[EAN: 9783642370113], Neubuch, [SC: 0.0], [PU: Springer Berlin Heidelberg], COMPUTATIONALLINGUISTICS; FOUNDATIONSOFMATHEMATICS; MATHEMATICALLANGUAGE; PHILOSOPHYOFMATHEMATICS; SEMANTICS, Druck auf Anfrage Neuware - 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 280 pp. Englisch, Books<
[EAN: 9783642370113], Neubuch, [SC: 0.0], [PU: Springer Berlin Heidelberg], COMPUTATIONALLINGUISTICS; FOUNDATIONSOFMATHEMATICS; MATHEMATICALLANGUAGE; PHILOSOPHYOFMATHEMATICS; SEMANTICS, Druck auf Anfrage Neuware -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 280 pp. Englisch, Books<
The Language of Mathematics by Mohan Ganesalingam Paperback | Indigo Chapters - neues Buch
ISBN: 9783642370113
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 techniq… Mehr…
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 | The Language of Mathematics by Mohan Ganesalingam Paperback | Indigo Chapters Books > Computers > Computer Science P10116, Mohan Ganesalingam<
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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 techniqu… Mehr…
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 Books, [PU: Springer, Berlin/Heidelberg/New York, NY]<
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[EAN: 9783642370113], Neubuch, [SC: 0.0], [PU: Springer Berlin Heidelberg], COMPUTATIONALLINGUISTICS; FOUNDATIONSOFMATHEMATICS; MATHEMATICALLANGUAGE; PHILOSOPHYOFMATHEMATICS; SEMANTICS, Druck auf Anfrage Neuware - 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 280 pp. Englisch, Books<
[EAN: 9783642370113], Neubuch, [SC: 0.0], [PU: Springer Berlin Heidelberg], COMPUTATIONALLINGUISTICS; FOUNDATIONSOFMATHEMATICS; MATHEMATICALLANGUAGE; PHILOSOPHYOFMATHEMATICS; SEMANTICS, Druck auf Anfrage Neuware -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 280 pp. Englisch, Books<
The Language of Mathematics by Mohan Ganesalingam Paperback | Indigo Chapters - neues Buch
ISBN: 9783642370113
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 techniq… Mehr…
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 | The Language of Mathematics by Mohan Ganesalingam Paperback | Indigo Chapters Books > Computers > Computer Science P10116, Mohan Ganesalingam<
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 techniqu… Mehr…
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 Books, [PU: Springer, Berlin/Heidelberg/New York, NY]<
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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
Detailangaben zum Buch - The Language of Mathematics
EAN (ISBN-13): 9783642370113 ISBN (ISBN-10): 364237011X Gebundene Ausgabe Taschenbuch Erscheinungsjahr: 2013 Herausgeber: Springer Berlin 280 Seiten Gewicht: 0,421 kg Sprache: Englisch
Buch in der Datenbank seit 2009-01-01T10:11:02+01:00 (Vienna) Detailseite zuletzt geändert am 2022-08-31T00:26:59+02:00 (Vienna) ISBN/EAN: 9783642370113
ISBN - alternative Schreibweisen: 3-642-37011-X, 978-3-642-37011-3 Alternative Schreibweisen und verwandte Suchbegriffe: Autor des Buches: mohan, gane, ganesalingam, timothy gowers Titel des Buches: mathematics, lecture notes computer science
Daten vom Verlag:
Autor/in: Mohan Ganesalingam Titel: Theoretical Computer Science and General Issues; Lecture Notes in Computer Science; The Language of Mathematics - A Linguistic and Philosophical Investigation Verlag: Springer; Springer Berlin 260 Seiten Erscheinungsjahr: 2013-02-10 Berlin; Heidelberg; DE Gedruckt / Hergestellt in Niederlande. Sprache: Englisch 76,99 € (DE)
BC; Hardcover, Softcover / Informatik, EDV/Anwendungs-Software; Bildverarbeitung; Verstehen; computational linguistics; foundations of mathematics; mathematical language; philosophy of mathematics; semantics; Computer Imaging, Vision, Pattern Recognition and Graphics; Formal Languages and Automata Theory; Natural Language Processing (NLP); Artificial Intelligence; Theoretische Informatik; Natürliche Sprachen und maschinelle Übersetzung; Künstliche Intelligenz; EA
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.
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