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Developing Corpus-based Translation Methods between Informal and Formal Mathematics: Project Description
[article]

2014
*
arXiv
*
pre-print

The goal of this

arXiv:1405.3451v1
fatcat:iskrxhcukzh2fn7ihk7n4vasyu
*project*is to (i) accumulate annotated*informal*/*formal**mathematical*corpora suitable for training semi-automated*translation**between**informal**and**formal**mathematics*by statistical machine-*translation*...*methods*, (ii) to*develop*such*methods*oriented at the*formalization*task,*and*in particular (iii) to combine such*methods*with learning-assisted automated reasoning that will serve as a strong semantic ... We have already written programs that collect the links*between*the*informal**and**formal*Flyspeck parts (theorems*and*definitions),*and*used such annotations for example for the joint*informal*/*formal*HTML ...##
###
Developing Corpus-Based Translation Methods between Informal and Formal Mathematics: Project Description
[chapter]

2014
*
Lecture Notes in Computer Science
*

The goal of this

doi:10.1007/978-3-319-08434-3_34
fatcat:o75tw3gz2rh7pawh355d7anlga
*project*4 is to (i) accumulate annotated*informal*/*formal**mathematical*corpora suitable for training semi-automated*translation**between**informal**and**formal**mathematics*by statistical machinetranslation ...*methods*, (ii) to*develop*such*methods*oriented at the*formalization*task,*and*in particular (iii) to combine such*methods*with learning-assisted automated reasoning that will serve as a strong semantic ... We have already written programs that collect the links*between*the*informal**and**formal*Flyspeck parts (theorems*and*definitions),*and*used such annotations for example for the joint*informal*/*formal*HTML ...##
###
Machine Translation of Mathematical Text

2021
*
IEEE Access
*

We have trained a Transformer-

doi:10.1109/access.2021.3063715
fatcat:7qkivd7e2fhcrir7pwj4frpliy
*based**translator*model, using OpenNMT, on a combined*corpus*containing a small proportion of domain-specific sentences. ... We have published our test*corpus*of*mathematical*text. The PolyMath*Translator*is available as a web service at www.polymathtrans.ai. ... ACKNOWLEDGMENT The authors thank Blair Drummond for suggesting the use of pandoc,*and*Monica Nevins for contributing the source material for our ''linear code''*corpus*. ...##
###
Classification of Alignments Between Concepts of Formal Mathematical Systems
[chapter]

2017
*
Lecture Notes in Computer Science
*

*Mathematical*knowledge is publicly available in dozens of different formats

*and*languages, ranging from

*informal*(e.g. Wikipedia) to

*formal*corpora (e.g., Mizar). ... proofs from different

*formal*proof libraries or semi-

*formal*libraries even if the latter is

*based*on a different

*mathematical*foundation. ... Acknowledgements We were supported by the German Science Foundation (DFG) under grants KO 2428/13-1

*and*RA-1872/3-1, the Austrian Science Fund (FWF) grant P26201,

*and*the ERC starting grant no. 714034 ...

##
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Machine Translation of Mathematical Text
[article]

2020
*
arXiv
*
pre-print

We have trained a Transformer-

arXiv:2010.05229v1
fatcat:eve2k74pt5hetnmqglw3ipd2cy
*based**translator*model, using OpenNMT, on a combined*corpus*containing a small proportion of domain-specific sentences. ... The current implementation*translates*English LaTeX to French LaTeX, attaining a BLEU score of 53.5 on a held-out test*corpus*of*mathematical*sentences. ... in the related areas of*mathematical*ontology*and*semantics [25]*and**translation*from*informal**mathematical*writing into*formal**mathematics*[23] . ...##
###
Theorem Proving in Large Formal Mathematics as an Emerging AI Field
[article]

2012
*
arXiv
*
pre-print

In the recent years, we have linked a large

arXiv:1209.3914v2
fatcat:cu7sqlillra5pm4akx4p7kh6pe
*corpus*of*formal**mathematics*with automated theorem proving (ATP) tools,*and*started to*develop*combined AI/ATP systems working in this setting. ... In this paper we first relate this*project*to the earlier large-scale automated*developments*done by Quaife with McCune's Otter system,*and*to the discussions of the QED*project*about*formalizing*a significant ... A*translates*the queries*and**information*produced by P to the*formalism*used by a particular E,*and**translates*E's guidance back to the*formalism*used by P. ...##
###
Engineering Mathematical Knowledge
[chapter]

2006
*
Lecture Notes in Computer Science
*

In this paper, we combine the

doi:10.1007/11618027_17
fatcat:cj2apveytjae5ee2vufrvtzina
*projects*MMiSS 3*and*CDET. 4 That way, we achieve major benefits for*mathematical*knowledge management: (1) Semantic annotations relate*mathematical*constructs. ... This reaches beyond*mathematics**and*thus fosters integration of*mathematical*content into a broader context. (2) Fine-grained version control enables change management*and*configuration management. (3) ... Approaches for representing*and**formalizing*the dependencies*between**formal*parts of*mathematical*documents*and*their*informal*counterparts are needed but rarely found (the HELM approach described in ...##
###
Formal Mathematics on Display: A Wiki for Flyspeck
[chapter]

