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Aperiodic Languages and Generalizations [chapter]

Lila KARI, Gabriel THIERRIN
1994 Mathematical Aspects of Natural and Formal Languages  
For every integer k ≥ 0, a class of languages, called k-aperiodic languages, is defined, generalizing the class of aperiodic languages.  ...  Properties of these classes are investigated, in particular the operations under which they are preserved. A characterization of the syntactic monoid of a kaperiodic language is also obtained.  ...  * This research was supported by Grant OGP0007877 of the Natural Sciences and Engineering Research Council of Canada  ... 
doi:10.1142/9789814447133_0013 fatcat:ztfptek25zhdvbza3haswolxem

Computerizing Mathematical Text with MathLang

Fairouz Kamareddine, J.B. Wells
2008 Electronical Notes in Theoretical Computer Science  
Another aspect allows weaving together mathematical meaning and visual presentation and can associate natural language text with its mathematical meaning.  ...  mathematical meaning and have proofs expressed in a formal foundation of mathematics.  ...  The aspects of MathLang The Core Grammatical aspect (CGa) CGa [23, 24, 30, 19 ] is a formal language inspired initially by WTT [25] and MV [10] , and then later shaped by repeated experiences of  ... 
doi:10.1016/j.entcs.2008.03.063 fatcat:km2j4mpujfarpbhkxrn5evu7eq

Page 274 of Computational Linguistics Vol. 24, Issue 2 [page]

1998 Computational Linguistics  
In Gheorghe Pdun, editor, Mathematical Aspects of Natural and Formal Languages. World Scientific, Singapore, pages 375-392. Pullum, Geoffrey K. 1985.  ...  ., Alexis Manaster Ramer, and Joyce Friedman. 1987. Finding natural languages a home in formal language theory. In Alexis Manaster Ramer, editor, Mathematics of Language.  ... 

The mathematical state of the world – explorations into the characteristics of mathematical descriptions

Ole Ravn Christensen, Ole Skovsmose, Keiko Yasukawa
2008 Alexandria Revista de Educação em Ciência e Tecnologia  
We illustrate why the concepts of "mathematical description" and "mathematical model" are inadequate to evaluate the use of mathematics in decision-making processes.  ...  In this article we try to analyse the conditions for describing the world mathematically. We consider the role played by mathematics in discussing and analysing "the state of the world".  ...  Formal language is a derivative of natural language, which draws attention to certain aspects of natural language.  ... 
doaj:cd4e8f762ce64a70a57749d3d0bc1fc6 fatcat:h3ep2d53kvcutpr23uyp6qubzy

Can mathematics explain the evolution of human language?

Guenther Witzany
2011 Communicative & Integrative Biology  
Therefore mathematics is viewed not only as an appropriate tool to investigate human language and genetic code structures through computer sciencebased formal language theory but is itself a depiction  ...  The features of human language are also the object of investigation within the realm of formal language theories.  ...  the twentieth century for the use of mathematics in investigating natural languages/ codes are rather surprising: • There can be no formal system which is entirely reflectable in all its aspects while  ... 
doi:10.4161/cib.16426 pmid:22046452 pmcid:PMC3204117 fatcat:vzjiwfkhgzhjpkb47gmxdpi7ru

Z Formal Specification Language

TAMEEM HEZAM
2021 figshare.com  
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.  ...  Formal specifications can be used to provide an unambiguous and consistent supplement to natural language descriptions and can be rigorously validated and verified leading to the early detection of specification  ...  In the Z notation there are two languages [1]: 5.2.1 Mathematical Language The mathematical language is used to describe various aspects of a design: objects and the relationships between them by using  ... 
doi:10.6084/m9.figshare.14938338.v1 fatcat:mwhhkzy7mjenhmsxgnoubpeyve

Infinity and the foundations of linguistics

Ryan M. Nefdt
2017 Synthese  
The main product of this error has been the assumption that natural, like some formal, languages are discretely infinite.  ...  a strong analogy with discrete mathematics and especially arithmetic.  ...  various drafts of this paper.  ... 
doi:10.1007/s11229-017-1574-x fatcat:knqznzc6t5dhfp76hap65zg6gm

Applied Linguistics and Mathematics Education: More than Words and Numbers

Richard Barwell, Constant Leung, Candia Morgan, Brian Street
2005 Language and Education  
In the papers in this collection, we have explored aspects of the role of language in mathematics education.  ...  The preceding set of papers has explored various aspects of the role of language in mathematics education. The papers reflect the work of individual contributors.  ...  In the papers in this collection, we have explored aspects of the role of language in mathematics education.  ... 
doi:10.1080/09500780508668670 fatcat:6rbmwemj3fbhxnb3glk4izvusq

