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Mathematical Vernacular and Conceptual Well-Formedness in Mathematical Language [chapter]

Zhaohui Luo, Paul Callaghan
1999 Lecture Notes in Computer Science  
The idea of semantic well-formedness in mathematical language is motivated with examples.  ...  The typetheoretic analysis provides a formal semantic basis in the design and implementation of Mathematical Vernacular (MV), a natural language suitable for interactive development of mathematics with  ...  Acknowledgements We would like to thank the following for many useful discussions: Peter Aczel, James McKinna, Aarne Ranta, and members of the Computer Assisted Reasoning Group in Durham.  ... 
doi:10.1007/3-540-48975-4_12 fatcat:5uyytioahfhvfmvocddkyamkre

Page 3844 of Mathematical Reviews Vol. , Issue 2000f [page]

2000 Mathematical Reviews  
“The idea of semantic well-formedness in mathematical language is motivated with examples.  ...  2000f:03015 The type-theoretic analysis provides a formal semantic basis in the design and implementation of mathematical vernacular (MV), a natural language suitable for interactive development of mathemat  ... 

Page 3125 of Mathematical Reviews Vol. , Issue 2000e [page]

2000 Mathematical Reviews  
Alonso Pardo] and David Cabrero, An operational model for parsing definite clause grammars with infinite terms (212-230); Zhaohui Luo and Paul Callaghan, Mathematical vernacular and conceptual well-formedness  ...  in mathematical language (231-250).  ... 

The Mizar Mathematical Library in OMDoc: Translation and Applications

Mihnea Iancu, Michael Kohlhase, Florian Rabe, Josef Urban
2012 Journal of automated reasoning  
As in natural languages, the meaning of an expression is influenced by its (mathematical) context in a way that is natural to humans, but harder to specify for machine manipulation.  ...  The Mizar Mathematical Library is one of the largest libraries of formalized mathematics. Its language is highly optimized for authoring by humans.  ...  Acknowledgements We gratefully acknowledge the contribution of two colleagues in this article: Fulya Horozal for sharing her work on patterns and their elaboration at a very early stage, and Corneliu Prodescu  ... 
doi:10.1007/s10817-012-9271-4 fatcat:rlmbkz7ccrcspeyp7z6rdxs7om

Big Math and the One-Brain Barrier A Position Paper and Architecture Proposal [article]

Jacques Carette and William M. Farmer and Michael Kohlhase and Florian Rabe
2019 arXiv   pre-print
narration around a well-organized core of mathematical knowledge.  ...  The challenge for mathematical software systems is that these four aspects need to be integrated as well. We briefly survey the state of the art.  ...  Acknowledgments The authors gratefully acknowledge fruitful discussions with many of our colleagues in the mechanized mathematics community.  ... 
arXiv:1904.10405v2 fatcat:xo5v2h6xdbhuvm6d3xfhuwpt4q

Toward an Object-Oriented Structure for Mathematical Text [chapter]

Fairouz Kamareddine, Manuel Maarek, J. B. Wells
2006 Lecture Notes in Computer Science  
For this reason, we have been developing MathLang, a language for representing mathematical texts that has weak type checking and support for the special mathematical use of natural language.  ...  We have restructured and simplified the core of the language, replaced our old notion of "context" by a new system of blocks and local scoping, and made other changes.  ...  Computerizing the mathematical vernacular. N.  ... 
doi:10.1007/11618027_15 fatcat:zkeydsxphrgt5npmc3gmkrrhwe

Big Math and the One-Brain Barrier: The Tetrapod Model of Mathematical Knowledge

Jacques Carette, William M. Farmer, Michael Kohlhase, Florian Rabe
2020 The Mathematical intelligencer  
are traditionally expressed in a natural language: mathematical vernacular [10] , a stylized form of English with interspersed mathematical formulas, tables, and diagrams.  ...  In mathematics, vertical tasks include the exploration, conceptualization, and intuitive understanding of mathematical theories and the production of mathematical insights, conjectures, and proofs from  ... 
doi:10.1007/s00283-020-10006-0 fatcat:bxwdexjey5h5zo2nnfxpd7cmju

A Refinement of de Bruijn's Formal Language of Mathematics

Fairouz Kamareddine, Rob Nederpelt
2004 Journal of Logic, Language and Information  
WTT is a refinement of de Bruijn's Mathematical Vernacular (MV) and hence: WTT is faithful to the mathematician's language yet is formal and avoids ambiguities.  ...  The derivation system allows one to establish that a book written in WTT is well-formed following the syntax of WTT, and has great resemblance with ordinary mathematics books.  ...  This vernacular is a formally defined language meant for the development of mathematical theories and to prove specifications of programs.  ... 
doi:10.1023/b:jlli.0000028393.47593.b8 fatcat:4fvkefihbngpddqzcjc5qb7q7a

