The Language of Mathematics (Record no. 40047)

000 -LEADER
fixed length control field 06341nam a22005655i 4500
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN 9783642370120
-- 978-3-642-37012-0
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 006.6
100 1# - MAIN ENTRY--AUTHOR NAME
Personal name Ganesalingam, Mohan.
245 14 - TITLE STATEMENT
Title The Language of Mathematics
Sub Title A Linguistic and Philosophical Investigation /
Statement of responsibility, etc by Mohan Ganesalingam.
260 #1 - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication Berlin, Heidelberg :
Name of publisher Springer Berlin Heidelberg :
-- Imprint: Springer,
Year of publication 2013.
300 ## - PHYSICAL DESCRIPTION
Number of Pages XX, 260 p. 15 illus.
Other physical details online resource.
490 1# - SERIES STATEMENT
Series statement Lecture Notes in Computer Science,
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Introduction.-1.1 Challenges -- 1.2 Concepts.-1.2.1 Linguistics and Mathematic.-1.2.2 Time -- 1.2.3 Full Adaptivity -- .3 Scope -- 1.4 Structure -- 1.5 Previous Analyses -- 1.5.1 Ranta -- 1.5.2 de Bruijn -- 1.5.3 Computer Languages -- 1.5.4 Other Work -- 2 The Language of Mathematics -- 2.1 Text and Symbol -- 2.2 Adaptivity -- 2.3 Textual Mathematics -- 2.4 Symbolic Mathematics. -2.4.1 Ranta’s Account and Its Limitations -- 2.4.2 Surface Phenomena -- 2.4.3 Grammatical Status -- 2.4.4 Variables -- 2.4.5 Presuppositions -- 2.4.6 Symbolic Constructions -- 2.5 Rhetorical Structure -- 2.5.1 Blocks -- 2.5.2 Variables and Assumptions -- 2.6 Reanalysis -- 3 Theoretical Framework -- 3.1 Syntax -- 3.2 Types -- 3.3 Semantics -- 3.3.1 The Inadequacy of First-Order Logic -- 3.3.2 Discourse Representation Theory -- 3.3.3 Semantic Functions -- 3.3.4 Representing Variables -- 3.3.5 Localisable Presuppositions -- 3.3.6 Plurals -- 3.3.7 Compositionality -- 3.3.8 Ambiguity and Type -- 3.4 Adaptivity -- 3.4.1 Definitions in Mathematics -- 3.4.2 Real Definitions and Functional Categories -- 3.5 Rhetorical Structure -- 3.5.1 Explanation -- 3.5.2 Blocks -- 3.5.3 Variables and Assumptions -- 3.5.4 Related Work: DRT in NaProChe -- 3.6 Conclusion -- 4 Ambiguity.-4.1 Ambiguity in Symbolic Mathematics.-4.1.1 Ambiguity in Symbolic Material.-4.1.2 Survey: Ambiguity in Formal Languages.-4.1.3 Failure of Standard Mechanisms -- 4.1.4 Discussion.-4.1.5 Disambiguation without Type -- 4.2 Ambiguity in Textual Mathematics.-4.2.1 Survey: Ambiguity in Natural Languages.-4.2.2 Ambiguity in Textual Mathematics -- 4.2.3 Disambiguation without Type -- 4.3 Text and Symbol -- 4.3.1 Dependence of Symbol on Text -- 4.3.2 Dependence of Text on Symbol -- 4.3.3 Text and Symbol: Conclusion -- 4.4 Conclusion -- 5 Type -- 5.1 Distinguishing Notions of Type -- 5.1.1 Types as Formal Tags -- 5.1.2 Types as Properties -- 5.2 Notions of Type in Mathematics -- 5.2.1 Aspect as Formal Tags -- .2.2 Aspect as Properties -- 5.3 Type Distinctions in Mathematics -- 5.3.1 Methodology -- 5.3.2 Examining the Foundations -- 5.3.3 Simple Distinctions -- 5.3.4 Non-extensionality.-5.3.5 Homogeneity and Open Types -- 5.4 Types in Mathematics -- 5.4.1 Presenting Type: Syntax and Semantics -- 5.4.2 Fundamental Type -- 5.4.3 Relational Type -- 5.4.4 Inferential Type -- 5.4.5 Type Inference -- 5.4.6 Type Parametrism -- 5.4.7 Subtyping -- 5.4.8 Type Coercion -- 5.5 Types and Type Theory -- 6 TypedParsing -- 6.1 Type Assignment -- .1.1 Mechanisms -- 6.1.2 Example -- 6.2 Type Requirements -- 6.3 Parsing -- 6.3.1 Type -- 6.3.2 Variables.