Set theory for computing: from decision procedures to declarative programming with sets
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York ; Berlin ; Heidelberg ; Barcelona ; Hong Kong ; London
Springer
2001
|
| Schriftenreihe: | Monographs in computer science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 374 - 391 |
| Beschreibung: | XVIII, 409 S. graph. Darst. : 24 cm |
| ISBN: | 0387951970 |
Internformat
MARC
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| 264 | 1 | |a New York ; Berlin ; Heidelberg ; Barcelona ; Hong Kong ; London |b Springer |c 2001 | |
| 300 | |a XVIII, 409 S. |b graph. Darst. : 24 cm | ||
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| 700 | 1 | |a Omodeo, Eugenio |e Verfasser |4 aut | |
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Datensatz im Suchindex
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|---|---|
| adam_text |
DOMENICO CANTONE EUGENIO OMODEO ALBERTO POLICRITI SET THEORY FOR
COMPUTING FROM DECISION PROCEDURES TO DECLARATIVE PROGRAMMING WITH SETS
FOREWORD BY JACOB T. SCHWARTZ WITH 67 FIGURES SPRINGER CONTENTS FOREWORD
VII PREFACE XI I INTRODUCTION 1 1 WHAT IS COMPUTABLE SET THEORY? 3 1.1
TENTATIVE SUBDIVISION OF COMPUTATIONAL LOGIC . 5 1.2 ONE OR SEVERAL
THEORIES ON SETS? 6 1.3 COMPUTABLE MODELS OF AGGREGATE THEORIES 8 1.4
DECIDABILITY ISSUES IN SET THEORY 9 1.5 FURTHER MEANS OF AUTOMATION FOR
REASONING ON AGGREGATES 11 1.6 APPLICATION SCENARIOS FOR COMPUTABLE SET
THEORY 12 2 LOGICAL BACKGROUND 14 2.1 FREE EXPRESSIONS OVER A SIGNATURE
. 16 2.2 PROPOSITIONAL CALCULUS 19 2.3 PREDICATE CALCULUS AND MAP
CALCULUS 28 2.4 THEORIES, IN VARIOUS FORMALISMS 49 XVI CONTENTS R II
BASICS FOR SET-THEORETIC REASONING 59 3 AXIOMATIC VIEWS OF AGGREGATES 61
3.1 THE BAREST RUDIMENTS OF SET THEORY 62 3.2 THE THEORY OF PURE FINITE
SETS 66 3.3 VARIANT AXIOMATIZATIONS OF AGGREGATE THEORIES 77 4 SEMANTIC
VIEWS OF AGGREGATES 87 4.1 UNIVERSES OF FINITE (NESTED) AGGREGATES 88
4.2 COMPUTABLE SET MODELS 97 4.3 APPENDIX: TINY-SETL PROGRAMS 108 5 SETS
FOR PROBLEM SOLVING 112 5.1 CONVENIENCES BASED ON NOTATION 112 5.2
SET-BASED CONCEPTUAL TOOLS 113 5.3 ABSTRACT CHARACTERIZATION OF DATA
TYPES 119 5.4 PROBLEM SPECIFICATIONS 124 5.5 SPECIFICATION OF ALGORITHMS
AND PROBLEM SOLUTION TECHNIQUES 128 5.6 SETS FOR PROGRAM VERIFICATION
130 5.7 DECLARATIVE SPECIFICATION OF A PROBLEM SOLUTION TECHNIQUE 138
5.8 (*) SYNTHESIS OF STRONGLY COMPUTABLE SET MODELS . . . . 142 6
DECISION PROBLEMS AND SOME SOLUTIONS 148 6.1 SATISFIABILITY AND VALIDITY
149 6.2 UNIFICATION UNDER GIVEN AXIOMS 168 6.3 TAXONOMY AND
NORMALIZATION OF FORMULAS 179 6.4 REVIEW OF SOLVABLE FRAGMENTS OF SET
THEORY 190 7 INFERENCE TECHNIQUES AND METHODS 196 7.1 RESOLUTION-LIKE
INFERENTIAL SYSTEMS 196 7.2 SEMANTIC TABLEAUX 207 7.3 LOGIC PROGRAMMING
AND ITS EXTENSIBILITY 223 III DECISION METHODS 245 8 SET/HYPERSET
UNIFICATION ALGORITHMS 247 8.1 BLIND-SEARCH UNIFICATION IN PURE CONTEXT
248 8.2 GOAL-DIRECTED SET-UNIFICATION IN THE BLENDED CONTEXT . . 256 8.3
(*) INGREDIENTS OF GOAL-DRIVEN HYPERSET UNIFICATION . . . 259 CONTENTS
XVII 9 -(*) A SYLLOGISTIC SOLITAIRE 265 9.1 DECIDING A FRAGMENT OF SET
THEORY BY SIMULATING A PARTITION 266 9.2 THE TRACE THEOREM 269 9.3
MIMICKING A SYLLOGISTIC GAME BY ONE OF PREDICTABLE LENGTH 275 9.4
SYLLOGISTIC GAMES APPLIED TO THE SET-SATISFIABILITY PROBLEM 281 10
STRATIFIED SYLLOGISTICS 284 10.1 TWO-LEVEL SYLLOGISTIC 284 10.2 (*)
TOPOLOGICAL TWO-LEVEL SYLLOGISTIC 287 10.3 THREE-LEVEL SYLLOGISTIC WITH
SINGLETON, POWERSET, AND UNIONSET 291 IV SET-SPECIFIC INFERENCE ENGINES
305 11 QUANTITATIVE SET REASONING 307 11.1 CASE STUDY: MULTILEVEL
SYLLOGISTIC WITH A CARDINALITY OPERATOR 307 11.2 A FURTHER EXTENSION OF
MULTILEVEL SYLLOGISTIC, WITH MAPS 313 11.3 REDUCTION OF MULTILEVEL
SYLLOGISTIC TO PROPOSITIONAL CALCULUS 314 12 SET THEORY FOR NONCLASSIC
LOGICS 318 12.1 MODAL LOGICS 318 12.2 TRANSLATION OF PROPOSITIONAL MODAL
FORMULAS INTO SET TERMS 322 12.3 ELICITING SET PRINCIPLES THAT ENSURE
FAITHFULNESS OF THE TRANSLATION 326 12.4 FAITHFULNESS OF THE TRANSLATION
IN MEANS OF PROOF . 327 12.5 SET-BASED RESOLUTION FOR NONCLASSIC
LOGICS 331 12.6 (*) OTHER LOGICS 335 13 LOGIC PROGRAMMING WITH SETS 340
13.1 AXIOMATIC DESCRIPTION OF THE BLENDED UNIVERSE OF SETS 341 13.2 A
VARIANT OF SLD-RESOLUTION SPECIALIZED FOR SET-HANDLING 342 14
SYLLOGISTIC TABLEAUX 350 14.1 A DECIDABLE TABLEAU CALCULUS FOR MLSS 351
