Lakatos-style collaborative mathematics through dialectical, structured and abstract argumentation

The simulation of mathematical reasoning has been a driving force throughout the history of Artificial Intelligence research. However, despite significant successes in computer mathematics, computers are not widely used by mathematicians apart from their quotidian applications. An oft-cited reason f...

Full description

Saved in:
Bibliographic Details
Published in:Artificial intelligence Vol. 246; pp. 181 - 219
Main Authors: Pease, Alison, Lawrence, John, Budzynska, Katarzyna, Corneli, Joseph, Reed, Chris
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.05.2017
Elsevier Science Ltd
Subjects:
ISSN:0004-3702, 1872-7921
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract The simulation of mathematical reasoning has been a driving force throughout the history of Artificial Intelligence research. However, despite significant successes in computer mathematics, computers are not widely used by mathematicians apart from their quotidian applications. An oft-cited reason for this is that current computational systems cannot do mathematics in the way that humans do. We draw on two areas in which Automated Theorem Proving (ATP) is currently unlike human mathematics: firstly in a focus on soundness, rather than understandability of proof, and secondly in social aspects. Employing techniques and tools from argumentation to build a framework for mixed-initiative collaboration, we develop three complementary arcs. In the first arc – our theoretical model – we interpret the informal logic of mathematical discovery proposed by Lakatos, a philosopher of mathematics, through the lens of dialogue game theory and in particular as a dialogue game ranging over structures of argumentation. In our second arc – our abstraction level – we develop structured arguments, from which we induce abstract argumentation systems and compute the argumentation semantics to provide labelings of the acceptability status of each argument. The output from this stage corresponds to a final, or currently accepted proof artefact, which can be viewed alongside its historical development. Finally, in the third arc – our computational model – we show how each of these formal steps is available in implementation. In an appendix, we demonstrate our approach with a formal, implemented example of real-world mathematical collaboration. We conclude the paper with reflections on our mixed-initiative collaborative approach.
AbstractList The simulation of mathematical reasoning has been a driving force throughout the history of Artificial Intelligence research. However, despite significant successes in computer mathematics, computers are not widely used by mathematicians apart from their quotidian applications. An oft-cited reason for this is that current computational systems cannot do mathematics in the way that humans do. We draw on two areas in which Automated Theorem Proving (ATP) is currently unlike human mathematics: firstly in a focus on soundness, rather than understandability of proof, and secondly in social aspects. Employing techniques and tools from argumentation to build a framework for mixed-initiative collaboration, we develop three complementary arcs. In the first arc – our theoretical model – we interpret the informal logic of mathematical discovery proposed by Lakatos, a philosopher of mathematics, through the lens of dialogue game theory and in particular as a dialogue game ranging over structures of argumentation. In our second arc – our abstraction level – we develop structured arguments, from which we induce abstract argumentation systems and compute the argumentation semantics to provide labelings of the acceptability status of each argument. The output from this stage corresponds to a final, or currently accepted proof artefact, which can be viewed alongside its historical development. Finally, in the third arc – our computational model – we show how each of these formal steps is available in implementation. In an appendix, we demonstrate our approach with a formal, implemented example of real-world mathematical collaboration. We conclude the paper with reflections on our mixed-initiative collaborative approach.
Author Budzynska, Katarzyna
Pease, Alison
Lawrence, John
Corneli, Joseph
Reed, Chris
Author_xml – sequence: 1
  givenname: Alison
  orcidid: 0000-0003-1856-9599
  surname: Pease
  fullname: Pease, Alison
  email: a.pease@dundee.ac.uk
  organization: Centre for Argument Technology, University of Dundee, UK
– sequence: 2
  givenname: John
  surname: Lawrence
  fullname: Lawrence, John
  organization: Centre for Argument Technology, University of Dundee, UK
– sequence: 3
  givenname: Katarzyna
  surname: Budzynska
  fullname: Budzynska, Katarzyna
  organization: Centre for Argument Technology, University of Dundee, UK
– sequence: 4
  givenname: Joseph
  surname: Corneli
  fullname: Corneli, Joseph
  organization: Department of Computing, Goldsmiths, University of London, UK
– sequence: 5
  givenname: Chris
  surname: Reed
  fullname: Reed, Chris
  organization: Centre for Argument Technology, University of Dundee, UK
BookMark eNqFkMtLAzEQxoNUsD7-Aw8LXt01r-7DgyDiCwpe9BymyWybut3UJFvof2_KevKgh5khH_Ob8H2nZNK7Hgm5ZLRglJU36wJ8tH0sOGVVQXlBaXlEpqyueF41nE3IlFIqc1FRfkJOQ1inp2gaNiWLOXxCdCEPcd9hpl3XwcJ5iHaH2QbiClOzOmRx5d2wXGXGQoc6SdBdZyH6QcfBo8mgT7VIAuiYgV8OG-xjQl1_To5b6AJe_Mwz8vH0-P7wks_fnl8f7ue5FjWNOdcVAJWSm1RljbKkumlNkgyg1ka0LTSmXjDRYF0ZWcFMYEUbLoWUumXijFyNd7fefQ0Yolq7wffpS8UaVooy2Z-lLTluae9C8Niqrbcb8HvFqDqkqdZqTFMd0lSUq5Rmwm5_YdqO9pJj2_0H340wJvs7i14FbbHXaKxPWSrj7N8HvgFSBpfn
CitedBy_id crossref_primary_10_1007_s11299_024_00304_x
crossref_primary_10_1007_s10516_023_09685_z
crossref_primary_10_1007_s11858_020_01181_7
crossref_primary_10_1007_s10472_019_09654_6
crossref_primary_10_1007_s11128_018_1918_6
crossref_primary_10_1016_j_pragma_2021_10_029
crossref_primary_10_1007_s11858_019_01049_5
crossref_primary_10_1093_logcom_exy033
crossref_primary_10_1007_s10699_023_09926_9
crossref_primary_10_1007_s13347_017_0260_8
crossref_primary_10_1111_phis_12119
Cites_doi 10.1017/S0269888906000865
10.1007/s00454-009-9148-4
10.1016/0004-3702(84)90016-X
10.1007/BF00370166
10.1093/logcom/exs033
10.1162/coli.2000.28.1.96
10.1023/A:1015586128739
10.1007/BF00567741
10.1093/logcom/exi046
10.1016/j.artint.2007.04.015
10.1007/s10458-005-1166-x
10.1016/j.jal.2012.09.001
10.1207/s15516709cog0404_2
10.1145/2500891
10.1016/j.artint.2007.05.001
10.1145/2629559
10.1090/S0273-0979-1994-00502-6
10.1017/S0269888906001044
10.1007/s10472-011-9248-8
10.1080/19462166.2013.869766
10.1016/S0039-3681(96)00002-7
10.1016/j.artint.2012.11.007
10.1016/0004-3702(94)00041-X
10.1093/mind/fzv140
10.1007/s10699-008-9158-3
10.1080/0308107042000193552
10.1111/j.1467-8640.1988.tb00089.x
10.1016/j.artint.2014.12.006
10.1007/978-94-007-6534-4_3
10.1207/s15516709cog1302_7
10.1287/opre.6.1.1
10.1016/j.artint.2008.09.004
10.4018/jcini.2013010101
10.1016/j.entcs.2005.11.063
10.1080/19462160903564592
10.1007/s10503-005-4417-8
ContentType Journal Article
Copyright 2017 The Authors
Copyright Elsevier Science Ltd. May 2017
Copyright_xml – notice: 2017 The Authors
– notice: Copyright Elsevier Science Ltd. May 2017
DBID 6I.
AAFTH
AAYXX
CITATION
7SC
8FD
JQ2
L7M
L~C
L~D
DOI 10.1016/j.artint.2017.02.006
DatabaseName ScienceDirect Open Access Titles
Elsevier:ScienceDirect:Open Access
CrossRef
Computer and Information Systems Abstracts
Technology Research Database
ProQuest Computer Science Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle CrossRef
Computer and Information Systems Abstracts
Technology Research Database
Computer and Information Systems Abstracts – Academic
Advanced Technologies Database with Aerospace
ProQuest Computer Science Collection
Computer and Information Systems Abstracts Professional
DatabaseTitleList
Computer and Information Systems Abstracts
DeliveryMethod fulltext_linktorsrc
Discipline Computer Science
Mathematics
EISSN 1872-7921
EndPage 219
ExternalDocumentID 10_1016_j_artint_2017_02_006
S0004370217300267
GroupedDBID --K
--M
--Z
-~X
.DC
.~1
0R~
1B1
1~.
1~5
23N
4.4
457
4G.
5GY
5VS
6I.
