Understanding informal mathematical discourse:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English German |
| Veröffentlicht: |
Erlangen
Inst. für Informatik
2004
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| Schriftenreihe: | Arbeitsberichte des Instituts für Informatik, Friedrich-Alexander-Universität Erlangen-Nürnberg
37,4 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Zugl.: Erlangen-Nürnberg, Univ., Diss., 2004. - Enth. Zsfassung in engl. und dt. Spr. |
| Beschreibung: | XIV, 181 S. graph. Darst. |
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Datensatz im Suchindex
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ARBEITSBERICHTE DES INSTITUTS FIIR INFORMATIK
FRIEDRICH-ALEXANDER-UNIVERSITAT ERIANGEN NURNBERG BAND 37 * NUMMER 4 *
SEPTEMBER 2004 CLAUS ZINN UNDERSTANDING INFORMAL MATHEMATICAL DISCOURSE
DISSERTATION HERAUSGEBER: M. DAL CIN, R. GERMAN, G. GORZ, G. GREINER, U.
HERZOG, F. HOFMANN, J. HORNEGGER, S. JABLONSKI, K. LEEB, ULB DARMSTADT
MULLER - H - NIEMANN, E, F. SAGHETTI, 16041530 DIE REIHE DER
ARBEITSBERICHTE DES INSTITUTS FUR INFORMATIK (EHEM. INSTITUT FUR
MATHEMATISCHE MASCHINEN UND DATENVERARBEITUNG) DER UNIVERSITAT
ERLANGEN-NIIRNBERG ERSCHEINT SEIT 1967. BEGRIINDET VON PROF. DR. DR. H.
C. MULT. WOLFGANG HANDLER CONTENTS 1 INTRODUCTION 1 1.1 THE AUTOMATED
REASONING VIEW: VERIFYING TEXTBOOK PROOFS 2 1.1.1 ON THE NOTION OF
FORMAL PROOF 2 1.1.2 PROOFS IN MATHEMATICAL PRACTISE 4 1.2 THE
LINGUISTIC VIEW: UNDERSTANDING MATHEMATICAL DISCOURSE 8 1.2.1 THE
GRICEAN VIEW 8 1.2.2 A COMPUTATIONAL LINGUIST'S VIEW 10 1.2.3 THE
SEMANTICIST'S VIEW 10 1.3 RESEARCH PROGRAM AND RESEARCH QUESTIONS 10
1.3.1 DOING FORMALISED MATHEMATICS WITH COMPUTER SUPPORT 10 1.3.2 THE
MATHEMATICIAN'S ASSISTANT 12 1.3.3 RESEARCH QUESTIONS 13 1.4 THE
ORGANISATION OF THE THESIS 15 1.4.1 THE SYSTEM'S ARCHITECTURE 15 1.4.2
THESIS OVERVIEW 16 1.4.3 THREE NOTES 16 2 REVIEW OF RELATED WORK 19 2.1
A SYSTEMS' REVIEW 19 2.1.1 ABRAHAMS' PROOFCHECKER 19 2.1.2 BOBROW'S
STUDENT 20 2.1.3 MECHO * A PROGRAM TO SOLVE MECHANICS PROBLEMS 20 2.1.4
SIMON'S NTHCHECKER 22 2.2 AUTOMATED REASONING 25 2.2.1 CONSTRUCTING AND
CHECKING FORMAL PROOFS 25 2.2.2 TOWARDS A MATHEMATICAL VERNACULAR 28
2.2.3 CAPTURING AND OPERATIONALISING MATHEMATICAL REASONING 29 2.2.4
PROOF REPRESENTATION 30 2.3 UNDERSTANDING MULTI-SENTENCE DISCOURSE 32
2.3.1 THE SCRIPTS OF SCHANK ET AL 32 2.3.2 HOBBS ET AL'S INTERPRETATION
AS ABDUCTION * TACITUS 33 2.3.3 DISCOURSE REPRESENTATION THEORY (DRT) 35
3 A MATHEMATICAL ANALYSIS OF PROOFS 37 3.1 BASIC PROOF TECHNIQUES 37 3.2
THE FUNDAMENTAL THEOREM OF ARITHMETIC (EXISTENCE) 41 3.2.1 HARDY AND
WRIGHT'S EXISTENCE PROOF 41 3.2.2 LEVEQUE'S EXISTENCE PROOF 45 3.3 THE
FUNDAMENTAL THEOREM OF ARITHMETIC (UNIQUENESS) 47 3.3.1 USING ELLIPSIS
48 3.3.2 HARDY AND WRIGHT'S UNIQUENESS PROOF 49 3.4 HARDY AND WRIGHT'S
