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Mathematical Reasoning via Self-supervised Skip-tree Training [article]

Markus N. Rabe and Dennis Lee and Kshitij Bansal and Christian Szegedy
2020 arXiv   pre-print
To train language models for formal mathematics, we propose a novel skip-tree task.  ...  We suggest several logical reasoning tasks that can be used to evaluate language models trained on formal mathematical statements, such as type inference, suggesting missing assumptions and completing  ...  For training language models on formal mathematics, we propose a novel skip-tree task.  ... 
arXiv:2006.04757v3 fatcat:yrmqpmijjzh6rcnkm3b77k3mwy

Mathematics and Religion [chapter]

Javier Leach
2013 Encyclopedia of Sciences and Religions  
The formal mathematical theories are interpreted in formal models. For example, the formal theories of Minkowski are interpreted in a formal mathematical model of a non-Euclidean geometry. 5.  ...  Academic languages Scientific theories Mathematics and logic Formal theories Empirical semantics Representational models Formal semantics Formal models Empirical observations Mathematical intuitions  ... 
doi:10.1007/978-1-4020-8265-8_1582 fatcat:ccgdknky4nhfzjkqd2cbq27tje

Z Formal Specification Language

Z is a model oriented formal specification language based on Zermelo-Fränkel axiomatic set theory and first order predicate logic.  ...  It is a mathematical specification language, with the help of which natural language requirements can be converted into mathematical form. In this report an overview of formal method is presented.  ...  A specific implicit model for concurrency is the basis for these languages.  ... 
doi:10.6084/m9.figshare.14938338.v1 fatcat:mwhhkzy7mjenhmsxgnoubpeyve


Lyubov Badyorina
2013 Vìsnik Nacìonalʹnogo Avìacìjnogo Unìversitetu  
The paper considers the application of mathematical tools for formalizing of grammatical structures to facilitate the Phrases processing by computer means.  ...  Significant contribution to the creation of mathematical tools of predicative models and methods for in-depth studies and mathematical modeling of discrete processes and objects including natural languages  ...  Thanks to the models decomposition with the set of variables and mathematical models of natural language it is possible to determine the variables being necessary for further modeling (Abstracts…2009).  ... 
doi:10.18372/2306-1472.54.3862 fatcat:dscklyvn2bflhj44c3eraypile

Mathematical Knowledge Representation: Semantic Models and Formalisms [article]

Alexander Elizarov and Alexander Kirillovich and Evgeny Lipachev and Olga Nevzorova and Valery Solovyev and Nikita Zhiltsov
2014 arXiv   pre-print
The paper provides a survey of semantic methods for solution of fundamental tasks in mathematical knowledge management. Ontological models and formalisms are discussed.  ...  We propose an ontology of mathematical knowledge, covering a wide range of fields of mathematics. We demonstrate applications of this representation in mathematical formula search, and learning.  ...  Kirillovich would like to thank Evelina Khakimova (University of Virginia), Claudia Acevedo (Lemoine Editores), and Maria Isabel Duarte (EAFIT University) for the assistance in the work with bibliographic  ... 
arXiv:1408.6806v2 fatcat:zhgqrfztqrdz7nhacppjictbbe

The role of early language abilities on math skills among Chinese children

Juan Zhang, Xitao Fan, Sum Kwing Cheung, Yaxuan Meng, Zhihui Cai, Bi Ying Hu, Mitchell Rabinowitz
2017 PLoS ONE  
Results The current findings indicate 1) Children's language abilities are of strong predictive values for both informal and formal math skills; 2) Language abilities impacts formal math skills partially  ...  Both of the two sub-domains of language are essential for developing mathematical skills [13, 14] . In what follows, the role of each language domain on mathematical learning is discussed.  ...  Acknowledgments We would like to thank all the students and schools that have been involved in this study for their participation.  ... 
doi:10.1371/journal.pone.0181074 pmid:28749950 pmcid:PMC5531550 fatcat:a376m3dyk5acjoqq4ripwdz4n4

Using mathematical models of language experimentally

Timothy J. O'Donnell, Marc D. Hauser, W. Tecumseh Fitch
2005 Trends in Cognitive Sciences  
The advantage of constructing such precise, and often mathematically formalized models is that the consequences of modeling decisions can be deduced directly from assumptions [1].  ...  We suggest that this problem can be mitigated by tapping equally rich, but more formal mathematical approaches to language.  ...  We would like to thank Jelle Zuidema for comments.  ... 
doi:10.1016/j.tics.2005.04.011 pmid:15925807 fatcat:z7six35zrja2rp3mn4s6woihgi

Editor's Preface [chapter]