6J9
6TJ
7-5
71M
77K
8P~
9JN
AACTN
AAEDT
AAEDW
AAFTH
AAIAV
AAIKJ
AAKOC
AAKPC
AALRI
AAOAW
AAQFI
AAQXK
AAXUO
AAYFN
ABBOA
ABFNM
ABFRF
ABJNI
ABMAC
ABVKL
ABXDB
ABYKQ
ACDAQ
ACGFO
ACGFS
ACNCT
ACNNM
ACRLP
ACWUS
ACZNC
ADBBV
ADEZE
ADMUD
AEBSH
AECPX
AEFWE
AEKER
AENEX
AETEA
AEXQZ
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AHJVU
AHZHX
AIALX
AIEXJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
AOUOD
ASPBG
AVWKF
AXJTR
AZFZN
BJAXD
BKOJK
BLXMC
CS3
E3Z
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
F0J
F5P
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
G8K
GBLVA
GBOLZ
HLZ
HVGLF
HZ~
IHE
IXB
J1W
JJJVA
KOM
KQ8
LG9
LY7
M41
MO0
MVM
N9A
NCXOZ
O-L
O9-
OAUVE
OK1
OZT
P-8
P-9
P2P
PC.
PQQKQ
Q38
R2-
RIG
RNS
ROL
RPZ
SBC
SDF
SDG
SDP
SES
SET
SEW
SPC
SPCBC
SST
SSV
SSZ
T5K
TAE
TN5
TR2
TWZ
UPT
UQL
VQA
WH7
WUQ
XFK
XJE
XJT
XPP
XSW
ZMT
~02
~G-
77I
9DU
AATTM
AAXKI
AAYWO
AAYXX
ABDPE
ABWVN
ACLOT
ACRPL
ACVFH
ADCNI
ADNMO
ADVLN
AEIPS
AEUPX
AFJKZ
AFPUW
AGQPQ
AIGII
AIIUN
AKBMS
AKRWK
AKYEP
ANKPU
APXCP
CITATION
EFKBS
~HD
7SC
8FD
JQ2
L7M
L~C
L~D
ID FETCH-LOGICAL-c380t-2c7aa0442d44268e460c9fda04daeccd3ffa9d8b139e87d47a53e70924344cf13
ISICitedReferencesCount 24
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000399844800008&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0004-3702
IngestDate Sun Nov 09 07:53:08 EST 2025
Sat Nov 29 06:08:10 EST 2025
Tue Nov 18 21:45:30 EST 2025
Fri Feb 23 02:31:58 EST 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Keywords Automated reasoning
Abstract argumentation
Argumentation
Mathematical argument
Structured argumentation
Philosophy of mathematical practice
Automated theorem proving
Lakatos
Collaborative intelligence
Social creativity
Dialogue games
Language English
License This is an open access article under the CC BY license.
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c380t-2c7aa0442d44268e460c9fda04daeccd3ffa9d8b139e87d47a53e70924344cf13
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0003-1856-9599
OpenAccessLink https://dx.doi.org/10.1016/j.artint.2017.02.006
PQID 1916363705
PQPubID 2038285
PageCount 39
ParticipantIDs proquest_journals_1916363705
crossref_primary_10_1016_j_artint_2017_02_006
crossref_citationtrail_10_1016_j_artint_2017_02_006
elsevier_sciencedirect_doi_10_1016_j_artint_2017_02_006
PublicationCentury 2000
PublicationDate May 2017
2017-05-00
20170501
PublicationDateYYYYMMDD 2017-05-01
PublicationDate_xml – month: 05
  year: 2017
  text: May 2017
PublicationDecade 2010
PublicationPlace Amsterdam
PublicationPlace_xml – name: Amsterdam
PublicationTitle Artificial intelligence
PublicationYear 2017
Publisher Elsevier B.V
Elsevier Science Ltd
Publisher_xml – name: Elsevier B.V
– name: Elsevier Science Ltd
References Koons (br0520) 2014
Searle (br0850) 1969
Pease, Martin (br1170) 2012
Martin, Pease (br0630) 2013; vol. 7961
Traum, Larsson (br0960) 2003
Weigand (br1040) 2009
Gowers (br0410) 2000
Cauchy (br0230) 1813; 9
Epstein (br0340) 1988; 4
Hobbs, Evans (br0480) 1980; 4
Hayes-Roth (br0460) 1983
Modgil, Prakken (br0660) 2014; 5
Wyner, van Engers, Hunter (br1070) 2016
Turing (br0980) 1937; 42
Pease (br0710) April 2013; 27
McBurney, Parsons (br0650) 2003
Simon, Newell (br0860) 1958; 6
Cramer (br0280) 2013
Prakken (br0790) 2006; 21
Aberdein (br0010) 1998
Bundy (br0210) 2011; 61
Hardy (br0440) 1928; 38
br1080
Pietarinen (br0740) 2004; 33
Aberdein (br0040) 2007; vol. 5
Lorenz, Lorenzen (br0590) 1978
Sutcliffe (br0920) 2007
Pease, Aberdein (br0720) 2011; 20
Hales (br0420) 2010; 44
Bundy (br0200) 2005
Confalonieri, Corneli, Pease, Plaza, Schorlemmer (br0270) 2015
Aberdein (br0020) 2005; 19
Lenat, Brown (br0580) 1984; 23
Cerutti, Giacomin, Vallati (br0240) 2014
Budzynska, Debowska (br0190) 2010
Snaith, Reed (br0900) 2012
Walton (br1000) 1996
Stahl (br1180) Sep. 2010
Snaith, Devereux, Lawrence, Reed (br0880) 2010
Bex, Prakken, Modgil, Reed (br0160) 2013; 23
br1090
Jennings, Moreau, Nicholson, Ramchurn, Roberts, Rodden, Rogers (br0490) 2014; 57
Aberdein (br0060) 2011
Bex, Lawrence, Snaith, Reed (br0150) Oct. 2013; 56
Clark, Schaefer (br0260) 1989; 13
Epstein (br0350) 2015; 221
Prakken (br0800) 2010; 1
Aschbacher (br0090) 2005
Bex, Lawrence, Reed (br0140) 2014
McBurney, Parsons (br0640) 2002
Ernest (br0670) 2008
Wilder (br1060) 1968
Thurston (br0940) 1994; 30
Aberdein (br0050) 2009; 14
Paseau (br0690) 2016; 125
Pease (br0700) 2007
Fiedler (br0360) 2005
Snaith, Lawrence, Reed (br0890) 2010
Black, Atkinson (br0170) 2011
Hersh (br1140) 1991; 88
Atkinson, Wyner (br0110) 2013
Bunt, Black (br0220) 2000
Chesñevar, McGinnis, Modgil, Rahwan, Reed, Simari, South, Vreeswijk, Willmott (br0250) 2006; 21
Devereux, Reed (br0310) 2009
MacKenzie (br0610) 2005
Dung (br0320) 1995; 77
MacKenzie (br0600) 2001
Martin, Pease (br1150) 2013; vol. 7961
Prakken, Wyner, Bench-Capon, Atkinson (br0810) 2013
Schoenfeld (br0840) 2014
Alcolea Banegas (br0080) 1998
Toulmin, Rieke, Janik (br0950) 1979
Dvorák, Gaggl, Wallner, Woltran (br0330) 2011
Stone (br0910) Mar. 2002; 28
Vreeswijk (br0990) 1992
Rahwan, Reed (br0820) 2009
Sloman (br0870) December 2008; 172
Blanchette, Kaliszyk, Paulson, Urban (br0180) 2016; 9
E.C.W. Krabbe, Arguments, proofs, and dialogues
Ernest (br1120) 1997
Lawrence, Bex, Reed (br0560) 2012
McBurney, Parsons (br1160) 2002; 11
Hamblin (br0430) 1970
Gaizauskas, Kruschwitz, Poesio (br0370) 2016; vol. 9577
Pólya (br0750) 1945
Berners-Lee, Fischetti (br0130) 2000
Ganesalingam (br0380) 2013
Rahwan, Zablith, Reed (br0830) 2007; 171
Feferman (br1130) 1978
Harrison (br0450) 2009
Prakken (br0780) 2005; 15
Traum (br0970) 1999
Aberdein, Dove (br0070) 2013; vol. 30
Hersh (br0470) 1991; 88
Lakatos (br0540) 1970
Corfield (br1110) 1997; 28
Kamar, Gal, Grosz (br0510) 2013; 195
Thurston (br1190) 1994; 30
Denney, Power, Tourlas (br0300) 2006; 155
Lawrence, Bex, Reed, Snaith (br0570) 2012
Cramer, Fisseni, Koepke, Kühlwein, Schröder, Veldman (br0290) 2010
Bench-Capon, Dunne (br0120) 2007; 171
Joshi, Weber, Sag (br0500) 1980
Walton (br1020) 1996
Peldszus, Stede (br0730) 2013; 7
Mackenzie (br0620) 1990; 51
Aberdein (br0030) 2006; vol. 4108
Wells, Reed (br1050) 2012; 10
Popper (br0770) 1972
Walton, Reed, Macagno (br1010) 2009
br1100
Atkinson, Bench-Capon, McBurney (br0100) 2005; 11
Ganesalingam, Gowers (br0390) 2016
chapter 3, pp. 31–45.
