Holdings: Algebraic methods in philosophical logic

Algebraic methods in philosophical logic:

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Bibliographic Details
Main Authors:	Dunn, J. Michael 1941-2021 (Author), Hardegree, Gary M. (Author)
Format:	Book
Language:	English
Published:	Oxford Clarendon Press 2001
Series:	Oxford logic guides 41
Subjects:	Algebra Logica Logique algébrique Modale logica Partiële orde Semantiek Logik Semantik Algebraic logic Mathematische Logik Nichtklassische Logik Algebraische Methode Klassische Logik Vollständigkeit
Online Access:	Inhaltsverzeichnis
Physical Description:	XV, 470 S. graph. Darst.
ISBN:	0198531923

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Record in the Search Index

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adam_text	ALGEBRAIC METHODS IN PHILOSOPHICAL LOGIC J. MICHAEL DUNN AND GARY M. HARDEGREE CLARENDON PRESS * OXFORD 2001 CONTENTS 1 INTRODUCTION 2 UNIVERSAL ALGEBRA 10 2.1 INTRODUCTION 10 2.2 RELATIONAL AND OPERATIONAL STRUCTURES (ALGEBRAS) 10 2.3 SUBRELATIONAL STRUCTURES AND SUBALGEBRAS 11 2.4 INTERSECTION, GENERATORS, AND INDUCTION FROM GENERATORS 13 2.5 HOMOMORPHISMS AND ISOMORPHISMS 15 2.6 CONGRUENCE RELATIONS AND QUOTIENT ALGEBRAS 19 2.7 DIRECT PRODUCTS 25 2.8 SUBDIRECT PRODUCTS AND THE FUNDAMENTAL THEOREM OF UNIVERSAL ALGEBRA 28 2.9 WORD ALGEBRAS AND INTERPRETATIONS 33 2.10 VARIETIES AND EQUATIONAL DEFINABILITY 36 2.11 EQUATIONAL THEORIES 37 2.12 EXAMPLES OF FREE ALGEBRAS 39 2.13 FREEDOM AND TYPICALITY 41 2.14 THE EXISTENCE OF FREE ALGEBRAS; FREEDOM IN VARIETIES AND SUBDIRECT CLASSES 44 2.15 BIRKHOFF S VARIETIES THEOREM 47 2.16 QUASI-VARIETIES 49 2.17 LOGIC AND ALGEBRA: ALGEBRAIC STATEMENTS OF SOUNDNESS AND COMPLETENESS 51 3 ORDER, LATTICES, AND BOOLEAN ALGEBRAS - 55 3.1 INTRODUCTION 55 3.2 PARTIALLY ORDERED SETS , 55 3.3 STRICT ORDERINGS , 58 3.4 COVERING AND HASSE DIAGRAMS . 60 3.5 INFIMA AND SUPREMA 63 3.6 LATTICES 67 3.7 THE LATTICE OF CONGRUENCES 70 3.8 LATTICES AS ALGEBRAS 71 3.9 ORDERED ALGEBRAS 74 3.10 TONOIDS 77 3.11 TONOID VARIETIES 82 3.12 CLASSICAL COMPLEMENTATION 85 3.13 NON-CLASSICAL COMPLEMENTATION 88 3.14 CLASSICAL DISTRIBUTION 92 3.15 NON-CLASSICAL DISTRIBUTION 98 3.16 CLASSICAL IMPLICATION 105 3.17 NON-CLASSICAL IMPLICATION 109 3.18 FILTERS AND IDEALS 115 CONTENTS 4 SYNTAX 4.1 INTRODUCTION 4.2 THE ALGEBRA OF STRINGS 4.3 THE ALGEBRA OF SENTENCES 4.4 LANGUAGES AS ABSTRACT STRUCTURES: CATEGORIAL GRAMMAR 4.5 SUBSTITUTION VIEWED ALGEBRAICALLY (ENDOMORPHISMS) 4.6 EFFECTIVITY 4.7 ENUMERATING STRINGS AND SENTENCES 5 SEMANTICS 141 5.1 INTRODUCTION 141 5.2 CATEGORIAL SEMANTICS 142 5.3 ALGEBRAIC SEMANTICS FOR SENTENTIAL LANGUAGES 144 5.4 