14.2 EXTENDING MLSS WITH FUNCTION SYMBOLS AND RESTRICTED QUANTIFICATION
361 XVIII CONTENTS REFERENCES . . 3714 TABLES AND INDEX OF SYMBOLS 393
ASSOCIATION AND PRIORITY RULES 393 TRUTH TABLES . . 393 COMMON
ABBREVIATIONS IN FIRST-ORDER LANGUAGES 394 SUBSTITUTION-RELATED NOTATION
394 MAP-RELATED NOTATION 395 FUNCTION-RELATED NOTATION 395 BASIC LAWS ON
SETS . 396 ABBREVIATIONS IN MATHEMATICAL ENGLISH . . . 397 INDEX OF
TERMS 399 |
| any_adam_object | 1 |
| author | Cantone, Domenico Omodeo, Eugenio Policriti, Alberto |
| author_facet | Cantone, Domenico Omodeo, Eugenio Policriti, Alberto |
| author_role | aut aut aut |
| author_sort | Cantone, Domenico |
| author_variant | d c dc e o eo a p ap |
| building | Verbundindex |
| bvnumber | BV013993354 |
| callnumber-first | Q - Science |
| callnumber-label | QA248 |
| callnumber-raw | QA248 |
| callnumber-search | QA248 |
| callnumber-sort | QA 3248 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | ST 300 |
| ctrlnum | (OCoLC)248543978 (DE-599)BVBBV013993354 |
| dewey-full | 511.3/22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/22 |
| dewey-search | 511.3/22 |
| dewey-sort | 3511.3 222 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV013993354 |
| illustrated | Illustrated |
| indexdate | 2024-09-10T00:55:33Z |
| institution | BVB |
| isbn | 0387951970 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009578281 |
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| physical | XVIII, 409 S. graph. Darst. : 24 cm |
| publishDate | 2001 |
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| publisher | Springer |
| record_format | marc |
| series2 | Monographs in computer science |
| spelling | Cantone, Domenico Verfasser aut Set theory for computing from decision procedures to declarative programming with sets Domenico Cantone ; Eugenio Omodeo ; Alberto Policriti New York ; Berlin ; Heidelberg ; Barcelona ; Hong Kong ; London Springer 2001 XVIII, 409 S. graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier Monographs in computer science Literaturverz. S. 374 - 391 Computable functions Set theory Deklarative Programmierung (DE-588)4293503-9 gnd rswk-swf Berechenbare Funktion (DE-588)4135762-0 gnd rswk-swf Mengenlehre (DE-588)4074715-3 gnd rswk-swf Deklarative Programmierung (DE-588)4293503-9 s Mengenlehre (DE-588)4074715-3 s Berechenbare Funktion (DE-588)4135762-0 s DE-604 Omodeo, Eugenio Verfasser aut Policriti, Alberto Verfasser aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009578281&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cantone, Domenico Omodeo, Eugenio Policriti, Alberto Set theory for computing from decision procedures to declarative programming with sets Computable functions Set theory Deklarative Programmierung (DE-588)4293503-9 gnd Berechenbare Funktion (DE-588)4135762-0 gnd Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4293503-9 (DE-588)4135762-0 (DE-588)4074715-3 |
| title | Set theory for computing from decision procedures to declarative programming with sets |
| title_auth | Set theory for computing from decision procedures to declarative programming with sets |
| title_exact_search | Set theory for computing from decision procedures to declarative programming with sets |
| title_full | Set theory for computing from decision procedures to declarative programming with sets Domenico Cantone ; Eugenio Omodeo ; Alberto Policriti |
| title_fullStr | Set theory for computing from decision procedures to declarative programming with sets Domenico Cantone ; Eugenio Omodeo ; Alberto Policriti |
| title_full_unstemmed | Set theory for computing from decision procedures to declarative programming with sets Domenico Cantone ; Eugenio Omodeo ; Alberto Policriti |
| title_short | Set theory for computing |
| title_sort | set theory for computing from decision procedures to declarative programming with sets |
| title_sub | from decision procedures to declarative programming with sets |
| topic | Computable functions Set theory Deklarative Programmierung (DE-588)4293503-9 gnd Berechenbare Funktion (DE-588)4135762-0 gnd Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Computable functions Set theory Deklarative Programmierung Berechenbare Funktion Mengenlehre |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009578281&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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