Parsons, Wooldridge, Amgoud (br0680) 2002
Walton, Krabbe (br1030) 1995
Gonthier (br0400) 2011; vol. 6898
Pólya (br0760) 1981
Lakatos (br0550) 1976
Thimm (br0930) July 2014
Lorenz (10.1016/j.artint.2017.02.006_br0590) 1978
Denney (10.1016/j.artint.2017.02.006_br0300) 2006; 155
Gonthier (10.1016/j.artint.2017.02.006_br0400) 2011; vol. 6898
Popper (10.1016/j.artint.2017.02.006_br0770) 1972
Weigand (10.1016/j.artint.2017.02.006_br1040) 2009
Wyner (10.1016/j.artint.2017.02.006_br1070) 2016
Mackenzie (10.1016/j.artint.2017.02.006_br0620) 1990; 51
Aberdein (10.1016/j.artint.2017.02.006_br0030) 2006; vol. 4108
Aberdein (10.1016/j.artint.2017.02.006_br0060) 2011
Rahwan (10.1016/j.artint.2017.02.006_br0820) 2009
Wells (10.1016/j.artint.2017.02.006_br1050) 2012; 10
Pólya (10.1016/j.artint.2017.02.006_br0750) 1945
Bex (10.1016/j.artint.2017.02.006_br0150) 2013; 56
Devereux (10.1016/j.artint.2017.02.006_br0310) 2009
Epstein (10.1016/j.artint.2017.02.006_br0340) 1988; 4
Gaizauskas (10.1016/j.artint.2017.02.006_br0370) 2016; vol. 9577
Turing (10.1016/j.artint.2017.02.006_br0980) 1937; 42
Atkinson (10.1016/j.artint.2017.02.006_br0100) 2005; 11
Martin (10.1016/j.artint.2017.02.006_br0630) 2013; vol. 7961
MacKenzie (10.1016/j.artint.2017.02.006_br0610) 2005
Stone (10.1016/j.artint.2017.02.006_br0910) 2002; 28
Pease (10.1016/j.artint.2017.02.006_br1170) 2012
Lenat (10.1016/j.artint.2017.02.006_br0580) 1984; 23
Snaith (10.1016/j.artint.2017.02.006_br0890) 2010
Fiedler (10.1016/j.artint.2017.02.006_br0360) 2005
Bundy (10.1016/j.artint.2017.02.006_br0200) 2005
Thurston (10.1016/j.artint.2017.02.006_br0940) 1994; 30
Bex (10.1016/j.artint.2017.02.006_br0140) 2014
Ernest (10.1016/j.artint.2017.02.006_br0670) 2008
Berners-Lee (10.1016/j.artint.2017.02.006_br0130) 2000
McBurney (10.1016/j.artint.2017.02.006_br0640) 2002
Chesñevar (10.1016/j.artint.2017.02.006_br0250) 2006; 21
Peldszus (10.1016/j.artint.2017.02.006_br0730) 2013; 7
Epstein (10.1016/j.artint.2017.02.006_br0350) 2015; 221
Lawrence (10.1016/j.artint.2017.02.006_br0560) 2012
Black (10.1016/j.artint.2017.02.006_br0170) 2011
Cramer (10.1016/j.artint.2017.02.006_br0280) 2013
Searle (10.1016/j.artint.2017.02.006_br0850) 1969
Aberdein (10.1016/j.artint.2017.02.006_br0020) 2005; 19
Modgil (10.1016/j.artint.2017.02.006_br0660) 2014; 5
Joshi (10.1016/j.artint.2017.02.006_br0500) 1980
Aberdein (10.1016/j.artint.2017.02.006_br0070) 2013; vol. 30
Pease (10.1016/j.artint.2017.02.006_br0720) 2011; 20
Feferman (10.1016/j.artint.2017.02.006_br1130) 1978
Hersh (10.1016/j.artint.2017.02.006_br0470) 1991; 88
Pietarinen (10.1016/j.artint.2017.02.006_br0740) 2004; 33
Thurston (10.1016/j.artint.2017.02.006_br1190) 1994; 30
Prakken (10.1016/j.artint.2017.02.006_br0800) 2010; 1
Harrison (10.1016/j.artint.2017.02.006_br0450) 2009
Walton (10.1016/j.artint.2017.02.006_br1010) 2009
Walton (10.1016/j.artint.2017.02.006_br1030) 1995
Parsons (10.1016/j.artint.2017.02.006_br0680) 2002
Toulmin (10.1016/j.artint.2017.02.006_br0950) 1979
Prakken (10.1016/j.artint.2017.02.006_br0780) 2005; 15
Hayes-Roth (10.1016/j.artint.2017.02.006_br0460) 1983
Bench-Capon (10.1016/j.artint.2017.02.006_br0120) 2007; 171
Aberdein (10.1016/j.artint.2017.02.006_br0040) 2007; vol. 5
Gowers (10.1016/j.artint.2017.02.006_br0410) 2000
Stahl (10.1016/j.artint.2017.02.006_br1180) 2010
Cramer (10.1016/j.artint.2017.02.006_br0290) 2010
Lawrence (10.1016/j.artint.2017.02.006_br0570) 2012
Martin (10.1016/j.artint.2017.02.006_br1150) 2013; vol. 7961
Aberdein (10.1016/j.artint.2017.02.006_br0010) 1998
McBurney (10.1016/j.artint.2017.02.006_br1160) 2002; 11
Hersh (10.1016/j.artint.2017.02.006_br1140) 1991; 88
Budzynska (10.1016/j.artint.2017.02.006_br0190) 2010
Simon (10.1016/j.artint.2017.02.006_br0860) 1958; 6
Kamar (10.1016/j.artint.2017.02.006_br0510) 2013; 195
Confalonieri (10.1016/j.artint.2017.02.006_br0270) 2015
Hales (10.1016/j.artint.2017.02.006_br0420) 2010; 44
Walton (10.1016/j.artint.2017.02.006_br1000) 1996
Walton (10.1016/j.artint.2017.02.006_br1020) 1996
Sutcliffe (10.1016/j.artint.2017.02.006_br0920) 2007
Alcolea Banegas (10.1016/j.artint.2017.02.006_br0080) 1998
Pólya (10.1016/j.artint.2017.02.006_br0760) 1981
Snaith (10.1016/j.artint.2017.02.006_br0900) 2012
Prakken (10.1016/j.artint.2017.02.006_br0790) 2006; 21
Hardy (10.1016/j.artint.2017.02.006_br0440) 1928; 38
Atkinson (10.1016/j.artint.2017.02.006_br0110) 2013
Bex (10.1016/j.artint.2017.02.006_br0160) 2013; 23
Wilder (10.1016/j.artint.2017.02.006_br1060) 1968
Cerutti (10.1016/j.artint.2017.02.006_br0240) 2014
Pease (10.1016/j.artint.2017.02.006_br0710) 2013; 27
Jennings (10.1016/j.artint.2017.02.006_br0490) 2014; 57
Ernest (10.1016/j.artint.2017.02.006_br1120) 1997
Dung (10.1016/j.artint.2017.02.006_br0320) 1995; 77
Corfield (10.1016/j.artint.2017.02.006_br1110) 1997; 28
Blanchette (10.1016/j.artint.2017.02.006_br0180) 2016; 9
Aschbacher (10.1016/j.artint.2017.02.006_br0090) 2005
Paseau (10.1016/j.artint.2017.02.006_br0690) 2016; 125
Sloman (10.1016/j.artint.2017.02.006_br0870) 2008; 172
Rahwan (10.1016/j.artint.2017.02.006_br0830) 2007; 171
Traum (10.1016/j.artint.2017.02.006_br0970) 1999
Cauchy (10.1016/j.artint.2017.02.006_br0230) 1813; 9
Lakatos (10.1016/j.artint.2017.02.006_br0540) 1970
Ganesalingam (10.1016/j.artint.2017.02.006_br0380) 2013
Lakatos (10.1016/j.artint.2017.02.006_br0550) 1976
Koons (10.1016/j.artint.2017.02.006_br0520) 2014
Clark (10.1016/j.artint.2017.02.006_br0260) 1989; 13
Schoenfeld (10.1016/j.artint.2017.02.006_br0840) 2014
Bunt (10.1016/j.artint.2017.02.006_br0220) 2000
Ganesalingam (10.1016/j.artint.2017.02.006_br0390) 2016
Traum (10.1016/j.artint.2017.02.006_br0960) 2003
Prakken (10.1016/j.artint.2017.02.006_br0810) 2013
10.1016/j.artint.2017.02.006_br0530
Vreeswijk (10.1016/j.artint.2017.02.006_br0990) 1992
Snaith (10.1016/j.artint.2017.02.006_br0880) 2010
Thimm (10.1016/j.artint.2017.02.006_br0930) 2014
Hobbs (10.1016/j.artint.2017.02.006_br0480) 1980; 4
MacKenzie (10.1016/j.artint.2017.02.006_br0600) 2001
Bundy (10.1016/j.artint.2017.02.006_br0210) 2011; 61
Pease (10.1016/j.artint.2017.02.006_br0700) 2007
Aberdein (10.1016/j.artint.2017.02.006_br0050) 2009; 14
Hamblin (10.1016/j.artint.2017.02.006_br0430) 1970
McBurney (10.1016/j.artint.2017.02.006_br0650) 2003
Dvorák (10.1016/j.artint.2017.02.006_br0330)
References_xml – volume: vol. 4108
  start-page: 208
  year: 2006
  end-page: 221
  ident: br0030
  article-title: Managing informal mathematical knowledge: techniques from informal logic
  publication-title: MKM 2006
– start-page: 342
  year: 2005
  end-page: 363
  ident: br0360
  article-title: Natural language proof explanation
  publication-title: Mechanizing Mathematical Reasoning
– start-page: 69
  year: 2016
  end-page: 89
  ident: br1070
  article-title: Working on the argument pipeline: through flow issues between natural language argument, instantiated arguments, and argumentation frameworks
  publication-title: Argument & Computation, vol. 7
– volume: vol. 5
  start-page: 135
  year: 2007
  end-page: 151
  ident: br0040
  article-title: The informal logic of mathematical proof
  publication-title: Perspectives on Mathematical Practices: Bringing Together Philosophy of Mathematics, Sociology of Mathematics, and Mathematics Education
– volume: 15
  start-page: 1009
  year: 2005
  end-page: 1040
  ident: br0780
  article-title: Coherence and flexibility in dialogue games for argumentation
  publication-title: J. Log. Comput.
