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

Cezary Kaliszyk and Josef Urban and Jiri Vyskocil and Herman Geuvers
2014 arXiv   pre-print
The goal of this 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  ... 
arXiv:1405.3451v1 fatcat:iskrxhcukzh2fn7ihk7n4vasyu

Developing Corpus-Based Translation Methods between Informal and Formal Mathematics: Project Description [chapter]

Cezary Kaliszyk, Josef Urban, Jiří Vyskočil, Herman Geuvers
2014 Lecture Notes in Computer Science  
The goal of this 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  ... 
doi:10.1007/978-3-319-08434-3_34 fatcat:o75tw3gz2rh7pawh355d7anlga

Machine Translation of Mathematical Text

Aditya Ohri, Tanya Schmah
2021 IEEE Access  
We have trained a Transformer-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.  ... 
doi:10.1109/access.2021.3063715 fatcat:7qkivd7e2fhcrir7pwj4frpliy

Classification of Alignments Between Concepts of Formal Mathematical Systems [chapter]

Dennis Müller, Thibault Gauthier, Cezary Kaliszyk, Michael Kohlhase, Florian Rabe
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  ... 
doi:10.1007/978-3-319-62075-6_7 fatcat:25nchzaurjbarpg4rkav4xdztu

Machine Translation of Mathematical Text [article]

Aditya Ohri, Tanya Schmah
2020 arXiv   pre-print
We have trained a Transformer-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] .  ... 
arXiv:2010.05229v1 fatcat:eve2k74pt5hetnmqglw3ipd2cy

Theorem Proving in Large Formal Mathematics as an Emerging AI Field [article]

Josef Urban, Jiri Vyskocil
2012 arXiv   pre-print
In the recent years, we have linked a large 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.  ... 
arXiv:1209.3914v2 fatcat:cu7sqlillra5pm4akx4p7kh6pe

Engineering Mathematical Knowledge [chapter]

Achim Mahnke, Jan Scheffczyk
2006 Lecture Notes in Computer Science  
In this paper, we combine the 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  ... 
doi:10.1007/11618027_17 fatcat:cj2apveytjae5ee2vufrvtzina

Formal Mathematics on Display: A Wiki for Flyspeck [chapter]

Carst Tankink, Cezary Kaliszyk, Josef Urban, Herman Geuvers
2013 Lecture Notes in Computer Science  
Such 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.  ... 
doi:10.1007/978-3-642-39320-4_10 fatcat:vgqco7drfrfd3jyi7iqlxkthdm

Semi-Automatic Systematic Literature Reviews and Information Extraction of COVID-19 Scientific Evidence: Description and Preliminary Results of the COKE Project

Davide Golinelli, Andrea Giovanni Nuzzolese, Francesco Sanmarchi, Luana Bulla, Misael Mongiovì, Aldo Gangemi, Paola Rucci
2022 Information  
Trustworthy guidelines should be 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.  ... 
doi:10.3390/info13030117 fatcat:aj6vc4ltabgddb2n62jw74hoqa

Formal Mathematics on Display: A Wiki for Flyspeck [article]

Carst Tankink, Cezary Kaliszyk, Josef Urban, Herman Geuvers
2013 arXiv   pre-print
Such 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.  ... 
arXiv:1305.5710v1 fatcat:5uvlra6fofdfpimlq5kahnwm4i

The GF Mathematics Library

Jordi Saludes, Sebastian Xambó
2012 Electronic Proceedings in Theoretical Computer Science  
We explain the context in which it originated, its current design 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.  ... 
doi:10.4204/eptcs.79.6 fatcat:3brclkxfxvhtdaos4sdxr67coi

MATHEMATICAL KNOWLEDGE

1976 Philosophical Books  
This thesis will deliver a 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 ).  ... 
doi:10.1111/j.1468-0149.1976.tb01690.x fatcat:cgilk7w3gjgwncz5fcswubr3f4

Mathematical methods for diffusion MRI processing

C. Lenglet, J.S.W. Campbell, M. Descoteaux, G. Haro, P. Savadjiev, D. Wassermann, A. Anwander, R. Deriche, G.B. Pike, G. Sapiro, K. Siddiqi, P.M. Thompson
2009 NeuroImage  
In this article, we review recent 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  ... 
doi:10.1016/j.neuroimage.2008.10.054 pmid:19063977 pmcid:PMC2678879 fatcat:of2nb3nnozhp5dz2uwk5tj5bui

Modelling the way mathematics is actually done

Joseph Corneli, Ursula Martin, Dave Murray-Rust, Alison Pease, Raymond Puzio, Gabriela Rino Nesin
2017 Proceedings of the 5th ACM SIGPLAN International Workshop on Functional Art, Music, Modeling, and Design - FARM 2017  
Whereas 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).  ... 
doi:10.1145/3122938.3122942 dblp:conf/icfp/CorneliMMPPN17 fatcat:3avruyjwpnd5nkmjdyl6mtu6jq

Digitisation, Representation, and Formalisation Digital Libraries of Mathematics [chapter]

Andrew A. Adams
2003 Lecture Notes in Computer Science  
The main ideas presented are about the differences 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.  ... 
doi:10.1007/3-540-36469-2_1 fatcat:t4tvenhrvzamraxrvvxivxmvga
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