The Language of Mathematics (Record no. 54227)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 06142nam a22005535i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-642-37012-0 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20200421111207.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 130321s2013 gw | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9783642370120 |
| -- | 978-3-642-37012-0 |
| 082 04 - CLASSIFICATION NUMBER | |
| Call Number | 006.6 |
| 100 1# - AUTHOR NAME | |
| Author | Ganesalingam, Mohan. |
| 245 14 - TITLE STATEMENT | |
| Title | The Language of Mathematics |
| Sub Title | A Linguistic and Philosophical Investigation / |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | XX, 260 p. 15 illus. |
| 490 1# - SERIES STATEMENT | |
| Series statement | Lecture Notes in Computer Science, |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Remark 2 | 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. |
| 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 | eBooks |
| 264 #1 - | |
| -- | Berlin, Heidelberg : |
| -- | Springer Berlin Heidelberg : |
| -- | Imprint: Springer, |
| -- | 2013. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
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| -- | rda |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Computer science. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Mathematical logic. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Artificial intelligence. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Computational linguistics. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Computer graphics. |
| 650 14 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Computer Science. |
| 650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Computer Imaging, Vision, Pattern Recognition and Graphics. |
| 650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Mathematical Logic and Formal Languages. |
| 650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Language Translation and Linguistics. |
| 650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Artificial Intelligence (incl. Robotics). |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| -- | 0302-9743 ; |
| 912 ## - | |
| -- | ZDB-2-SCS |
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| -- | ZDB-2-LNC |
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