Language Heedless of Logic - Philosophy Mindful of What? Failures of Distributive and Absorption Laws [article]

Arthur Merin
2014 arXiv   pre-print
Much of philosophical logic and all of philosophy of language make empirical claims about the vernacular natural language.  ...  They presume semantics under which 'and' and 'or' are related by the dually paired distributive and absorption laws. However, at least one of each pair of laws fails in the vernacular.  ...  The bad cases arise when the provenance of this language is forgotten and when appeal to Mr and Ms Natural's vernacular language intuitions is made in philosophical argument about what language (or mind  ... 
arXiv:1403.3668v2 fatcat:aqum6trdcjgkthy5yhsotexsl4

MBase: Representing Knowledge and Context for the Integration of Mathematical Software Systems

Michael Kohlhase, Andreas Franke
2001 Journal of symbolic computation  
This "mathematical vernacular" is an extension of a sorted λ-calculus by records, dependent record sorts and selection sorts.  ...  On the other hand they define higher language features from simpler ones and ultimately serve as a means to found the whole knowledge base in axiomatic set theory.  ...  Mathematical Vernacular In this section, we develop the basic concepts for a representation language MV for formalizing and reasoning about mathematics in MBase.  ... 
doi:10.1006/jsco.2000.0468 fatcat:2agiisxofbf2rljqrbmkll5xhu

Semantics of OpenMath and MathML3

Michael Kohlhase, Florian Rabe
2012 Mathematics in Computer Science  
While this two-leveled way to interpret objects is well-understood in logic, it has not been spelt out rigorously for OpenMath.  ...  We present two denotational semantics for OpenMath: a constructionoriented semantics that achieves full coverage of all legal OpenMath expressions at the cost of great conceptual complexity, and a symbol-oriented  ...  In OpenMath there are two kinds of mathematical properties: "commented mathematical properties" (encoded as CMP elements which contain mathematical vernacular) and "formal mathematical properties" (encoded  ... 
doi:10.1007/s11786-012-0113-x fatcat:6cco3uaqwbcxbnvcc7tsen67vi

Linguistic Variation in Time, Space, and Society: Dialectology . J. K. Chambers, Peter Trudgill. ; Locating Language in Time and Space . William Labov. ; Language Diversity and Language Contact . Stanley Lieberson. ; Language and Social Networks . Lesley Milroy. ; Sociolinguistic Patterns in British English . Peter Trudgill

Susan Gal
1982 American Anthropologist  
Semantic information was found necessary to ac- count for well-formedness in syntax and some semantic and syntactic interpretations could be explained only by recourse to pragmatic information (Lakoff  ...  languages as well as newly formulated universals.  ... 
doi:10.1525/aa.1982.84.4.02a00090 fatcat:irtzeapefzbzpa6lumfusxfj3m

Computational Music Aesthetics

Stefano Kalonaris, Anna Jordanous
2018 Zenodo  
and agency in inducing aesthetic responses.  ...  Computational aesthetic evaluation is not to be confounded with numerical evaluation of the system's output; such a notion is in danger of offering a reduced and impoverished interpretation of the aesthetic  ...  (Music) Aesthetics In its historical trajectory starting from music as mathematics (going back to Pythagoras) up to music as emotional expression [10, 11] via music as language [12, 13] , music aesthetics  ... 
doi:10.5281/zenodo.4285466 fatcat:4bk6m45jtjgktl3qpypcnlkpvu

On Becoming a Physicist of Mind

Willem J.M. Levelt
2020 Annual Review of Linguistics  
It led, among other work, to my book Speaking (1989) and to my research team's article in Brain and Behavioral Sciences "A Theory of Lexical Access in Speech Production" (1999).  ...  As will become clear, many people inspired and joined me in these undertakings.  ...  I showed that self-repairs follow a well-formedness rule comparable to the well-formedness of coordinations and of question-answer pairs.  ... 
doi:10.1146/annurev-linguistics-011619-030256 fatcat:kxbsi5s4rrcgxhmpm6zisbfysy

Manifest domains: analysis and description

Dines Bjørner
2016 Formal Aspects of Computing  
conceptual phenomena that "exists" inside computers and, in a wider context than just computers and computing, of the theories "behind" their formal description languages ⊙ Computer science is often also  ...  And the main tools of the TripTych domain analysis and description approach are the analysis and description prompts and the description language, here the Raise Specification Language RSL [GHH + 92].  ...  Peter brought me to the IBM Wiener Labor in 1973. The two years I spent with him became the most important years in my scientific life. Peter was a great scientist and a lovely person.  ... 
doi:10.1007/s00165-016-0385-z fatcat:wqetfrpxjbfyrgbdjsqzuprh6u
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