781501502620
150150262X
9781501502644
1501502646
Edition 1
Editor Probst, Dieter
Schuster, Peter
Editor_xml – sequence: 1
  fullname: Probst, Dieter
– sequence: 2
  fullname: Schuster, Peter
ExternalDocumentID 9781501502644
9781501502620
EBC4644584
BB22815155
GroupedDBID -VX
20A
38.
AABBV
AANXU
AAUSU
AAVCP
AAZEP
ABARN
ABAWK
ABHWV
ABMRC
ABONK
ABQPQ
ACBCG
ACEOQ
ACEOT
ACISH
ACLGV
ADDXO
ADVEM
ADVQQ
AEAED
AEDVL
AEQUH
AERYV
AETUO
AFHFQ
AFRFP
AGLJD
AHPFH
AIBWD
AIOLA
AIUUY
AIXPE
AJFER
AJWNA
ALMA_UNASSIGNED_HOLDINGS
APFVE
ARPAB
AUXLQ
AZVGL
AZZ
BBABE
BECJT
BFRBX
BKKPX
CZZ
DUGUG
EBSCA
ECOWB
FIECY
MTCAI
PQQKQ
QD8
RYH
XI1
AGIZT
AIADE
AMYDA
I4C
DLQEV
ID FETCH-LOGICAL-a45349-f8bd5e71fbd179d1c82c1954decb269e3a4a3b10ace2ae2b8e87e80fa165649d3
ISBN 1501510800
9781501510809
IngestDate Tue Jan 14 03:44:27 EST 2025
Fri Nov 08 05:51:21 EST 2024
Thu Aug 14 17:00:59 EDT 2025
Wed Sep 03 01:35:47 EDT 2025
Thu Jun 26 23:15:26 EDT 2025
IsPeerReviewed false
IsScholarly false
Keywords Theoretical Computer Science
Mathematical Logic
Philosophy of Mathematics
LCCN 2016030276
LCCallNum_Ident QA9.54.C663 2016eb
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-a45349-f8bd5e71fbd179d1c82c1954decb269e3a4a3b10ace2ae2b8e87e80fa165649d3
Notes Includes bibliographical references
OCLC 958120545
956701728
PQID EBC4644584
PageCount 384
ParticipantIDs askewsholts_vlebooks_9781501502644
askewsholts_vlebooks_9781501502620
walterdegruyter_marc_9781501502620
proquest_ebookcentral_EBC4644584
nii_cinii_1130282271154978176
PublicationCentury 2000
PublicationDate c2016
2016
[2016]
2016-07-25
PublicationDateYYYYMMDD 2016-01-01
2016-07-25
PublicationDate_xml – year: 2016
  text: c2016
PublicationDecade 2010
PublicationPlace Berlin
PublicationPlace_xml – name: Berlin
– name: Boston, MA
– name: Boston
PublicationSeriesTitle Ontos Mathematical Logic
PublicationYear 2016
Publisher De Gruyter
Walter de Gruyter GmbH
Publisher_xml – name: De Gruyter
– name: Walter de Gruyter GmbH
RestrictionsOnAccess restricted access
SSID ssj0001703085
ssj0003400787
ssib025968172
ssib026498228
Score 1.9841396
Snippet In the last decades, mathematical logic has developed into a technically quite sophisticated area of mathematics. Nevertheless, inspirations from philosophy...
A proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context...
This book provides the reader with research arising from the Humboldt-Kolleg 'Proof' held in Bern in fall 2013, which gathered more than sixty leading experts...
