Verfügbarkeit: Set theory for computing | Technische Universität München

Set theory for computing: from decision procedures to declarative programming with sets

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Bibliographische Detailangaben
Beteiligte Personen:	Cantone, Domenico (VerfasserIn), Omodeo, Eugenio (VerfasserIn), Policriti, Alberto (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York ; Berlin ; Heidelberg ; Barcelona ; Hong Kong ; London Springer 2001
Schriftenreihe:	Monographs in computer science
Schlagwörter:	Computable functions Set theory Berechenbare Funktion Deklarative Programmierung Mengenlehre
Links:	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
Beschreibung:	Literaturverz. S. 374 - 391
Umfang:	XVIII, 409 S. graph. Darst. : 24 cm
ISBN:	0387951970

Internformat

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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
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author	Cantone, Domenico Omodeo, Eugenio Policriti, Alberto
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dewey-tens	510 - Mathematics
discipline	Informatik Mathematik
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indexdate	2024-12-20T10:57:12Z
institution	BVB
isbn	0387951970
language	English
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oclc_num	248543978
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owner	DE-739 DE-634
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physical	XVIII, 409 S. graph. Darst. : 24 cm
publishDate	2001
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publisher	Springer
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series2	Monographs in computer science
spellingShingle	Cantone, Domenico Omodeo, Eugenio Policriti, Alberto Set theory for computing from decision procedures to declarative programming with sets Computable functions Set theory Berechenbare Funktion (DE-588)4135762-0 gnd Deklarative Programmierung (DE-588)4293503-9 gnd Mengenlehre (DE-588)4074715-3 gnd
subject_GND	(DE-588)4135762-0 (DE-588)4293503-9 (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 Berechenbare Funktion (DE-588)4135762-0 gnd Deklarative Programmierung (DE-588)4293503-9 gnd Mengenlehre (DE-588)4074715-3 gnd
topic_facet	Computable functions Set theory Berechenbare Funktion Deklarative Programmierung 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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