A functional graphic approach to inequations

Vera H.G. de Souza, Rosana Nogueira, Tânia M. M. Campos
2015 Revista Latinoamericana de Investigación en Matemática Educativa  
Analyses of teachers' protocols were undertaken to identify formal, intuitive and algorithmic aspects (Fischbein, 1993) .  ...  the formal aspects of the algebraic solving methods they normally use to solve inequations.  ...  and natural language -may help subjects to interrelate formal, intuitive and algorithmic aspects of algebraic solutions.  ... 
doi:10.12802/relime.13.1814 fatcat:a4nt26yg7va2nkkibxqghmvgcq

A Survey of Languages for Formalizing Mathematics [article]

Cezary Kaliszyk, Florian Rabe
2020 arXiv   pre-print
We evaluate their advantages based on our experience in designing and applying languages and tools for formalizing mathematics.  ...  In this paper we discuss languages that have been created for this purpose, including logical languages of proof assistants and other formal systems, semi-formal languages, intermediate languages for exchanging  ...  of natural mathematical languages with the automation support of formal logics and programming languages.  ... 
arXiv:2005.12876v1 fatcat:lwpxnq4wdjexxar3ocod3ncdvy

THE SHAPES OF MATHEMATIC MODELS IN COMPUTER LINGUISTICS DISCOVER

Sodiqova Baxtigul Ibodullayevna, Xasanov Faxriddin Zokirovich
2020 Zenodo  
It is possible to trace the origin of mathematical linguistics based on computer linguistics and this article will focus on it.  ...  This article provides an overview of the specific trends and models of computer linguistics that are emerging as information technology evolves. Modern mathematical models can also be considered.  ...  In parallel with this, the theory of formal grammar emerged, with a focus on modeling the language and its particular aspects. These aspects of ISSN: 2320-5407 Int. J. Adv.  ... 
doi:10.5281/zenodo.3737782 fatcat:w3k37c4qrbaw3nxtjm3wuimf6q

Using mathematical models of language experimentally

Timothy J. O'Donnell, Marc D. Hauser, W. Tecumseh Fitch
2005 Trends in Cognitive Sciences  
Generative theory is built around several core ideas about the nature of language and its study.  ...  We use one set of tools from mathematical linguistics, formal language theory, to illustrate the potential power of mathematical approaches, sketching its basic concepts and discussing how they were used  ...  Acknowledgements This work was supported by the McDonnell 21st Century Bridging Brain, Mind, and Behavior Grant. We would like to thank Jelle Zuidema for comments.  ... 
doi:10.1016/j.tics.2005.04.011 pmid:15925807 fatcat:z7six35zrja2rp3mn4s6woihgi

Formal Tools and the Philosophy of Mathematics [chapter]

Thomas Hofweber
2009 New Waves in Philosophy of Mathematics  
There is no question that there are formal languages that capture various syntactic aspects of natural languages well. But L PA is not one of them.  ...  And the social sciences might rely on formal methods in their study of the social aspect of mathematics.  ... 
doi:10.1057/9780230245198_10 fatcat:sz2mgponynh47ncdrruilxxilu

Preface

Lawrence S. Moss, Richard T. Oehrle
2004 Electronical Notes in Theoretical Computer Science  
FGMOL'01 provided a forum for the presentation of new and original research on formal grammar and mathematical aspects of language, especially with regard to the application of formal methods to natural  ...  This volume contains the Proceedings of the joint meeting of two conferences: the sixth conference on Formal Grammar and the seventh on Mathematics of Language.  ...  , methodological and architectural issues in grammar; mathematical properties of linguistic frameworks; theories and models of natural language processing and generation; parsing theory; and statistical  ... 
doi:10.1016/s1571-0661(05)82569-1 fatcat:rqseploowjhphbmalw3bo3qjia

The Space of Mathematical Software Systems – A Survey of Paradigmatic Systems [article]

Katja Bercic, Jacques Carette, William M. Farmer, Michael Kohlhase, Dennis Müller, Florian Rabe, Yasmine Sharoda
2020 arXiv   pre-print
To give researchers a guide to this space of systems, we devise a novel conceptualization of mathematical software that focuses on five aspects: inference covers formal logic and reasoning about mathematical  ...  formal languages, typically with strong emphasis on expressivity and system interoperability.  ...  , the peculiar mixture of natural language, mathematical formulae, and diagrams digitally.  ... 
arXiv:2002.04955v1 fatcat:th2h5qrd4rcazhw2eqbqmy2zmq
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