Holdings: Protoalgebraic logics

Protoalgebraic logics:

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Bibliographic Details
Main Author:	Czelakowski, Janusz (Author)
Format:	Book
Language:	English
Published:	Dordrecht [u.a.] Kluwer 2001
Series:	Trends in logic 10
Subjects:	Algebraic logic
Online Access:	Inhaltsverzeichnis
Physical Description:	XI, 452 S. graph. Darst.
ISBN:	0792369408

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adam_text	JANUSZ CZELAKOWSKI INSTITUTE OF MATHEMATICS, OPOLE UNIVERSITY, OPOLE, POLAND PROTOALGEBRAIC LOGICS KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON CONTENTS PREFACE I J X INTRODUCTION I ON THE BOOK 1 MATHEMATICAL PREREQUISITES 11 EXERCISES 17 NOTES FOR MATHEMATICAL PREREQUISITES 20 CHAPTER 0. BASIC DEFINITIONS AND FACTS § 0.1. SENTENTIAL LANGUAGES. CONSEQUENCE OPERATIONS. SENTENTIAL LOGICS . 21 § 0.2. LOGICS AS DEDUCTIVE SYSTEMS 26 § 0.3. CONSEQUENCE OPERATIONS AND MATRIX MODELS. OPERATIONS ON MATRICES 29 § 0.4. MODEL-THEORETIC ASPECTS OF THE THEORY OF SENTENTIAL LOGICS . . . 36 § 0.5. THE LEIBNIZ CONGRUENCE. REDUCED MATRICES 41 § 0.6. THE CHARACTERIZATION THEOREM FOR MOD(C) 45 § 0.7. THE STRUCTURE OF THE CLASS MOD(C) 49 § 0.8. DEDUCTIVE NITERS 54 EXERCISES 59 NOTES FOR CHAPTER 0 64 PART I. PROTOALGEBRAIC LOGICS. THE LEIBNIZ OPERATOR CHAPTER 1. PROTOALGEBRAIC LOGICS § 1.1. PRELIMINARY REMARKS 69 § 1.2. PARAMETERIZED SYSTEMS OF EQUIVALENCE SENTENCES 78 § 1.3. PROTOALGEBRAICITY AND SUBDIRECT PRODUCTS 87 § 1.4. THE CHARACTERIZATION PROBLEM FOR THE CLASS MOD(C). LYNDON CLASSES 93 § 1.5. THE SUSZKO OPERATOR. FREE MATRICES 97 § 1.6. INJECTIVITY OF THE LEIBNIZ OPERATOR 100 § 1.7. THE TRANSFER PRINCIPLE 106 EXERCISES ILL NOTES FOR CHAPTER 1 119 CONTENTS CHAPTER 2. PROTOALGEBRAICITY AND THE DEDUCTION THEOREM § 2.1. THE PARAMETERIZED LOCAL DEDUCTION THEOREM 123 § 2.2. FIRST-ORDER DEFINABILITY OF PRINCIPAL DEDUCTIVE FILTERS ON C-MATRICES 132 § 2.3. THE FILTER EXTENSION PROPERTY 135 § 2.4. THE PARAMETERIZED DEDUCTION THEOREM 140 § 2.5. FILTER-DISTRIBUTIVE PROTALGEBRAIC LOGICS -.- 143 § 2.5.1. DISJUNCTIVE LOGICS 145 § 2.5.2. THE PLDT AND FILTER-DISTRIBUTIVITY 156 § 2.6. THE DEDUCTION THEOREM 162 § 2.7. FILTER-MODULARITY 172 EXERCISES 176 NOTES FOR CHAPTER 2 181 CHAPTER 3. EQUIVALENTIAL LOGICS § 3.1. BASIC FACTS 185 § 3.2. QUASIVARIETIES AND EQUIVALENTIAL LOGICS 188 § 3.3. THE LEIBNIZ OPERATOR AND EQUIVALENTIAL LOGICS 196 § 3.4. EQUIVALENTIAL MODAL LOGICS 201 § 3.5. EQUIVALENTIAL TENSE LOGICS 213 § 3.6. DYNAMIC LOGICS 216 § 3.7. MATRIX FRAMES X 218 EXERCISES 231 NOTES FOR CHAPTER 3 241 PART II. ALGEBRAIZABLE SENTENTIAL LOGICS CHAPTER Q. QUASIVARIETIES OF ALGEBRAS § Q.I. MAL CEV S THEOREM 245 § Q.2. RELATIVE CONGRUENCES 247 § Q.3.,LOCAL EQUATIONAL DEFINABILITY 250 § Q.4. EQUATIONAL CONSEQUENCE OPERATIONS 251 § Q.5. THE CONGRUENCE EXTENSION PROPERTY 258 § Q.6. FIRST-ORDER DEFINABILITY OF RELATIVE PRINCIPAL CONGRUENCES . . . 