TRUTH-VALUE SEMANTICS 146 5.5 POSSIBLE WORLDS SEMANTICS 148 5.6 LOGICAL MATRICES AND LOGICAL ATLASES 152 5.7 INTERPRETATIONS AND VALUATIONS 155 5.8 INTERPRETED AND EVALUATIONALLY CONSTRAINED LANGUAGES 158 5.9 SUBSTITUTIONS, INTERPRETATIONS, AND VALUATIONS 162 5.10 VALUATION SPACES 166 5.11 VALUATIONS AND LOGIC 169 5.12 EQUIVALENCE 172 5.13 COMPACTNESS 176 5.14 THE THREE-FOLD WAY 181 6 LOGIC 184 6.1 MOTIVATIONAL BACKGROUND 184 6.2 THE VARIETIES OF LOGICAL EXPERIENCE 185 6.3 WHAT IS (A) LOGIC? 187 6.4 LOGICS AND VALUATIONS 189 6.5 BINARY CONSEQUENCE IN THE CONTEXT OF PRE-ORDERED SETS 191 6.6 ASYMMETRIC CONSEQUENCE AND VALUATIONS (COMPLETENESS) 194 6.7 ASYMMETRIC CONSEQUENCE IN THE CONTEXT OF PRE-ORDERED GROUPOIDS 196 6.8 SYMMETRIC CONSEQUENCE AND VALUATIONS (COMPLETENESS AND ABSOLUTENESS) 199 6.9 SYMMETRIC CONSEQUENCE IN THE CONTEXT OF HEMI-DISTRIBUTOIDS 202 6.10 STRUCTURAL (FORMAL) CONSEQUENCE 208 6.11 LINDENBAUM MATRICES AND COMPOSITIONAL SEMANTICS FOR ASSERTIONAL FORMAL LOGICS 209 6.12 LINDENBAUM ATLAS AND COMPOSITIONAL SEMANTICS FOR FORMAL ASYMMETRIC CONSEQUENCE LOGICS 211 6.13 SCOTT ATLAS AND COMPOSITIONAL SEMANTICS FOR FORMAL SYMMETRIC CONSEQUENCE LOGICS 213 CONTENTS XIII 6.14 CO-CONSEQUENCE AS A CONGRUENCE 214 6.15 FORMAL PRESENTATIONS OF LOGICS (AXIOMATIZATIONS) 216 6.16 EFFECTIVENESS AND LOGIC 224 7 MATRICES AND ATLASES 226 7.1 MATRICES 226 7.1.1 BACKGROUND 226 7.1.2 LUKASIEWICZ MATRICES/SUBMATRICES, ISOMORPHISMS 227 7.1.3 G6DEL MATRICES/MORE SUBMATRICES 230 7.1.4 SUGIHARA MATRICES/HOMOMORPHISMS 230 7.1.5 DIRECT PRODUCTS 232 7.1.6 TAUTOLOGY PRESERVATION 232 7.1.7 INFINITE MATRICES 233 7.1.8 INTERPRETATION 234 7.2 RELATIONS AMONG MATRICES: SUBMATRICES, HOMOMORPHIC IMAGES, AND DIRECT PRODUCTS 237 7.3 PROTO-PRESERVATION THEOREMS 239 7.4 PRESERVATION THEOREMS 243 7.5 VARIETIES THEOREM ANALOGS FOR MATRICES 246 7.5.1 UNARY ASSERTIONAL LOGICS 246 7.5.2 ASYMMETRIC CONSEQUENCE LOGICS 247 7.5.3 SYMMETRIC CONSEQUENCE LOGICS 249 7.6 CONGRUENCES AND QUOTIENT MATRICES 249 7.7 THE STRUCTURE OF CONGRUENCES 254 7.8 THE CANCELLATION PROPERTY 257 7.9 NORMAL MATRICES .... 262 7.10 NORMAL ATLASES 266 7.11 NORMAL CHARACTERISTIC MATRICES FOR CONSEQUENCE LOGICS 270 7.12 MATRICES AND ALGEBRAS 271 7.13 WHEN IS A LOGIC ALGEBRAIZABLE ? V 273 8 REPRESENTATION THEOREMS 277 8.1 PARTIALLY ORDERED SETS WITH IMPLICATION(S) 277 8.1.1 PARTIALLY ORDERED SETS 277 8.1.2 IMPLICATION STRUCTURES 278 8.2 SEMI-LATTICES 287 8.3 LATTICES 288 8.4 FINITE DISTRIBUTIVE LATTICES 293 8.5 THE PROBLEM OF A GENERAL REPRESENTATION FOR DISTRIBUTIVE LATTICES 295 8.6 STONE S REPRESENTATION THEOREM FOR DISTRIBUTIVE LATTICES 297 8.7 BOOLEAN ALGEBRAS 300 8.8 FILTERS AND HOMOMORPHISMS 