– volume: vol. 6898
  year: 2011
  ident: br0400
  article-title: Advances in the Formalization of the Odd Order Theorem
  publication-title: Proc. of Interactive Theorem Proving
– volume: 88
  start-page: 127
  year: 1991
  end-page: 133
  ident: br1140
  article-title: Mathematics has a front and a back
  publication-title: Synthese
– year: 2009
  ident: br1040
  article-title: Language as Dialogue: From Rules to Principles of Probability
– year: 2013
  ident: br0380
  article-title: The Language of Mathematics
– year: 2000
  ident: br0130
  article-title: Weaving the Web – the Original Design and Ultimate Destiny of the World Wide Web by Its Inventor
– start-page: 170
  year: 2010
  end-page: 186
  ident: br0290
  article-title: The Naproche Project Controlled Natural Language Proof Checking of Mathematical Texts
– year: 2007
  ident: br0920
  article-title: SRASS: a semantic relevance axiom selection system
  publication-title: Proceedings of ARW'07
– start-page: 2329
  year: 2005
  end-page: 2461
  ident: br0200
  article-title: The nature of mathematical proof
  publication-title: Phil. Trans. of the Royal Society, vol. 363
– year: 2014
  ident: br0840
  article-title: Mathematical Problem Solving
– year: 2000
  ident: br0220
  article-title: Abduction, Belief, and Context in Dialogue: Studies in Computational Pragmatics
– volume: 30
  start-page: 161
  year: 1994
  end-page: 177
  ident: br1190
  article-title: On proof and progress in mathematics
  publication-title: Bull., New Ser., Am. Math. Soc.
– year: 2011
  ident: br0330
  article-title: Making use of advances in answer-set programming for abstract argumentation systems
– start-page: 269
  year: 2003
  end-page: 283
  ident: br0650
  article-title: Dialogue game protocols
  publication-title: Communication in Multiagent Systems
– volume: 27
  year: April 2013
  ident: br0710
  article-title: A computational model of Lakatos-style reasoning
  publication-title: Philos. Math. Educ. J.
– year: 1970
  ident: br0430
  article-title: Fallacies
– year: July 2014
  ident: br0930
  article-title: Tweety – a comprehensive collection of Java libraries for logical aspects of artificial intelligence and knowledge representation
  publication-title: Proceedings of the 14th International Conference on Principles of Knowledge Representation and Reasoning
– year: 1979
  ident: br0950
  article-title: An Introduction to Reasoning
– volume: 28
  start-page: 99
  year: 1997
  end-page: 121
  ident: br1110
  article-title: Assaying Lakatos's philosophy of mathematics
  publication-title: Stud. Hist. Philos. Sci.
– year: 1997
  ident: br1120
  article-title: Social Constructivism as a Philosophy of Mathematics
– volume: 14
  start-page: 1
  year: 2009
  end-page: 8
  ident: br0050
  article-title: Mathematics and argumentation
  publication-title: Found. Sci.
– year: 1968
  ident: br1060
  article-title: Evolution of Mathematical Concepts
– reference: E.C.W. Krabbe, Arguments, proofs, and dialogues,
– volume: 172
  start-page: 2015
  year: December 2008
  end-page: 2034
  ident: br0870
  article-title: The well-designed young mathematician
  publication-title: Artif. Intell.
– volume: 21
  start-page: 293
  year: 2006
  end-page: 316
  ident: br0250
  article-title: Towards an argument interchange format
  publication-title: Knowl. Eng. Rev.
– start-page: 309
  year: 1978
  end-page: 327
  ident: br1130
  article-title: The logic of mathematical discovery vs. the logical structure of mathematics
  publication-title: Proceedings of the 1978 Biennial Meeting of the Philosophy of Science Association, vol. 2
– ident: br1090
– start-page: 2401
  year: 2005
  end-page: 2406
  ident: br0090
  article-title: Highly complex proofs and implications of such proofs
  publication-title: Phil. Trans. of the Royal Society, vol. 363
– volume: 42
  start-page: 23065
  year: 1937
  ident: br0980
  article-title: On Computable Numbers, with an Application to the Entscheidungs problem
  publication-title: Proc. Lond. Math. Soc.
– start-page: 513
  year: 2012
  end-page: 514
  ident: br0560
  article-title: Dialogues on the argument web: mixed initiative argumentation with Arvina
  publication-title: Proceedings of the 4th International Conference on Computational Models of Argument
– volume: 4
  start-page: 42
  year: 1988
  end-page: 53
  ident: br0340
  article-title: Learning and discovery: one system's search for mathematical knowledge
  publication-title: Comput. Intell.
– start-page: 515
  year: 2012
  end-page: 516
  ident: br0570
  article-title: AIFdb: Infrastructure for the argument web
  publication-title: Proceedings of the Fourth International Conference on Computational Models of Argument
– start-page: 124
  year: 1999
  end-page: 131
  ident: br0970
  article-title: Computational models of grounding in collaborative systems
  publication-title: Psychological Models of Communication in Collaborative Systems – Papers from the AAAI Fall Symposium
– start-page: 455
  year: 2014
  end-page: 456
  ident: br0240
  article-title: Argsemsat: solving argumentation problems using SAT
  publication-title: Computational Models of Argument – Proceedings of COMMA 2014
– volume: 9
  start-page: 68
  year: 1813
  end-page: 86
  ident: br0230
  article-title: Recherches sur les polyèdres
  publication-title: J. Éc. Polytech.
– volume: 21
  start-page: 163
  year: 2006
  end-page: 188
  ident: br0790
  article-title: Formal systems for persuasion dialogue
  publication-title: Knowl. Eng. Rev.
– volume: 10
  start-page: 309
  year: 2012
  end-page: 329
  ident: br1050
  article-title: A domain specific language for describing diverse systems of dialogue
  publication-title: J. Appl. Log.
– volume: 171
  start-page: 619
  year: 2007
  end-page: 641
  ident: br0120
  article-title: Argumentation in artificial intelligence
  publication-title: Artif. Intell.
– volume: 7
  start-page: 1
  year: 2013
  end-page: 31
  ident: br0730
  article-title: From argument diagrams to argumentation mining in texts: a survey
  publication-title: Int. J. Cog. Inform. Nat. Intell.
– volume: vol. 7961
  start-page: 98
  year: 2013
  end-page: 119
  ident: br0630
  article-title: Mathematical practice, crowdsourcing, and social machines
  publication-title: Intelligent Computer Mathematics
– year: 2011
  ident: br0060
  article-title: The dialectical tier of mathematical proof
  publication-title: Argumentation: Cognition & Community
– start-page: 59
  year: 2010
  end-page: 66
  ident: br0190
  article-title: Dialogues with conflict resolution: goals and effects
  publication-title: Aspects of Semantics and Pragmatics of Dialogue. SemDial 2010, 14th Workshop on the Semantics and Pragmatics of Dialogue
– year: 1996
  ident: br1020
  article-title: Logical Dialogue—Games and Fallacies
– start-page: 325
  year: 2003
  end-page: 353
  ident: br0960
  article-title: The information state approach to dialogue management
  publication-title: Current and New Directions in Discourse and Dialogue
– year: 1996
  ident: br1000
  article-title: Argumentation Schemes for Presumptive Reasoning
– year: 2000
  ident: br0410
  article-title: Rough structure and classification
  publication-title: GAFA (Geometric and Functional Analysis)
– year: 1978
  ident: br0590
  article-title: Dialogische Logik
– volume: vol. 7961
  start-page: 98
  year: 2013
  end-page: 119
  ident: br1150
  article-title: Mathematical practice, crowdsourcing, and social machines
  publication-title: Intelligent Computer Mathematics
– volume: 23
  start-page: 951
  year: 2013
  end-page: 989
  ident: br0160
  article-title: On logical reifications of the argument interchange format
  publication-title: J. Log. Comput.