PROOF OF THEOREM 3 52 3.5 CONCLUSION 53 XI CONTENTS 4 A LINGUISTIC
ANALYSIS OF PROOFS 55 4.1 GENERAL REMARKS ON MATHEMATICAL WRITING 55 4.2
DENOTING IN MATHEMATICAL DISCOURSE 59 4.2.1 CONSTANT SYMBOLS AND OTHER
PROPER NAMES 60 4.2.2 VARIABLES 61 4.2.3 FUNCTIONS 66 4.2.4 PREDICATES
67 4.2.5 DEFINITE DESCRIPTIONS 68 4.3 LINGUISTIC PHENOMENA 69 4.3.1 A
DISCOURSE ANALYSIS FOCUSING ON TERMS AND FORMULAE 69 4.3.2 A SYSTEMATIC
ACCOUNT ON ANAPHORIC LINKAGE AND ELLIPTIC CONSTRUCTS 71 4.3.3
PROPOSITIONAL DISCOURSE ENTITIES 76 4.4 CONNECTIVES, CONDITIONAL AND
PSEUDO-CONDITIONAL STATEMENTS 79 4.4.1 CONJUNCTION, DISJUNCTION, AND
NEGATION 79 4.4.2 CONDITIONALS 81 5 MATHEMATICAL DISCOURSE AND DRT * THE
PARSER MODULE 89 5.1 DISCOURSE REPRESENTATION THEORY 89 5.1.1 FORMAL
DEFINITION OF DRSS 90 5.1.2 THE CONSTRUCTION OF DRSS FROM THE SYNTAX
TREE. 91 5.1.3 THE CONSTRUCTION OF DRSS FOR MULTI-SENTENCE DISCOURSE 93
5.2 SEMANTIC CONSTRUCTION FOR TERMS AND FORMULAE 94 5.2.1 CONSTANTS 94
5.2.2 VARIABLES 97 5.2.3 FUNCTIONS 104 5.2.4 COMPLEX TERMS 106 5.2.5
TYPE, QUANTIFICATION AND SCOPE OF DISCOURSE ENTITIES 107 5.3 A DRT
TREATMENT OF SELECTED LINGUISTIC PHENOMENA 110 5.3.1 RELATIONAL NOUNS
AND ADJECTIVES 110 5.3.2 LIGHT VERBS (HAVE PHRASES) 112 5.3.3 COMPLEX
REFERRING EXPRESSIONS 113 5.4 CONNECTIVES, CONDITITIONAL AND
PSEUDO-CONDITIONAL STATEMENTS 115 5.4.1 CONJUNCTION, DISJUNCTION AND
NEGATION 115 5.4.2 CONDITIONALS 116 6 PROOF REPRESENTATION STRUCTURES
125 6.1 MOTIVATION 125 6.1.1 ABSTRACT DISCOURSE REFERENTS 125 6.1.2
REPRESENTING DISCOURSE STRUCTURE 127 6.2 PROOF REPRESENTATION STRUCTURES
129 6.3 PROOF PLAN SCHEMATA * UNDERSPECIFIED PRSS 133 6.3.1 FORMAL
DESCRIPTION OF UPRS 134 6.3.2 A FEW EXAMPLE UPRSS 134 6.3.3 VIP'S
LIBRARY OF PROOF METHODS 135 6.4 THEORY REPRESENTATION STRUCTURES 136 7
CONSTRUCTION OF PROOF REPRESENTATION STRUCTURES 139 7.1 THE DISCOURSE
UPDATE ALGORITHM 139 7.1.1 DESCENDING A COMPLEX DRS 140 7.1.2
INTEGRATING A DRS INTO THE PROOF CONTEXT 142 7.1.3 ACCOMMODATING THE
CURRENT PROOF CONTEXT * THE PROOF PLANNER 143 7.2 TWO CONSTRUCTION
EXAMPLES 145 7.2.1 FIRST EXAMPLE 145 CONTENTS XIII 7.2.2 SECOND EXAMPLE
153 7.3 PROOF PLAN REFINEMENT 161 8 CONCLUSION AND FUTURE WORK 163 8.1
RECAPITULATION 163 8.2 SIGNIFICANCE 164 8.2.1 THE AUTOMATED REASONING
PERSPECTIVE 164 8.2.2 THE COMPUTATIONAL LINGUISTICS PERSPECTIVE 165 8.3
SYSTEM LIMITATIONS AND FUTURE SYSTEM EXTENSIONS 166 8.3.1 CURRENT SYSTEM
STATUS 166 8.3.2 EXTENSIONS TO VIP 166 8.4 FUTURE WORK 168 8.4.1
INVESTIGATING THE USE OF RHETORICAL RELATIONS 168 8.4.2 ON PROOF
REPRESENTATION 169 8.4.3 A SHALLOW PARSING APPROACH 169 8.4.4 A TUTORING
SYSTEM FOR MATHEMATICAL PROOFS 170 BIBLIOGRAPHY 172 |
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| title_short | Understanding informal mathematical discourse |
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