302 8.9 MAXIMAL FILTERS AND PRIME FILTERS 302 CONTENTS 8.10 STONE S REPRESENTATION THEOREM FOR BOOLEAN ALGEBRAS 303 8.11 MAXIMAL FILTERS AND TWO-VALUED HOMOMORPHISMS 305 8.12 DISTRIBUTIVE LATTICES WITH OPERATORS 313 8.13 LATTICES WITH OPERATORS 317 9 CLASSICAL PROPOSITIONAL LOGIC 321 9.1 PRELIMINARY NOTIONS 321 9.2 THE EQUIVALENCE OF (UNITAL) BOOLEAN LOGIC AND FREGE LOGIC 322 9.3 SYMMETRICAL ENTAILMENT 324 9.4 COMPACTNESS THEOREMS FOR CLASSICAL PROPOSITIONAL LOGIC 326 9.5 A THIRD LOGIC 333 9.6 AXIOMATIC CALCULI FOR CLASSICAL PROPOSITIONAL LOGIC 334 9.7 PRIMITIVE VOCABULARY AND DEFINITIONAL COMPLETENESS 335 9.8 THE CALCULUS BC 337 9.9 THE CALCULUS Z)(BC) 341 9.10 ASYMMETRICAL SEQUENT CALCULUS FOR CLASSICAL PROPOSITIONAL LOGIC 346 9.11 FRAGMENTS OF CLASSICAL PROPOSITIONAL LOGIC 348 9.12 THE IMPLICATIVE FRAGMENT OF CLASSICAL PROPOSITIONAL LOGIC: SEMI-BOOLEAN ALGEBRAS 349 9.13 AXIOMATIZING THE IMPLICATIVE FRAGMENT OF CLASSICAL PROPOSITIONAL LOGIC 350 9.14 THE POSITIVE FRAGMENT OF CLASSICAL PROPOSITIONAL LOGIC 352 10 MODAL LOGIC AND CLOSURE ALGEBRAS 356 10.1 MODAL LOGICS 356 10.2 BOOLEAN ALGEBRAS WITH A NORMAL UNITARY OPERATOR 358 10.3 FREE BOOLEAN ALGEBRAS WITH A NORMAL UNITARY OPERATOR AND MODAL LOGIC 361 10.4 THE KRIPKE SEMANTICS FOR MODAL LOGIC 361 10.5 COMPLETENESS 363 10.6 TOPOLOGICAL REPRESENTATION OF CLOSURE ALGEBRAS 364 10.7 THE ABSOLUTE SEMANTICS FOR S5 367 10.8 HENLE MATRICES 367 10.9 ALTERNATION PROPERTY FOR S4 AND COMPACTNESS 369 10.10 ALGEBRAIC DECISION PROCEDURES FOR MODAL LOGIC 370 10.11 S5 AND PRETABULARITY 375 11 INTUITIONISTIC LOGIC AND HEY TING ALGEBRAS 380 11.1 INTUITIONISTIC LOGIC 380 11.2 IMPLICATIVE LATTICES 381 11.3 HEYTING ALGEBRAS 383 11.4 REPRESENTATION OF HEYTING ALGEBRAS USING QUASI-ORDERED SETS 383 11.5 TOPOLOGICAL REPRESENTATION OF HEYTING ALGEBRAS 384 CONTENTS 11.6 EMBEDDING HEYTING ALGEBRAS INTO CLOSURE ALGEBRAS 386 11.7 TRANSLATION OF H INTO S4 386 11.8 ALTERNATION PROPERTY FOR H 387 11.9 ALGEBRAIC DECISION PROCEDURES FOR INTUITIONISTIC LOGIC 388 11.10 LC AND PRETABULARITY 390 12 GAGGLES: GENERAL GALOIS LOGICS 394 12.1 INTRODUCTION 394 12.2 RESIDUATION AND GALOIS CONNECTIONS 395 12.3 DEFINITIONS OF DISTRIBUTOID AND TONOID 398 12.4 REPRESENTATION OF DISTRIBUTOIDS 400 12.5 PARTIALLY ORDERED RESIDUATED GROUPOIDS 406 12.6 DEFINITION OF A GAGGLE 408 12.7 REPRESENTATION OF GAGGLES 409 12.8 MODIFICATIONS FOR DISTRIBUTOIDS AND GAGGLES WITH IDENTITIES AND CONSTANTS 412 12.9 APPLICATIONS 414 12.10 MONADIC MODAL OPERATORS 415 12.11 DYADIC MODAL OPERATORS 417 12.12 IDENTITY ELEMENTS 420 12.13 REPRESENTATION OF POSITIVE BINARY GAGGLES 421 12.14 IMPLICATION 422 12.14.1 IMPLICATION IN RELEVANCE LOGIC 423 12.14.2 IMPLICATION IN INTUITIONISTIC LOGIC 424 12.14.3 MODAL LOGIC 424 12.15 NEGATION ... 