– start-page: 39
  year: 2013
  end-page: 62
  ident: br0110
  article-title: The value of values in computational argumentation
  publication-title: From Knowledge Representation to Argumentation in AI, Law and Policy Making: A Festschrift in Honour of Trevor Bench-Capon on the Occasion of His 60th Birthday
– year: Sep. 2010
  ident: br1180
  article-title: Studying Virtual Math Teams
– volume: 38
  start-page: 11
  year: 1928
  end-page: 25
  ident: br0440
  article-title: Mathematical proof
  publication-title: Mind
– year: 2009
  ident: br0450
  article-title: Handbook of Practical Logic and Automated Reasoning
– start-page: 141
  year: 2014
  end-page: 152
  ident: br0140
  article-title: Generalising argument dialogue with the dialogue game execution platform
  publication-title: Proceedings of the Fifth International Conference on Computational Models of Argument
– year: 2007
  ident: br0700
  article-title: A Computational Model of Lakatos-style Reasoning
– start-page: 221
  year: 1983
  end-page: 240
  ident: br0460
  article-title: Using proofs and refutations to learn from experience
  publication-title: Machine Learning: An Artificial Intelligence Approach
– volume: 11
  start-page: 153
  year: 2005
  end-page: 171
  ident: br0100
  article-title: A dialogue game protocol for multi-agent argument over proposals for action
  publication-title: Auton. Agents Multi-Agent Syst.
– volume: 19
  start-page: 287
  year: 2005
  end-page: 301
  ident: br0020
  article-title: The uses of argument in mathematics
  publication-title: Argumentation
– year: 1998
  ident: br0010
  article-title: Persuasive definition
  publication-title: Argumentation and Rhetoric
– volume: 30
  start-page: 161
  year: 1994
  end-page: 177
  ident: br0940
  article-title: On proof and progress in mathematics
  publication-title: Bull., New Ser., Am. Math. Soc.
– volume: 1
  year: 2010
  ident: br0800
  article-title: An abstract framework for argumentation with structured arguments
  publication-title: Argument Comput.
– start-page: 135
  year: 1998
  end-page: 147
  ident: br0080
  article-title: L'argumentació en matemàtiques
  publication-title: XIIè Congrés Valencià de Filosofia
– year: 2009
  ident: br0310
  article-title: Strategic argumentation in rigorous persuasion dialogue
  publication-title: Proceedings of ArgMAS 2009
– reference: , chapter 3, pp. 31–45.
– volume: 20
  start-page: 7
  year: 2011
  end-page: 57
  ident: br0720
  article-title: Five theories of reasoning: inter-connections and applications to mathematics
  publication-title: Log. Log. Philos.
– volume: 6
  start-page: 1
  year: 1958
  end-page: 10
  ident: br0860
  article-title: Heuristic problem solving: the next advance in operations research
  publication-title: Oper. Res.
– volume: 77
  start-page: 321
  year: 1995
  end-page: 358
  ident: br0320
  article-title: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games
  publication-title: Artif. Intell.
– volume: 195
  start-page: 528
  year: 2013
  end-page: 550
  ident: br0510
  article-title: Modeling information exchange opportunities for effective human–computer teamwork
  publication-title: Artif. Intell.
– volume: 61
  start-page: 3
  year: 2011
  end-page: 14
  ident: br0210
  article-title: Automated theorem provers: a practical tool?
  publication-title: Ann. Math. Artif. Intell.
– volume: 23
  start-page: 269
  year: 1984
  end-page: 294
  ident: br0580
  article-title: Why AM and EURISKO appear to work
  publication-title: Artif. Intell.
– volume: 33
  start-page: 395
  year: 2004
  end-page: 414
  ident: br0740
  article-title: Multi-agent systems and game theory—a peircean manifesto
  publication-title: Int. J. Gen. Syst.
– start-page: 315
  year: 2002
  end-page: 343
  ident: br0640
  article-title: Games that agents play: a formal framework for dialogues between autonomous agents
  publication-title: J. Log. Lang. Inf.
– start-page: 394
  year: 2002
  end-page: 401
  ident: br0680
  article-title: An analysis of formal interagent dialogues
  publication-title: Proc. of AAMAS
– year: 1995
  ident: br1030
  article-title: Commitment in Dialogue
– ident: br1100
– year: 1945
  ident: br0750
  article-title: How to Solve It
– year: 2014
  ident: br0520
  article-title: Defeasible reasoning
  publication-title: The Stanford Encyclopedia of Philosophy
– year: 1972
  ident: br0770
  article-title: Objective Knowledge
– start-page: 1
  year: 2016
  end-page: 39
  ident: br0390
  article-title: A fully automatic theorem prover with human-style output
  publication-title: J. Autom. Reason.
– start-page: 447
  year: 2010
  end-page: 454
  ident: br0880
  article-title: Pipelining argumentation technologies
  publication-title: Proceedings of the 3rd International Conference on Computational Models of Argument
– volume: 4
  start-page: 349
  year: 1980
  end-page: 377
  ident: br0480
  article-title: Conversation as planned behavior
  publication-title: Cogn. Sci.
– volume: 171
  start-page: 897
  year: 2007
  end-page: 921
  ident: br0830
  article-title: Laying the foundations for a world wide argument web
  publication-title: Artif. Intell.
– volume: 5
  start-page: 31
  year: 2014
  end-page: 62
  ident: br0660
  article-title: The ASPIC+ framework for structured argumentation: a tutorial
  publication-title: Argument Comput.
– year: 1981
  ident: br0760
  article-title: Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving
– start-page: 189
  year: 1992
  end-page: 211
  ident: br0990
  article-title: Reasoning with defeasible arguments: examples and applications
  publication-title: European Workshop on Logics in Artificial Intelligence
– start-page: 19
  year: 2012
  end-page: 29
  ident: br1170
  article-title: Seventy four minutes of mathematics: an analysis of the third mini-polymath project
  publication-title: Proc. of the AISB Symp. on Mathematical Practice and Cognition II
– volume: 57
  start-page: 80
  year: 2014
  end-page: 88
  ident: br0490
  article-title: Human–agent collectives
  publication-title: Commun. ACM
– volume: 28
  start-page: 96
  year: Mar. 2002
  end-page: 98
  ident: br0910
  article-title: Abduction, Belief and Context in Dialogue: Studies in Computational Pragmatics Harry Bunt and William Black (editors) (Tilburg University and UMIST) Amsterdam: John Benjamins (Natural language processing series, edited by Ruslan Mitkov, volume 1), 2000
  publication-title: Comput. Linguist.
– volume: vol. 30
  year: 2013
  ident: br0070
  article-title: The Argument of Mathematics
  publication-title: Logic, Epistemology, and the Unity of Science Series
– volume: 51
  start-page: 567
  year: 1990
  end-page: 583
  ident: br0620
  article-title: Four dialogue systems
  publication-title: Stud. Log.
– year: 1969
  ident: br0850
  article-title: Speech Acts: An Essay in the Philosophy of Language
– year: 2012
  ident: br0900
  article-title: TOAST: online ASPIC+ implementation
  publication-title: Proceedings of the 4th International Conference on Computational Models of Argument
– year: 1976
  ident: br0550
  article-title: Proofs and Refutations
– year: 2009
  ident: br0820
  article-title: The argument interchange format
  publication-title: Argumentation in Artificial Intelligence
– start-page: 91
  year: 1970
  end-page: 195
  ident: br0540
  article-title: Falsification and the methodology of scientific research programmes
  publication-title: Criticism and the Growth of Knowledge
– start-page: 905
  year: 2011
  end-page: 912
  ident: br0170
  article-title: Choosing persuasive arguments for action
  publication-title: Proceedings of the 10th International Conference on Autonomous Agents and Multiagent Systems
– volume: vol. 9577
  start-page: 10
  year: 2016
  ident: br0370
  article-title: The SENSEI project: making sense of human conversations
  publication-title: Future and Emergent Trends in Language Technology: First International Workshop
– volume: 56
  start-page: 66
  year: Oct. 2013
  end-page: 73
  ident: br0150
  article-title: Implementing the argument web
  publication-title: Commun. ACM
– volume: 221
  start-page: 36
  year: 2015
  end-page: 45
  ident: br0350
  article-title: Wanted: collaborative intelligence
  publication-title: Artif. Intell.
– volume: 11
  start-page: 315
  year: 2002
  end-page: 334
  ident: br1160
  article-title: Games that agents play: a formal framework for dialogues between autonomous agents
  publication-title: J. Log. Lang. Inf.
– volume: 44
  year: 2010
  ident: br0420
  article-title: A revision of the proof of the Kepler conjecture
  publication-title: Discrete Comput. Geom.
– start-page: 2335
  year: 2005
  end-page: 2350
  ident: br0610
  article-title: Computing and the cultures of proving
  publication-title: Phil. Trans. of the Royal Society, vol. 363
– year: 2015
  ident: br0270
  article-title: Using argumentation to evaluate concept blends in combinatorial creativity
  publication-title: Proceedings of the Sixth International Conference on Computational Creativity
– volume: 13
  start-page: 259
  year: 1989
  end-page: 294
  ident: br0260
  article-title: Contributing to discourse
  publication-title: Cogn. Sci.