John Lehrberger
1983 Elements of Mathematical Linguistics  
The increasing use of the formalisms of mathematics and logic in describing the structure of human language has given rise to a large field of study called formal linguistics and, as expected in the age  ...  The emphasis on formal rules and derivations in syntax brought mathematics of a certain type into the foreground, and the attempt to formalize semantic representation in grammars of natural languages sent  ...  Solomon Marcus (1967) introduces the reader to the use of mathematical modeling for investigating language structure.  ... 
doi:10.1515/9783110810806-001 fatcat:ltnykhuby5alhkzbodzfjyojmu

Contents [chapter]

John Lehrberger
1983 Elements of Mathematical Linguistics  
Tree Grammars: A Formalism for Syntactic Transformations in Natural Languages 151 II. A.V. Gladkij. Toward a Formal Definition of Grammatical Case and Gender of Nouns 188 III. I.A. Mel'cuk.  ...  The modelling of languages 87 Categorial grammars (C grammars) 88 Push-down store automata (PDS automata) 98 Classifying formal grammars 109 Logical analysis of language 112 B.  ... 
doi:10.1515/9783110810806-toc fatcat:p3s67ifwefgtxew237hwd6htki

Methodological Teaching System of Mathematical Foundations of Formal Languages as a Means of Fundamentalization of Education

Natalya Bushmeleva, Tatiana Baklashova
2017 Eurasia Journal of Mathematics, Science and Technology Education  
The article suggests a system for studying mathematical foundations of formal languages as a system-forming element in the training of specialists in the field of computer science, programming, and IT-technologies  ...  of teaching formal languages, and to improve the content of training to specific formal languages.  ...  The resulting abstraction will be called a formal language -a mathematical model of a real language.  ... 
doi:10.12973/eurasia.2017.00989a fatcat:dovyaaaqfresbkakjutzw7mrvq


Kelly M. McGinn, Julie L. Booth
2018 Bordón Revista de Pedagogía  
The first explores the relation between students' use of formal and informal mathematical language and procedural knowledge in mathematics; the second replicates and extends these findings using a longitudinal  ...  Although teachers should still use formal language in their classrooms; they should not be discouraged if students are initially unable to use formal language correctly.  ...  The OWT model will help illustrate the development of mathematics language from the use of informal expressions to more formal expressions of mathematical concepts.  ... 
doi:10.13042/bordon.2018.62138 fatcat:6aafhg2unzb2vetfgjgzb7rsme

Infinity and the foundations of linguistics

Ryan M. Nefdt
2017 Synthese  
being informed by contemporary ideas on scientific modelling for the natural and social sciences.  ...  The main product of this error has been the assumption that natural, like some formal, languages are discretely infinite.  ...  Acknowledgements I would like to thank Josh Dever, Ephraim Glick, Patrick Greenough, Geoff Pullum, Kate Stanton, Zoltán Szabó, Bernhard Weiss and two anonymous referees for their insightful comments on  ... 
doi:10.1007/s11229-017-1574-x fatcat:knqznzc6t5dhfp76hap65zg6gm

Formal Methods in Requirements Phase of SDLC

S. K.Pandey, Mona Batra
2013 International Journal of Computer Applications  
As a result, formal methods are currently used to model complex security critical systems. Literature reveals that formal methods can be applied at various points through the development process.  ...  Accordingly, there appears a need for a critical review of these formal methods.  ...  A formal specification language can be used to model the most complex systems using relatively simple mathematical entities, such as sets, relations and functions.  ... 
doi:10.5120/12020-8017 fatcat:jnock2ajcbcgddqwo5nksnijty

Second-Order Logic and Foundations of Mathematics

Jouko Väänänen
2001 Bulletin of Symbolic Logic  
We discuss the differences between first-order set theory and second-order logic as a foundation for mathematics. We analyse these languages in terms of two levels of formalization.  ...  The analysis shows that if second-order logic is understood in its full semantics capable of characterizing categorically central mathematical concepts, it relies entirely on informal reasoning.  ...  Urlogic Formalization of mathematics involves defining a formal language with some intended meaning. Let us call this language urlogic 5 .  ... 
doi:10.2307/2687796 fatcat:flfveb42abc2lcujwr2pbtmndq

Lenguajes matemáticos y lenguajes metafísicos

Javier Leach
2015 Pensamiento. Revista de Investigación e Información Filosófica  
What was lacking until the twentieth century was a formal mathematical language to write down the instructions for such a calculation.  ...  That is the language of logic, but it sets the stage for the language of mathematics.  ... 
doaj:35ea7a4e47fd4f9abb27f6883f6c44a8 fatcat:wzk33au4avdkng35sqedj6ijga
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