-6.3.3 Structural Disambiguation -- 6.3.4 Type Cast Minimisation -- 6.3.5 Symmetry Breaking -- 6.4 Example -- 6.5 Further Work -- 7 Foundations -- 7.1 Approach -- 7.2 False Starts -- 7.2.1 All Objects as Sets -- 7.2.2 Hierarchy of Numbers -- 7.2.3 Summary of Standard Picture -- 7.2.4 Invisible Embeddings -- 7.2.5 Introducing Ontogeny -- 7.2.6 Redefinition -- 7.2.7 Manual Replacement -- 7.2.8 Identification and Conservativity -- 7.2.9 Isomorphisms Are Inadequate -- 7.3 Central Problems -- 7.3.1 Ontology and Epistemology -- 7.3.2 Identification -- 7.3.3 Ontogeny -- 7.4 Formalism -- 7.4.1 Abstraction -- 7.4.2 Identification -- 7.5 Application.-7.5.1 Simple Objects.-7.5.2 Natural Numbers -- 7.5.3 Integers -- 7.5.4 Other Numbers -- 7.5.5 Sets and Categories -- 7.5.6 Numbers and Late Identification -- 7.6 Further Work -- 8 Extensions -- 8.1 Textual Extensions -- 8.2 Symbolic Extensions -- 8.3 Covert Arguments -- Conclusion.
520 ## - SUMMARY, ETC.
Summary, etc The Language of Mathematics was awarded the E.W. Beth Dissertation Prize for outstanding dissertations in the fields of logic, language, and information. It innovatively combines techniques from linguistics, philosophy of mathematics, and computation to give the first wide-ranging analysis of mathematical language. It focuses particularly on a method for determining the complete meaning of mathematical texts and on resolving technical deficiencies in all standard accounts of the foundations of mathematics.   "The thesis does far more than is required for a PhD: it is more like a lifetime's work packed into three years, and is a truly exceptional achievement." Timothy Gowers.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Computer science.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Artificial intelligence.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Translators (Computer programs).
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Computer vision.
650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Computer Science.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Computer Imaging, Vision, Pattern Recognition and Graphics.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Computer Imaging, Vision, Pattern Recognition and Graphics.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Computer Imaging, Vision, Pattern Recognition and Graphics.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Mathematical Logic and Formal Languages.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Language Translation and Linguistics.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Artificial Intelligence (incl. Robotics).
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier http://dx.doi.org/10.1007/978-3-642-37012-0
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Koha item type E-BOOKS
264 #1 -
-- Berlin, Heidelberg :
-- Springer Berlin Heidelberg :
-- Imprint: Springer,
-- 2013.
336 ## -
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-- txt
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337 ## -
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338 ## -
-- online resource
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347 ## -
-- text file
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830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
-- 0302-9743 ;
Holdings
Withdrawn status Lost status Damaged status Not for loan Current library Accession Number Uniform Resource Identifier Koha item type
        IMSc Library EBK10753 http://dx.doi.org/10.1007/978-3-642-37012-0 E-BOOKS
The Institute of Mathematical Sciences, Chennai, India

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