This page contains references to papers that lack associated software. For software, see also this listing. The purpose of these references is to contextualize the Physics Derivation Graph.

Citation | Comment | Domain | Semantic Enrichment |
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@article{2023_Cornelio, title={Combining data and theory for derivable scientific discovery with AI-Descartes}, author = {C.~Cornelio and S.~Dash and V.~Austel and T.~R.~Josephson and J.~Goncalves, K.~L.~Clarkson and N.~Megiddo and B.~El~Khadir and L.~Horesh}, year = {2023}, journal = {Nat. Commun.}, volume = {17} url = {https://doi.org/10.1038/s41467-023-37236-y} | Machine Learning of Mathematical Physics | ||

@article{2023_Bobbin, title={Formalizing Chemical Theory Using the Lean Theorem Prover}, author = {M.~P.~Bobbin and S.~Sharlin and P.~Feyzishendi and A.~H.~Dang and C.~M.~Wraback and T.~R.~Josephson} year = {2023}, url = {https://arxiv.org/abs/2210.12150} | |||

@article{2022_Lemos, title = {Rediscovering orbital mechanics with machine learning}, author = {P.~Lemos and N.~Jeffrey and M.~Cranmer and S.~Ho and P.~Battaglia}, year = {2022}, url = {https://arxiv.org/abs/2202.02306} } |
Neural network and symbolic regression See also this twitter thread |
Science | No |

@book{1998_Wilson_Consilience, title = {Consilience: The Unity of Knowledge}, author = {Edward O. Wilson}, year = {1998}, url = {https://en.wikipedia.org/wiki/Consilience_(book)}, note = {Tackles "the synthesis of knowledge from different specialized fields of human endeavor."} } |
Science offers the boldest metaphysics of the age. It is a thoroughly human construct, driven by the faith that if we dream, press to discover, explain, and dream again, thereby plunging repeatedly into new terrain, the world will somehow come clearer and we will grasp the true strangeness of the universe. |
Science | No |

@article{2002_Hestenes, title = {Oersted Medal Lecture 2002: Reforming the Mathematical Language of Physics}, author = {D.~Hestenes}, year = {2002}, url = {} } |
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@book{1913_whiteheadrussell, title = {Principia Mathematica}, author = {Whitehead and Russell}, year = {1913}, url = {https://en.wikipedia.org/wiki/Principia_Mathematica; https://plato.stanford.edu/entries/principia-mathematica/}, note = {famous for proof of 1+1=2} } |
The ambitious effort of Whitehead and Russell to prove the foundations of
mathematics is not similar to the Physics Derivation Graph.
"Proof" doesn't apply in Physics. The Physics Derivation Graph is about documenting existing knowledge in a format which can be parsed by computers. |
Math | No |

@article{2018_Patterson, title = {Teaching machines to understand data science code by semantic enrichment of dataflow graphs}, author = {E. Patterson and I. Baldini and A. Mojsilovic and K. Varshney}, year= {2018} } |
machine-oriented controlled natural language, MONoidal Ontology and Computing Language (Monocl) for parsing software. | CNL | No |

@article{2021_Bucur_Kuhn, title = {Expressing High-level Scientific Claims with Formal Semantics}, author = {C.~Bucur and D.~Ceolin and T.~Kuhn and J.~van~Ossenbruggen}, year= {2021}, url={https://arxiv.org/pdf/2109.12907.pdf} } |
machine-oriented controlled natural language, MONoidal Ontology and Computing Language (Monocl) for parsing software. | CNL | No |

@article{2009_kuhn, title = {How to Evaluate Controlled Natural Languages}, author = {T.~Kuhn}, year = {2009}, url = {} } |
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@article{2019_Kohlhase_Rabe, title = {Big Math and the One-Brain Barrier}, author = {J.~Carette and W.~M.~Farmer and M.~Kohlhase and F.~Rabe}, year = {2019}, url = {https://arxiv.org/abs/1904.10405} } |
Clear writing. Broad survey of efforts in formalizing math. | ||

@article{2008_kuhn_schwitter, title = {Writing Support for Controlled Natural Languages}, author = {T.~Kuhn and R.~Schwitter}, year = {2008}, url = {} } |
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@presentation{2010_Schwitter, title = {Controlled Natural Languages for Knowledge Representation}, author = {R.~Schwitter}, year = {2010}, url = {schwitter_tutorial.pdf} } |
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@article{2008_Kuhn_eval, title = {An Evaluation Framework for Controlled Natural Languages}, author = {T.~Kuhn}, year = {2008}, url = {} } |
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@article{2014_Kuhn_survey, title = {A Survey and Classification of Controlled Natural Languages}, author = {T.~Kuhn}, year = {2014}, url = {} } |
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@article{2018_Kuhn, title = {Using the AIDA language to formally organize scientific claims}, author = {T. Kuhn}, year= {2018}, isbn = {978-1-61499-903-4}, doi = {10.3233/978-1-61499-904-1-52}, url = {https://ebooks.iospress.nl/} } |
human-oriented controlled natural language for scientific claims | CNL | No |