– start-page: 65
  year: 2008
  end-page: 80
  ident: br0670
  article-title: Opening the mathematics text: what does it say?
  publication-title: Opening the Research Text: Critical Insights and In(ter)ventions into Mathematics Education
– start-page: 1141
  year: 2013
  end-page: 1166
  ident: br0810
  article-title: A formalisation of argumentation schemes for case-based reasoning in ASPIC+
  publication-title: J. Log. Comput.
– year: 2013
  ident: br0280
  article-title: Proof-checking Mathematical Texts in Controlled Natural Language
– ident: br1080
– year: 1980
  ident: br0500
  article-title: Elements of Discourse Understanding: Proceedings of a Workshop on Computational Aspects of Linguistic Structure and Discourse Setting
– volume: 125
  start-page: 177
  year: 2016
  end-page: 207
  ident: br0690
  article-title: What's the point of complete rigour?
  publication-title: Mind
– start-page: 2
  year: 2010
  end-page: 13
  ident: br0890
  article-title: Mixed initiative argument in public deliberation
  publication-title: From e-Participation to Online Deliberation, Proceedings of the Fourth International Conference on Online Deliberation
– volume: 155
  start-page: 341
  year: 2006
  end-page: 359
  ident: br0300
  article-title: Hiproofs: a hierarchical notion of proof tree
  publication-title: Electron. Notes Theor. Comput. Sci.
– year: 2001
  ident: br0600
  article-title: Mechanizing Proof: Computing, Risk, and Trust
– year: 2009
  ident: br1010
  article-title: Argumentation Schemes
– volume: 9
  start-page: 101
  year: 2016
  end-page: 148
  ident: br0180
  article-title: Hammering towards QED
  publication-title: J. Formaliz. Reason.
– volume: 88
  start-page: 127
  year: 1991
  end-page: 133
  ident: br0470
  article-title: Mathematics has a front and a back
  publication-title: Synthese
– volume: 21
  start-page: 163
  year: 2006
  ident: 10.1016/j.artint.2017.02.006_br0790
  article-title: Formal systems for persuasion dialogue
  publication-title: Knowl. Eng. Rev.
  doi: 10.1017/S0269888906000865
– year: 2000
  ident: 10.1016/j.artint.2017.02.006_br0130
– year: 1972
  ident: 10.1016/j.artint.2017.02.006_br0770
– year: 2007
  ident: 10.1016/j.artint.2017.02.006_br0700
– year: 1980
  ident: 10.1016/j.artint.2017.02.006_br0500
– start-page: 394
  year: 2002
  ident: 10.1016/j.artint.2017.02.006_br0680
  article-title: An analysis of formal interagent dialogues
– start-page: 65
  year: 2008
  ident: 10.1016/j.artint.2017.02.006_br0670
  article-title: Opening the mathematics text: what does it say?
– year: 1945
  ident: 10.1016/j.artint.2017.02.006_br0750
– volume: 44
  year: 2010
  ident: 10.1016/j.artint.2017.02.006_br0420
  article-title: A revision of the proof of the Kepler conjecture
  publication-title: Discrete Comput. Geom.
  doi: 10.1007/s00454-009-9148-4
– volume: 23
  start-page: 269
  issue: 3
  year: 1984
  ident: 10.1016/j.artint.2017.02.006_br0580
  article-title: Why AM and EURISKO appear to work
  publication-title: Artif. Intell.
  doi: 10.1016/0004-3702(84)90016-X
– volume: 51
  start-page: 567
  year: 1990
  ident: 10.1016/j.artint.2017.02.006_br0620
  article-title: Four dialogue systems
  publication-title: Stud. Log.
  doi: 10.1007/BF00370166
– volume: 23
  start-page: 951
  issue: 5
  year: 2013
  ident: 10.1016/j.artint.2017.02.006_br0160
  article-title: On logical reifications of the argument interchange format
  publication-title: J. Log. Comput.
  doi: 10.1093/logcom/exs033
– year: 2009
  ident: 10.1016/j.artint.2017.02.006_br0450
– volume: 28
  start-page: 96
  issue: 1
  year: 2002
  ident: 10.1016/j.artint.2017.02.006_br0910
  article-title: Abduction, Belief and Context in Dialogue: Studies in Computational Pragmatics Harry Bunt and William Black (editors) (Tilburg University and UMIST) Amsterdam: John Benjamins (Natural language processing series, edited by Ruslan Mitkov, volume 1), 2000
  publication-title: Comput. Linguist.
  doi: 10.1162/coli.2000.28.1.96
– volume: 20
  start-page: 7
  issue: 1–2
  year: 2011
  ident: 10.1016/j.artint.2017.02.006_br0720
  article-title: Five theories of reasoning: inter-connections and applications to mathematics
  publication-title: Log. Log. Philos.
– volume: 11
  start-page: 315
  issue: 3
  year: 2002
  ident: 10.1016/j.artint.2017.02.006_br1160
  article-title: Games that agents play: a formal framework for dialogues between autonomous agents
  publication-title: J. Log. Lang. Inf.
  doi: 10.1023/A:1015586128739
– volume: 9
  start-page: 68
  year: 1813
  ident: 10.1016/j.artint.2017.02.006_br0230
  article-title: Recherches sur les polyèdres
  publication-title: J. Éc. Polytech.
– volume: 88
  start-page: 127
  issue: 2
  year: 1991
  ident: 10.1016/j.artint.2017.02.006_br0470
  article-title: Mathematics has a front and a back
  publication-title: Synthese
  doi: 10.1007/BF00567741
– year: 2013
  ident: 10.1016/j.artint.2017.02.006_br0280
– start-page: 189
  year: 1992
  ident: 10.1016/j.artint.2017.02.006_br0990
  article-title: Reasoning with defeasible arguments: examples and applications
– start-page: 1
  year: 2016
  ident: 10.1016/j.artint.2017.02.006_br0390
  article-title: A fully automatic theorem prover with human-style output
  publication-title: J. Autom. Reason.
– volume: 15
  start-page: 1009
  issue: 6
  year: 2005
  ident: 10.1016/j.artint.2017.02.006_br0780
  article-title: Coherence and flexibility in dialogue games for argumentation
  publication-title: J. Log. Comput.
  doi: 10.1093/logcom/exi046
– year: 2015
  ident: 10.1016/j.artint.2017.02.006_br0270
  article-title: Using argumentation to evaluate concept blends in combinatorial creativity
– start-page: 124
  year: 1999
  ident: 10.1016/j.artint.2017.02.006_br0970
  article-title: Computational models of grounding in collaborative systems
– start-page: 2
  year: 2010
  ident: 10.1016/j.artint.2017.02.006_br0890
  article-title: Mixed initiative argument in public deliberation
– volume: 171
  start-page: 897
  year: 2007
  ident: 10.1016/j.artint.2017.02.006_br0830
  article-title: Laying the foundations for a world wide argument web
  publication-title: Artif. Intell.
  doi: 10.1016/j.artint.2007.04.015
– year: 2007
  ident: 10.1016/j.artint.2017.02.006_br0920
  article-title: SRASS: a semantic relevance axiom selection system
– volume: 11
  start-page: 153
  issue: 2
  year: 2005
  ident: 10.1016/j.artint.2017.02.006_br0100
  article-title: A dialogue game protocol for multi-agent argument over proposals for action
  publication-title: Auton. Agents Multi-Agent Syst.
  doi: 10.1007/s10458-005-1166-x
– year: 2001
  ident: 10.1016/j.artint.2017.02.006_br0600
– year: 2012
  ident: 10.1016/j.artint.2017.02.006_br0900
  article-title: TOAST: online ASPIC+ implementation
– year: 2000
  ident: 10.1016/j.artint.2017.02.006_br0410
  article-title: Rough structure and classification
– start-page: 325
  year: 2003
  ident: 10.1016/j.artint.2017.02.006_br0960
  article-title: The information state approach to dialogue management
– start-page: 135
  year: 1998
  ident: 10.1016/j.artint.2017.02.006_br0080
  article-title: L'argumentació en matemàtiques
– year: 2000
  ident: 10.1016/j.artint.2017.02.006_br0220
– volume: 10
  start-page: 309
  issue: 4
  year: 2012
  ident: 10.1016/j.artint.2017.02.006_br1050
  article-title: A domain specific language for describing diverse systems of dialogue
  publication-title: J. Appl. Log.
  doi: 10.1016/j.jal.2012.09.001
– volume: vol. 4108
  start-page: 208
  year: 2006
  ident: 10.1016/j.artint.2017.02.006_br0030
  article-title: Managing informal mathematical knowledge: techniques from informal logic
– year: 1997
  ident: 10.1016/j.artint.2017.02.006_br1120
– year: 1996
  ident: 10.1016/j.artint.2017.02.006_br1020
– start-page: 69
  year: 2016
  ident: 10.1016/j.artint.2017.02.006_br1070
  article-title: Working on the argument pipeline: through flow issues between natural language argument, instantiated arguments, and argumentation frameworks
– year: 1978
  ident: 10.1016/j.artint.2017.02.006_br0590
– volume: 4
  start-page: 349
  issue: 4
  year: 1980
  ident: 10.1016/j.artint.2017.02.006_br0480
  article-title: Conversation as planned behavior
  publication-title: Cogn. Sci.