259 § Q.7. RELATIVELY SUBDIRECTLY IRREDUCIBLE ALGEBRAS 261 § Q.8. RELATIVELY CONGRUENCE-DISTRIBUTIVE QUASIVARIETIES 263 § Q.9. QUASIVARIETIES WITH EQUATIONALLY DEFINABLE RELATIVE PRINCIPAL CONGRUENCES 271 § Q.10. RELATIVELY CONGRUENCE-MODULAR QUASIVARIETIES 276 NOTES FOR CHAPTER Q 283 CHAPTER 4. ALGEBRAIZABLE LOGICS § 4.1. C-ALGEBRAS AND C-CONGRUENCES 287 § 4.2. TRANSFORMS 291 § 4.3. SURJECTIVELY STRUCTURAL CONSEQUENCES 300 § 4.4. ALGEBRAIZABILITY IN THE WEAK SENSE 307 CONTENTS VII § 4.5. ALGEBRAIZABLE LOGICS . 314 § 4.6. LOGICS ALGEBRAIZABLE IN THE SENSE OF BLOK AND PIGOZZI . . . . 318 § 4.7. ORTHOLOGICS 327 § 4.8. OTHER EXAMPLES 329 § 4.9. ENTAILMENT AND RELEVANCE LOGICS 333 NOTES FOR CHAPTER 4 343 IF * CHAPTER 5. REGULARLY ALGEBRAIZABLE LOGICS § 5.1. REGULAR ALGEBRAIZABILITY 347 § 5.2. RELATIVELY POINT-REGULAR QUASIVARIETIES 350 § 5.3. THE CONGRUENCE EXTENSION PROPERTY AND RELATIVELY POINT-REGULAR QUASIVARIETIES 359 § 5.4. RELATIVELY STRONGLY POINT-REGULAR QUASIVARIETIES 361 § 5.5. QUANTUM LOGICS 363 § 5.6. REGULARLY WEAKLY ALGEBRAIZABLE LOGICS 366 NOTES FOR CHAPTER 5 370 CHAPTER 6. FREGEAN LOGICS § 6.1. THE FREGEAN AXIOM 373 § 6.2. FREGEAN LOGICS 376 § 6.3. FREGEAN QUASIVARIETIES 378 § 6.4. HILBERTIAN QUASIVARIETIES 381 § 6.5. SKOLEM SEMILATTICES AND RELATED ALGEBRAS 390 § 6.6. THE CLASSICAL AND INTUITIONISTIC EQUIVALENCE LOGICS 397 § 6.7. REFERENTIAL FRAMES 403 EXERCISES 410 NOTES FOR CHAPTER 6 417 BIBLIOGRAPHY 419 SYMBOL INDEX 439 INDEX OF DEFINITIONS 445
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spelling	Czelakowski, Janusz Verfasser aut Protoalgebraic logics Janusz Czelakowski Dordrecht [u.a.] Kluwer 2001 XI, 452 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Trends in logic 10 Algebraic logic Trends in logic 10 (DE-604)BV011512969 10 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009441965&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Czelakowski, Janusz Protoalgebraic logics Trends in logic Algebraic logic
title	Protoalgebraic logics
title_auth	Protoalgebraic logics
title_exact_search	Protoalgebraic logics
title_full	Protoalgebraic logics Janusz Czelakowski
title_fullStr	Protoalgebraic logics Janusz Czelakowski
title_full_unstemmed	Protoalgebraic logics Janusz Czelakowski
title_short	Protoalgebraic logics
title_sort	protoalgebraic logics
topic	Algebraic logic
topic_facet	Algebraic logic
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009441965&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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