@article{2017_Cvjetkovic, title = {Web physics ontology: online interactive symbolic computation in physics}, author = {V.~Cvjetkovic}, year= {2017}, pages = {52--57}, url = {http://physics.kg.ac.rs} } |
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@article{2017_Gross, title = {Math and Physics using SymPy}, author = {Gross}, year = {2017}, url = {} } |
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@article{1961_Bergmann, title = {Physics and Ontology}, author = {G.~Bergmann}, year= {1961}, journal = {Philosophy of Science}, pages = {1--14}, url = {https://www.jstor.org/stable/185460} } |
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@article{2014_Collins_Clark, title = {Towards an Ontology of Physics}, author = {J.~B.~Collins and D.~Clark}, year= {2014}, url = {} } |
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@article{2004_Collins, title = {Standardizing an Ontology of Physics for Modeling and Simulation}, author = {J.~B.~Collins}, year= {2004}, url = {https://apps.dtic.mil/sti/pdfs/ADA610086.pdf} } |
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@article{2018_Schubotz, title = {Improving the Representation and Conversion of Mathematical Formulae by Considering their Textual Context}, author = {M. Schubotz and A. Greiner-Petter and P. Scharpf and N. Meuschke and H. S. Cohl and B. Gipp}, year= {2018}, url = {https://arxiv.org/pdf/1804.04956.pdf} } |
Math | ||

@article{2013_Cramer, title = {Proof-checking mathematical texts in controlled natural language}, author = {M. Cramer}, year= {2013}, url = {https://icr.uni.lu/mcramer/downloads/doktor.pdf}, note = {origin of Naproche} } |
Math | ||

@article{2013_Cramer, title = {The Naproche Project Controlled Natural Language Proof Checking of Mathematical Texts}, author = {M. Cramer and P. Koepke and D. Kuhlwein and B. Schroder and J. Veldman}, year= {2013}, url = {http://ceur-ws.org/Vol-448/paper10.pdf} } |
Math | ||

@article{2020_Kaliszyk_Rabe, title = {A Survey of Languages for Formalizing Mathematics}, author = {C. Kaliszyk and F. Rabe}, year= {2020}, url = {https://arxiv.org/pdf/2005.12876.pdf} } |
Math | Yes | |

@article{2005_Brandes, title = {GXL to GraphML and Vice Versa with XSLT}, author = {U.~Brandes and J.~Lerner and C.~Pich}, year = {2005}, url = {} } |
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@article{2000_Sowa, title = {Knowledge Representation: Logical, Philosophical, and Computational Foundations}, author = {J.~Sowa}, year = {2000}, url = {} } |
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@book{1994_Chou, title = {Machine Proofs in Geometry: Automated Production of Readable Proofs in Geometry}, author = {S.-C.~Chou and X.-S.~Gao and J.-Z.~Zhang}, year = {1994}, url = {} } |
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@chapter{1997_zeman, title = {The Tinctures and Implicit Quantification over Worlds}, author = {J.~Zeman}, year = {1997}, pages = {96--119} url = {} } |
Ruminations on how C.S. Peirce would use a computer for math diagrams. | ||