  doi: 10.1207/s15516709cog0404_2
– volume: 56
  start-page: 66
  issue: 10
  year: 2013
  ident: 10.1016/j.artint.2017.02.006_br0150
  article-title: Implementing the argument web
  publication-title: Commun. ACM
  doi: 10.1145/2500891
– volume: 88
  start-page: 127
  issue: 2
  year: 1991
  ident: 10.1016/j.artint.2017.02.006_br1140
  article-title: Mathematics has a front and a back
  publication-title: Synthese
  doi: 10.1007/BF00567741
– start-page: 455
  year: 2014
  ident: 10.1016/j.artint.2017.02.006_br0240
  article-title: Argsemsat: solving argumentation problems using SAT
– year: 2014
  ident: 10.1016/j.artint.2017.02.006_br0930
  article-title: Tweety – a comprehensive collection of Java libraries for logical aspects of artificial intelligence and knowledge representation
– start-page: 315
  issue: 13
  year: 2002
  ident: 10.1016/j.artint.2017.02.006_br0640
  article-title: Games that agents play: a formal framework for dialogues between autonomous agents
  publication-title: J. Log. Lang. Inf.
  doi: 10.1023/A:1015586128739
– volume: 171
  start-page: 619
  issue: 10–15
  year: 2007
  ident: 10.1016/j.artint.2017.02.006_br0120
  article-title: Argumentation in artificial intelligence
  publication-title: Artif. Intell.
  doi: 10.1016/j.artint.2007.05.001
– year: 1968
  ident: 10.1016/j.artint.2017.02.006_br1060
– ident: 10.1016/j.artint.2017.02.006_br0330
– volume: 38
  start-page: 11
  year: 1928
  ident: 10.1016/j.artint.2017.02.006_br0440
  article-title: Mathematical proof
  publication-title: Mind
– start-page: 309
  year: 1978
  ident: 10.1016/j.artint.2017.02.006_br1130
  article-title: The logic of mathematical discovery vs. the logical structure of mathematics
– year: 1970
  ident: 10.1016/j.artint.2017.02.006_br0430
– volume: 57
  start-page: 80
  issue: 12
  year: 2014
  ident: 10.1016/j.artint.2017.02.006_br0490
  article-title: Human–agent collectives
  publication-title: Commun. ACM
  doi: 10.1145/2629559
– volume: 30
  start-page: 161
  issue: 2
  year: 1994
  ident: 10.1016/j.artint.2017.02.006_br0940
  article-title: On proof and progress in mathematics
  publication-title: Bull., New Ser., Am. Math. Soc.
  doi: 10.1090/S0273-0979-1994-00502-6
– year: 2013
  ident: 10.1016/j.artint.2017.02.006_br0380
– start-page: 513
  year: 2012
  ident: 10.1016/j.artint.2017.02.006_br0560
  article-title: Dialogues on the argument web: mixed initiative argumentation with Arvina
– year: 1998
  ident: 10.1016/j.artint.2017.02.006_br0010
  article-title: Persuasive definition
– volume: vol. 7961
  start-page: 98
  year: 2013
  ident: 10.1016/j.artint.2017.02.006_br1150
  article-title: Mathematical practice, crowdsourcing, and social machines
– start-page: 39
  year: 2013
  ident: 10.1016/j.artint.2017.02.006_br0110
  article-title: The value of values in computational argumentation
– volume: 21
  start-page: 293
  issue: 4
  year: 2006
  ident: 10.1016/j.artint.2017.02.006_br0250
  article-title: Towards an argument interchange format
  publication-title: Knowl. Eng. Rev.
  doi: 10.1017/S0269888906001044
– year: 2009
  ident: 10.1016/j.artint.2017.02.006_br1040
– volume: 9
  start-page: 101
  issue: 1
  year: 2016
  ident: 10.1016/j.artint.2017.02.006_br0180
  article-title: Hammering towards QED
  publication-title: J. Formaliz. Reason.
– year: 2009
  ident: 10.1016/j.artint.2017.02.006_br0820
  article-title: The argument interchange format
– volume: 61
  start-page: 3
  year: 2011
  ident: 10.1016/j.artint.2017.02.006_br0210
  article-title: Automated theorem provers: a practical tool?
  publication-title: Ann. Math. Artif. Intell.
  doi: 10.1007/s10472-011-9248-8
– volume: 30
  start-page: 161
  issue: 2
  year: 1994
  ident: 10.1016/j.artint.2017.02.006_br1190
  article-title: On proof and progress in mathematics
  publication-title: Bull., New Ser., Am. Math. Soc.
  doi: 10.1090/S0273-0979-1994-00502-6
– start-page: 221
  year: 1983
  ident: 10.1016/j.artint.2017.02.006_br0460
  article-title: Using proofs and refutations to learn from experience
– start-page: 342
  year: 2005
  ident: 10.1016/j.artint.2017.02.006_br0360
  article-title: Natural language proof explanation
– volume: 27
  issn: 1465-2978
  year: 2013
  ident: 10.1016/j.artint.2017.02.006_br0710
  article-title: A computational model of Lakatos-style reasoning
  publication-title: Philos. Math. Educ. J.
– year: 1981
  ident: 10.1016/j.artint.2017.02.006_br0760
– start-page: 905
  year: 2011
  ident: 10.1016/j.artint.2017.02.006_br0170
  article-title: Choosing persuasive arguments for action
– start-page: 91
  year: 1970
  ident: 10.1016/j.artint.2017.02.006_br0540
  article-title: Falsification and the methodology of scientific research programmes
– year: 1976
  ident: 10.1016/j.artint.2017.02.006_br0550
– year: 2009
  ident: 10.1016/j.artint.2017.02.006_br1010
– volume: 5
  start-page: 31
  issue: 1
  year: 2014
  ident: 10.1016/j.artint.2017.02.006_br0660
  article-title: The ASPIC+ framework for structured argumentation: a tutorial
  publication-title: Argument Comput.
  doi: 10.1080/19462166.2013.869766
– volume: 28
  start-page: 99
  issue: 1
  year: 1997
  ident: 10.1016/j.artint.2017.02.006_br1110
  article-title: Assaying Lakatos's philosophy of mathematics
  publication-title: Stud. Hist. Philos. Sci.
  doi: 10.1016/S0039-3681(96)00002-7
– year: 1979
  ident: 10.1016/j.artint.2017.02.006_br0950
– year: 2010
  ident: 10.1016/j.artint.2017.02.006_br1180
– volume: 195
  start-page: 528
  year: 2013
  ident: 10.1016/j.artint.2017.02.006_br0510
  article-title: Modeling information exchange opportunities for effective human–computer teamwork
  publication-title: Artif. Intell.
  doi: 10.1016/j.artint.2012.11.007
– start-page: 2329
  year: 2005
  ident: 10.1016/j.artint.2017.02.006_br0200
  article-title: The nature of mathematical proof
– year: 2014
  ident: 10.1016/j.artint.2017.02.006_br0520
  article-title: Defeasible reasoning
– volume: 77
  start-page: 321
  issue: 2
  year: 1995
  ident: 10.1016/j.artint.2017.02.006_br0320
  article-title: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games
  publication-title: Artif. Intell.
  doi: 10.1016/0004-3702(94)00041-X
– volume: 125
  start-page: 177
  issue: 497
  year: 2016
  ident: 10.1016/j.artint.2017.02.006_br0690
  article-title: What's the point of complete rigour?
  publication-title: Mind
  doi: 10.1093/mind/fzv140
– start-page: 447
  year: 2010
  ident: 10.1016/j.artint.2017.02.006_br0880
  article-title: Pipelining argumentation technologies
– volume: 14
  start-page: 1
  issue: 1–2
  year: 2009
  ident: 10.1016/j.artint.2017.02.006_br0050
  article-title: Mathematics and argumentation
  publication-title: Found. Sci.
  doi: 10.1007/s10699-008-9158-3
– start-page: 2401
  year: 2005
  ident: 10.1016/j.artint.2017.02.006_br0090
  article-title: Highly complex proofs and implications of such proofs
– volume: vol. 30
  year: 2013
  ident: 10.1016/j.artint.2017.02.006_br0070
  article-title: The Argument of Mathematics
– volume: 42
  start-page: 23065
  issue: 2
  year: 1937
  ident: 10.1016/j.artint.2017.02.006_br0980
  article-title: On Computable Numbers, with an Application to the Entscheidungs problem
  publication-title: Proc. Lond. Math. Soc.