SourceID askewsholts
walterdegruyter
proquest
nii
SourceType Aggregation Database
Publisher
SubjectTerms Logic, Symbolic and mathematical
Mathematical Logic
Mathematics
Mathematische Logik
Philosophie der Mathematik
PHILOSOPHY / Epistemology
Philosophy of Mathematics
Proof theory
Theoretical Computer Science
Theoretische Informatik
TableOfContents Intro -- Contents -- Introduction -- Herbrand Confluence for First-Order Proofs with π 2-Cuts -- Proof-Oriented Categorical Semantics -- Logic for Gray-code Computation -- The Continuum Hypothesis Implies Excluded Middle -- Theories of Proof-Theoretic Strength -- Some Remarks about Normal Rings -- On Sets of Premises -- Non-Deterministic Inductive Definitions and Fullness -- Cyclic Proofs for Linear Temporal Logic -- Craig Interpolation via Hypersequents -- A General View on Normal Form Theorems for Lukasiewicz Logic with Product -- Relating Quotient Completions via Categorical Logic -- Some Historical, Philosophical and Methodological Remarks on Proof in Mathematics -- Cut Elimination in Sequent Calculi with Implicit Contraction, with a Conjecture on the Origin of Gentzen's Altitude Line Construction -- Hilbert's Programme and Ordinal Analysis -- Aristotle's Deductive Logic: a Proof-Theoretical Study -- Remarks on Barr's Theorem: Proofs in Geometric Theories
A General View on Normal Form Theorems for Łukasiewicz Logic with Product --
Some Historical, Philosophical and Methodological Remarks on Proof in Mathematics --
Proof-Oriented Categorical Semantics --
Theories of Proof-Theoretic Strength Ψ (ΓΩ +1) --
Contents --
On Sets of Premises --
Hilbert’s Programme and Ordinal Analysis --
Herbrand Confluence for First-Order Proofs with Π2-Cuts --
Preface --
Non-Deterministic Inductive Definitions and Fullness --
Some Remarks about Normal Rings --
Cut Elimination in Sequent Calculi with Implicit Contraction, with a Conjecture on the Origin of Gentzen’s Altitude Line Construction --
Cyclic Proofs for Linear Temporal Logic --
Aristotle’s Deductive Logic: a Proof-Theoretical Study --
Relating Quotient Completions via Categorical Logic --
Logic for Gray-code Computation --
Frontmatter --
Craig Interpolation via Hypersequents --
The Continuum Hypothesis Implies Excluded Middle --
Remarks on Barr’s Theorem: Proofs in Geometric Theories
Introduction --
Title Concepts of proof in mathematics, philosophy, and computer science
URI https://cir.nii.ac.jp/crid/1130282271154978176
https://ebookcentral.proquest.com/lib/[SITE_ID]/detail.action?docID=4644584
https://www.degruyter.com/isbn/9781501502620
https://www.vlebooks.com/vleweb/product/openreader?id=none&isbn=9781501502620&uid=none
https://www.vlebooks.com/vleweb/product/openreader?id=none&isbn=9781501502644
Volume 6
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3db9MwELe27mV9QMCGGDBkId62QOLYifPardOEVF4Y094if0I0SFE_QOOv5-zaSVtNGvBitdHZbv2z7s7O3e8QeksUlyRlJgHfwyRUSZ1IxmzCC2WJym2VKndQnHwsLj_TDzfspi-g5bNLFvKd-n1vXsn_oArPAFeXJfsPyHaDwgP4DPhCCwhDu-X8dl8Dp8Aq2dCHYYAK9LQPJ987BlaPzY9YpOAuRmiqUMHhJJi9Ti3OpnKV-nHerIfrflJfl7FwRx_HG64Isu0rgnPYb7PlXRSLh0dwBcHcg8dY3atKmWediHKpI67vbUYXyTcaEcKdLNtFu2UJemUP7Ol40t9zOZXCmcupi_NFqq1u_sB9CqO835hviIZifgvKHgzBYg7Wv22ajZPAo18-pkCbL6v_t-YaXD1GA5cu8gTtmPYpGk56DA7QKMKEpxZ7mHDT4jWYTnEP0ikGiHCECAeIDtH1xfjq7DIJNSsSQVlOq8RyqZkpMys16DqdKU6UY9XTRklSVCYXVOQyS4WrxGaI5IaXhqdWOBokWun8GRq009Y8R9jkNhPCMLBAhHLonysrQVgwbQqt6BF6s7Y89c9v_v36vN5Yw78QojDSMSxtrRrXZu5dNviNpWNqcmJlcYRwXPTa9w-Rw_V4dEahP3ixMM8WGLUjY9n8MS8emOcl2u_37ys0WMyW5hicvoV8HfbVH8PRTuY
linkProvider ProQuest Ebooks
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.title=Concepts+of+proof+in+mathematics%2C+philosophy%2C+and+computer+science&rft.au=Probst%2C+Dieter&rft.au=Schuster%2C+Peter&rft.date=2016-01-01&rft.pub=De+Gruyter&rft.isbn=9781501510809&rft_id=info:doi/10.1515%2F9781501502620&rft.externalDocID=BB22815155
thumbnail_m http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fwww.degruyter.com%2Fdocument%2Fcover%2Fisbn%2F9781501502620%2Foriginal
http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fvle.dmmserver.com%2Fmedia%2F640%2F97815015%2F9781501502620.jpg
http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fvle.dmmserver.com%2Fmedia%2F640%2F97815015%2F9781501502644.jpg