@article{2000_Wiedijk, title = {The De Bruijn Factor}, author = {F.~Wiedijk}, year= {2000}, url = {; }, note = {de Bruijn factor is the quotient of the size of a formalization of a mathematical text and the size of its informal original.} } |
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@article{1994_de_Bruijn, title = {A survey of the project Automath}, author = {N. G. de Bruijn}, year= {1994} } |
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@article{2007_Wiedijk, title = {The QED Manifesto Revisited}, author = {F.~Wiedijk}, year = {2007}, url = {http://mizar.org/trybulec65/8.pdf; https://www.cs.ru.nl/~freek/pubs/qed2.pdf} } |
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@article{2016_Hinsen, title = {Leibniz: A Digital Scientific Notation}, author = {K.~Hinsen}, year = {2016}, url = {} } |
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@thesis{2006_wu, title = {Authoring XML documents with XHTML and MathML support}, author = {X.~Wu}, year = {2006}, url = {} } |
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@unpublished{2009_McKain, title = {}, year = {2009}, author = {D.~McKain}, url = {math-content-conversion; mc09_david_mckain_conversion.pdf} } |
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@article{1997_Caspi, title = {Parsing Mathematics Typeset in Tex}, author = {E.~Caspi}, year = {1997}, url = {} } |
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@book{2009_Chein, author={M.~Chein and M.~Mugnier}, year={2009}, title={Graph-based Knowledge Representation: Computational Foundations of Conceptual Graphs}, publisher={Springer}, ISBN={978-1-84800-285-2} } |
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@article{2008_Sowa, title = {Conceptual Graphs}, author = {J.~F.~Sowa}, year = {2008}, url = {} } |
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@article{1976_Sowa, author={J.~.F.~Sowa}, month={July}, year={1976}, title={Conceptual Graphs for a Data Base Interface}, journal={IBM Journal of Research and Development}, url={http://www.jfsowa.com/pubs/cg1976.pdf}, pages={336–-357} } |
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@article{1979_Sowa, title = {Semantics of Conceptual Graphs}, author = {J.~.F.~Sowa}, year = {1979}, url = {} } |
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@article{1988_Stokman, title = {Structuring Knowledge in a Graph}, author = {F.~N.~Stokman and P.~H.~de~Vries}, year = {1988}, url = {} } |
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@thesis{2013_Barry, title = {Mathlex: a web-based Mathematical Entry System}, author = {M.~J.~Barry}, year = {2013}, url = {} } |
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@article{2012_Lange, author={C.~Lange}, year={2012}, title={Ontologies and Languages for Representing Mathematical Knowledge on the Semantic Web}, url={http://www.semantic-web-journal.net/sites/default/files/swj122_3.pdf} } |
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@article{Kumar, author={N.~Kumar}, year={}, title={Comprehensive Physics XI}, url={https://books.google.com/books?id=Yp6gBq4lXEgC} } |
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@article{2012_Paleo, author={B.~Paleo}, year={2012}, month={Sept}, title={Physics and proof theory}, journal={Appl. Math. Comput.}, doi={10.1016/j.amc.2011.06.058} } |
logic-based; impractical | Logic | No |

@misc{2014_Wolfram, author={S.~Wolfram}, month={August}, year={2014}, title={Computational Knowledge and the Future of Pure Mathematics}, url={blog entry}, pages={336–-357} } |
see the "step-by-step" reference for the closest association with the PDG. | ||

@book{2013_Gellish, author={A. Van Renssen}, month={Nov}, year={2013}, title={Formalized Natural Languages} } |
Author of Gellish
Previous edition was |
knowledge management | no |

@article{2005_Renssen, title = {Gellish: A Generic Extensible Ontological Language}, author = {A.~van~Renssen}, year = {2005}, url = {} } |
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@book{OWL, title = {Ontological Web Language}, author = {}, url = {https://en.wikipedia.org/wiki/Web_Ontology_Language} } |
Data structure for knowledge | Data structure syntax | Yes |

@article{1968_Suppes, title = {The Desirability of Formalization in Science}, author = {P. Suppes}, year = {1968}, journal = {Journal of Philosophy}, volume = {65}, pages = {651--664} } |
Argues for a set-theory-based need for science to support explicitness, standardization, generality, objectivity, self-contained assumptions, and minimal assumptions. | ||

@ARTICLE{2011_Lamport, year={2011}, author={L.~Lamport}, title={How to Write a 21st Century Proof}, url={http://research.microsoft.com/en-us/um/people/lamport/pubs/proof.pdf}, note={http://research.microsoft.com/en-us/um/people/lamport/pubs/pubs.html#lamport-how-to-write} } |
Leslie Lamport math proof notation | ||

@article{2019_Frerix, title = {Making Set Theory Great Again: the Naproche-SAD project}, author = {Frerix}, year = {2019}, url = {} } |
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@article{1993_Boyer, title = {QED manifesto}, author = {R. Boyer}, year = {1993}, url = {https://en.wikipedia.org/wiki/QED_manifesto; https://www.cs.ru.nl/~freek/qed/qed.html} } |
Content after 1994 is likely based on or influenced by the QED manifesto, so that is useful to read.
Goal: To build a computer system that effectively represents all important mathematical knowledge and techniques. The QED system will conform to the highest standards of mathematical rigor, including the use of strict formality in the internal representation of knowledge and the use of mechanical methods to check proofs of the correctness of all entries in the system. |
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@article{2012_Zanibbi, title = {Recognition and Retrieval of Mathematical Expressions}, author = {R.~Zanibbi and D.~Blostein}, year = {2012}, url = {} } |
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@article{2020_Kirillovich, title = {OntoMathEdu: a Linguistically Grounded Educational Math Ontology}, author = {A.~Kirillovich and O.~Nevzorova and M.~Falileeva and E.~Lipachev and L.~Shakirova}, year = {2020}, url = {} } |
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@article{2003_Strotmann, title = {Content Markup Language Design Principles}, author = {A.~Strotmann}, year = {2003}, url = {} } |
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@article{2020_DeLon, title = {Integrating ForTheL with Latex}, author = {A.~De~Lon}, year = {2020}, url = {} } |
CICM 2020 | ||