2013
*
Lecture Notes in Computer Science
*

Such

doi:10.1007/978-3-642-39320-4_10
fatcat:vgqco7drfrfd3jyi7iqlxkthdm
*informal*pages may contain islands of*formal*text, which is used here for providing an initial cross-linking*between*Hales's*informal*Flyspeck book,*and*the*formal*Flyspeck*development*. ... The Agora system is a prototype "Wiki for*Formal**Mathematics*", with an aim to support*developing**and*documenting large*formalizations*of*mathematics*in a proof assistant. ... in L A T E X [11] contains explicit connections*between*the*informal**mathematics**and*the related*formal*concepts in the*development*. ...##
###
Semi-Automatic Systematic Literature Reviews and Information Extraction of COVID-19 Scientific Evidence: Description and Preliminary Results of the COKE Project

2022
*
Information
*

Trustworthy guidelines should be

doi:10.3390/info13030117
fatcat:aj6vc4ltabgddb2n62jw74hoqa
*based*on a systematic evidence review which uses reproducible analytical*methods*to collect secondary data*and*analyse them. ... The COVID-19 pandemic highlighted the importance of validated*and*updated scientific*information*to help policy makers, healthcare professionals,*and*the public. ...*Informed*Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest. ...##
###
Formal Mathematics on Display: A Wiki for Flyspeck
[article]

2013
*
arXiv
*
pre-print

Such

arXiv:1305.5710v1
fatcat:5uvlra6fofdfpimlq5kahnwm4i
*informal*pages may contain islands of*formal*text, which is used here for providing an initial cross-linking*between*Hales's*informal*Flyspeck book,*and*the*formal*Flyspeck*development*. ... The Agora system is a prototype "Wiki for*Formal**Mathematics*", with an aim to support*developing**and*documenting large*formalizations*of*mathematics*in a proof assistant. ... in L A T E X [14] contains explicit connections*between*the*informal**mathematics**and*the related*formal*concepts in the*development*. ...##
###
The GF Mathematics Library

2012
*
Electronic Proceedings in Theoretical Computer Science
*

We explain the context in which it originated, its current design

doi:10.4204/eptcs.79.6
fatcat:3brclkxfxvhtdaos4sdxr67coi
*and*functionality*and*the current*development*goals. ... We also present two prototype services*and*comment on possible future applications in the area of artificial*mathematics*assistants. ... We are also thankful to Pedro Quaresma for his kind*and*helpful handling of the correspondence concerning this paper. ...##
###
MATHEMATICAL KNOWLEDGE

1976
*
Philosophical Books
*

This thesis will deliver a

doi:10.1111/j.1468-0149.1976.tb01690.x
fatcat:cgilk7w3gjgwncz5fcswubr3f4
*method*for answering questions like the above, using statistical techniques,*and*the basic components of a "lab" for testing claims about*mathematics*learning. ... course*and*in the Peeragogy*project*. ... Computer*Mathematics*introduced me to the work of Vilém Flusser*and*its use in the context of*mathematical*communication 80 ). ...##
###
Mathematical methods for diffusion MRI processing

2009
*
NeuroImage
*

In this article, we review recent

doi:10.1016/j.neuroimage.2008.10.054
pmid:19063977
pmcid:PMC2678879
fatcat:of2nb3nnozhp5dz2uwk5tj5bui
*mathematical*models*and*computational*methods*for the processing of diffusion Magnetic Resonance Images, including state-of-the-art reconstruction of diffusion models, ... We focus on Diffusion Tensor Images (DTI)*and*Q-Ball Images (QBI). ... In this*method*, F c is*based*on a regional*description*of the inner*and*outer compartments: F c = −D f D; D in À Á + D f D; D out À Á = −jj D−D in jj 2 F + jj D−D out jj 2 F ; ð8Þ where D in*and*D out ...##
###
Modelling the way mathematics is actually done

2017
*
Proceedings of the 5th ACM SIGPLAN International Workshop on Functional Art, Music, Modeling, and Design - FARM 2017
*

Whereas

doi:10.1145/3122938.3122942
dblp:conf/icfp/CorneliMMPPN17
fatcat:3avruyjwpnd5nkmjdyl6mtu6jq
*formal**mathematical*theories are well studied, computers cannot yet adequately represent*and*reason about*mathematical*dialogues*and*other*informal*texts. ... To address this gap, we have*developed*a representation*and*reasoning strategy that draws on contemporary argumentation theory*and*classic AI techniques for representing*and*querying narratives*and*dialogues ... The authors acknowledge the financial support of the EPSRC via Ursula Martin's fellowship "The Social Machine of*Mathematics*" (EP/K040251/1). ...##
###
Digitisation, Representation, and Formalisation Digital Libraries of Mathematics
[chapter]

2003
*
Lecture Notes in Computer Science
*

The main ideas presented are about the differences

doi:10.1007/3-540-36469-2_1
fatcat:t4tvenhrvzamraxrvvxivxmvga
*between*digitised*mathematics*, digitally represented*mathematics**and*formalised*mathematics*. ... Given the range of*mathematical**information*to which access is desired,*and*the limited resources available for managing that*information*, we must ensure that these resources are applied to digitise, form ... I would also like to thank the anonymous referees for a number of good suggestions including the list of related EU*project*which have contributed to the*development*of the MKMNet*project*. ...
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