– start-page: 170
  year: 2010
  ident: 10.1016/j.artint.2017.02.006_br0290
– volume: 33
  start-page: 395
  issue: 4
  year: 2004
  ident: 10.1016/j.artint.2017.02.006_br0740
  article-title: Multi-agent systems and game theory—a peircean manifesto
  publication-title: Int. J. Gen. Syst.
  doi: 10.1080/0308107042000193552
– year: 2011
  ident: 10.1016/j.artint.2017.02.006_br0060
  article-title: The dialectical tier of mathematical proof
– volume: vol. 6898
  year: 2011
  ident: 10.1016/j.artint.2017.02.006_br0400
  article-title: Advances in the Formalization of the Odd Order Theorem
– start-page: 141
  year: 2014
  ident: 10.1016/j.artint.2017.02.006_br0140
  article-title: Generalising argument dialogue with the dialogue game execution platform
– start-page: 59
  year: 2010
  ident: 10.1016/j.artint.2017.02.006_br0190
  article-title: Dialogues with conflict resolution: goals and effects
– year: 1996
  ident: 10.1016/j.artint.2017.02.006_br1000
– volume: 4
  start-page: 42
  issue: 1
  year: 1988
  ident: 10.1016/j.artint.2017.02.006_br0340
  article-title: Learning and discovery: one system's search for mathematical knowledge
  publication-title: Comput. Intell.
  doi: 10.1111/j.1467-8640.1988.tb00089.x
– volume: 221
  start-page: 36
  year: 2015
  ident: 10.1016/j.artint.2017.02.006_br0350
  article-title: Wanted: collaborative intelligence
  publication-title: Artif. Intell.
  doi: 10.1016/j.artint.2014.12.006
– start-page: 2335
  year: 2005
  ident: 10.1016/j.artint.2017.02.006_br0610
  article-title: Computing and the cultures of proving
– year: 1995
  ident: 10.1016/j.artint.2017.02.006_br1030
– year: 2009
  ident: 10.1016/j.artint.2017.02.006_br0310
  article-title: Strategic argumentation in rigorous persuasion dialogue
– ident: 10.1016/j.artint.2017.02.006_br0530
  doi: 10.1007/978-94-007-6534-4_3
– volume: vol. 7961
  start-page: 98
  year: 2013
  ident: 10.1016/j.artint.2017.02.006_br0630
  article-title: Mathematical practice, crowdsourcing, and social machines
– volume: 13
  start-page: 259
  issue: 2
  year: 1989
  ident: 10.1016/j.artint.2017.02.006_br0260
  article-title: Contributing to discourse
  publication-title: Cogn. Sci.
  doi: 10.1207/s15516709cog1302_7
– start-page: 515
  year: 2012
  ident: 10.1016/j.artint.2017.02.006_br0570
  article-title: AIFdb: Infrastructure for the argument web
– volume: 6
  start-page: 1
  issue: 1
  year: 1958
  ident: 10.1016/j.artint.2017.02.006_br0860
  article-title: Heuristic problem solving: the next advance in operations research
  publication-title: Oper. Res.
  doi: 10.1287/opre.6.1.1
– volume: vol. 5
  start-page: 135
  year: 2007
  ident: 10.1016/j.artint.2017.02.006_br0040
  article-title: The informal logic of mathematical proof
– year: 2014
  ident: 10.1016/j.artint.2017.02.006_br0840
– year: 1969
  ident: 10.1016/j.artint.2017.02.006_br0850
– volume: 172
  start-page: 2015
  issue: 18
  year: 2008
  ident: 10.1016/j.artint.2017.02.006_br0870
  article-title: The well-designed young mathematician
  publication-title: Artif. Intell.
  doi: 10.1016/j.artint.2008.09.004
– start-page: 19
  year: 2012
  ident: 10.1016/j.artint.2017.02.006_br1170
  article-title: Seventy four minutes of mathematics: an analysis of the third mini-polymath project
– volume: 7
  start-page: 1
  issue: 1
  year: 2013
  ident: 10.1016/j.artint.2017.02.006_br0730
  article-title: From argument diagrams to argumentation mining in texts: a survey
  publication-title: Int. J. Cog. Inform. Nat. Intell.
  doi: 10.4018/jcini.2013010101
– start-page: 1141
  year: 2013
  ident: 10.1016/j.artint.2017.02.006_br0810
  article-title: A formalisation of argumentation schemes for case-based reasoning in ASPIC+
  publication-title: J. Log. Comput.
– volume: 155
  start-page: 341
  year: 2006
  ident: 10.1016/j.artint.2017.02.006_br0300
  article-title: Hiproofs: a hierarchical notion of proof tree
  publication-title: Electron. Notes Theor. Comput. Sci.
  doi: 10.1016/j.entcs.2005.11.063
– volume: 1
  year: 2010
  ident: 10.1016/j.artint.2017.02.006_br0800
  article-title: An abstract framework for argumentation with structured arguments
  publication-title: Argument Comput.
  doi: 10.1080/19462160903564592
– volume: 19
  start-page: 287
  year: 2005
  ident: 10.1016/j.artint.2017.02.006_br0020
  article-title: The uses of argument in mathematics
  publication-title: Argumentation
  doi: 10.1007/s10503-005-4417-8
– volume: vol. 9577
  start-page: 10
  year: 2016
  ident: 10.1016/j.artint.2017.02.006_br0370
  article-title: The SENSEI project: making sense of human conversations
– start-page: 269
  year: 2003
  ident: 10.1016/j.artint.2017.02.006_br0650
  article-title: Dialogue game protocols
SSID ssj0003991
Score 2.3585162
Snippet The simulation of mathematical reasoning has been a driving force throughout the history of Artificial Intelligence research. However, despite significant...
SourceID proquest
crossref
elsevier
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 181
SubjectTerms Abstract argumentation
Argumentation
Automated reasoning
Automated theorem proving
Collaboration
Collaborative intelligence
Computer simulation
Dialogue games
Game theory
Lakatos
Logic
Mathematical analysis
Mathematical argument
Mathematical models
Mathematics
Philosophy of mathematical practice
Reasoning
Semantics
Social creativity
Social factors
Structured argumentation
Theorem proving
Title Lakatos-style collaborative mathematics through dialectical, structured and abstract argumentation
URI https://dx.doi.org/10.1016/j.artint.2017.02.006
https://www.proquest.com/docview/1916363705
Volume 246
WOSCitedRecordID wos000399844800008&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVESC
  databaseName: Elsevier SD Freedom Collection Journals 2021
  customDbUrl:
  eissn: 1872-7921
  dateEnd: 20180131
  omitProxy: false
  ssIdentifier: ssj0003991
  issn: 0004-3702
  databaseCode: AIEXJ
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3Pb9MwFLaqjQMXfiPGBvKB2wiKY8dxjgUNAZomDkPqzXIcBzG6bErSbuMv4c_l-UfStAPGDhwatVFjpf2-fn52v_ceQq8MS0tiEhppEZcR0zyPCs1oxDVLFSeFIsolCh9mR0diNss_TyY_-1yY5Tyra3F5mZ__V6jhHIBtU2dvAfcwKJyA5wA6HAF2OP4T8IfK5gS1Udtdza0VfcB5ab2qfZHWdujQYzNHrOppV_p_3xeUXVhbuqvjWti9EN3tq-br4jQkKtXjkHbaOLuRa_4xqu850lzfu3E6t8alwQCkLlye4aYd-O2i_HFVt99DplqnGni5chOdNbXxCd3hr4vRpgVMhINFcBBiBtoWrwlxwsZSSnwrlzArB2G9Jvh-7-Hkjau5YL2xJPM1WH9TX3tj3hvciL3R7UT6UaQdRcaJdLXct5MszUEvt6cfD2afhlkeArvQjdF_kD4t03kHr9_Nn8KejQDARTXHD9C9sBzBU0-jh2hi6kfoft_qAwflf4yKNVbhNVbhEatwYBUeseo1XnEKA6dwzym8xqkn6Mv7g-N3H6LQniPSVMRdlOhMqZixpIQHF4bxWOdVCadKBcJQ0qpSeSkKWGMYkZUsUyk1WQwLfsqYrgh9irbqs9o8Q1iRquJEw-JBcJYbmjMC0sFtknfCqRY7iPbfntShdr1toTKXf8NuB0XDVee-dssN7896YGSIP31cKYFtN1y51-MogxS0ksDKi3LgRvr8ljeyi-6ufjR7aAtAMi_QHb3svrXNy8DEX1WKuZQ
linkProvider Elsevier
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%3Ajournal&rft.genre=article&rft.atitle=Lakatos-style+collaborative+mathematics+through+dialectical%2C+structured+and+abstract+argumentation&rft.jtitle=Artificial+intelligence&rft.au=Pease%2C+Alison&rft.au=Lawrence%2C+John&rft.au=Budzynska%2C+Katarzyna&rft.au=Corneli%2C+Joseph&rft.date=2017-05-01&rft.issn=0004-3702&rft.volume=246&rft.spage=181&rft.epage=219&rft_id=info:doi/10.1016%2Fj.artint.2017.02.006&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_artint_2017_02_006
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0004-3702&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0004-3702&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0004-3702&client=summon