@article{2020_Kirillovich_ecosystem, title = {OntoMath Digital Ecosystem}, author = {A.~Kirillovich}, year = {2020}, url = {} } |
CICM 2020 | ||

@article{2007_Groza, title = {SALT - Semantically Annotated LaTeX for Scientific Publications}, author = {T.~Groza and S.~Handschuh and K.~Moller and S.~Decker}, year = {2007}, volume = {4519}, pages = {518--532}, url = {springer.com} } |
focuses on decorators like "claim" and "explanation." No suggestion of handling mathematics. | ||

@article{2019_Asakura, title = {Understanding Scientific Documents with Synthetic Analysis on Mathematical Expressions and Natural Language}, author = {T.~Asakura}, year = {2019}, url = {} } |
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@article{2001_Fateman, title = {A Critique of OpenMath and Thoughts on Encoding Mathematics}, author = {R.~Fateman}, year = {2001}, url = {} } |
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@proceedings{1994_Boyer, title = {The QED Manifesto}, author = {R.~Boyer}, journal = {Automated Deduction - CADE 12} volume = {814} year = {1994}, pages = {238--251}, url = {} } |
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@article{1994_Thurston, title = {On Proof and Progress in Mathematics}, author = {W.~P.~Thurston}, year = {1994}, url = {https://arxiv.org/abs/math/9404236v1} } |
response to "Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics" | ||

@article{1993_Jaffe_Quinn, title = {Theoretical mathematics: Toward a cultural synthesis of mathematics and theoretical physics}, author = {A.~Jaffe and F.~Quinn}, year = {1993}, url = {https://arxiv.org/abs/math/9307227} } |
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@article{2016_Weiss, title = {The QED Manifesto after Two Decades -- Version 2.0}, author = {Weiss}, year = {2016}, url = {source} } |
Describes "Mathropolis" and a "mathematical content markup language"
A non-CAS based metalanguage is attempted in "The QED Manifesto after Two Decades -- Version 2.0"
The paper discusses Mathropolis, which is intended to optimize for readability over formality.
The paper describes a "mathematical content markup language" and provides an example.
In email conversation with Weiss, he said, "I started fleshing out some code but when I realised the extent of the project is huge and that it would consume my maths research I decided to stop."He also said, "I still think that the idea of MCML would be extremely helpful in academia and particularly in subjects such as mathematics and physics (and others)." |
Math | |

@article{2003_Stuber_Brand, title = {Extracting mathematical semantics from LATEX documents}, author = {J. Stuber and M. Brand}, year = {2003}, url = {semanticscholar.org} } |
Document Markup and Enrichment | ||

@article{2015_Moore, title = {Semantic Enrichment of Mathematics via tooltips}, author = {Moore}, year = {2015}, url = {https://tug.org/tug2015/preprints/moore-mathsem-cicm2015-v7.pdf} } |
"mathsem" source code not found online | Document Markup and Enrichment | |

@article{2019_Szegedy, title = {Graph Representations for Higher-Order Logic and Theorem Proving}, author = {C. Szegedy and }, year = {2019} } |
comment thread: https://news.ycombinator.com/item?id=24389058 This paper is not related to the Physics Derivation Graph as far as I can tell. |
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@article{2009_redish_gupta, title = {Making Meaning with Math in Physics: A semantic analysis}, author = {E. F. Redish and A. Gupta}, year = {2009}, url = {https://arxiv.org/abs/1002.0472} } |
Document Markup and Enrichment |

Derivation sites to assess:

- http://www.dfcd.net/articles/derivations/derivations.html
- https://physics.info/
- Wiki pages with "Derivation" in title
- Wiki pages with "Derive" in title

Quotations

There is nothing that can be said by mathematical symbols and relations which cannot also be said by words. The converse, however, is false. Much that can be and is said by words cannot be put into equations – because it is nonsense.