425 12.15.1 THE GAGGLE TREATMENT OF NEGATION 425 12.15.2 NEGATION IN INTUITIONISTIC LOGIC 426 12.15.3 NEGATION IN RELEVANCE LOGIC 427 12.15.4 NEGATION IN CLASSICAL LOGIC 429 12.16 FUTURE DIRECTIONS 430 13 REPRESENTATIONS AND DUALITY 431 13.1 REPRESENTATIONS AND DUALITY 431 13.2 SOME TOPOLOGY 433 13.3 DUALITY FOR BOOLEAN ALGEBRAS * 435 13.4 DUALITY FOR DISTRIBUTIVE LATTICES 438 13.5 EXTENSIONS OF STONE S AND PRIESTLEY S RESULTS 441 REFERENCES 445 INDEX 455
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series	Oxford logic guides
series2	Oxford logic guides
spelling	Dunn, J. Michael 1941-2021 Verfasser (DE-588)124999123 aut Algebraic methods in philosophical logic J. Michael Dunn and Gary M. Hardagree Oxford Clarendon Press 2001 XV, 470 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford logic guides 41 Algebra gtt Logica gtt Logique algébrique Modale logica gtt Partiële orde gtt Semantiek gtt Logik Semantik Algebraic logic Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Nichtklassische Logik (DE-588)4197462-1 gnd rswk-swf Logik (DE-588)4036202-4 gnd rswk-swf Algebraische Methode (DE-588)4141841-4 gnd rswk-swf Klassische Logik (DE-588)4333219-5 gnd rswk-swf Vollständigkeit (DE-588)4284513-0 gnd rswk-swf Logik (DE-588)4036202-4 s Algebraische Methode (DE-588)4141841-4 s DE-604 Mathematische Logik (DE-588)4037951-6 s Klassische Logik (DE-588)4333219-5 s Vollständigkeit (DE-588)4284513-0 s Nichtklassische Logik (DE-588)4197462-1 s Hardegree, Gary M. Verfasser aut Oxford logic guides 41 (DE-604)BV000013997 41 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009400917&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Dunn, J. Michael 1941-2021 Hardegree, Gary M. Algebraic methods in philosophical logic Oxford logic guides Algebra gtt Logica gtt Logique algébrique Modale logica gtt Partiële orde gtt Semantiek gtt Logik Semantik Algebraic logic Mathematische Logik (DE-588)4037951-6 gnd Nichtklassische Logik (DE-588)4197462-1 gnd Logik (DE-588)4036202-4 gnd Algebraische Methode (DE-588)4141841-4 gnd Klassische Logik (DE-588)4333219-5 gnd Vollständigkeit (DE-588)4284513-0 gnd
subject_GND	(DE-588)4037951-6 (DE-588)4197462-1 (DE-588)4036202-4 (DE-588)4141841-4 (DE-588)4333219-5 (DE-588)4284513-0
title	Algebraic methods in philosophical logic
title_auth	Algebraic methods in philosophical logic
title_exact_search	Algebraic methods in philosophical logic
title_full	Algebraic methods in philosophical logic J. Michael Dunn and Gary M. Hardagree
title_fullStr	Algebraic methods in philosophical logic J. Michael Dunn and Gary M. Hardagree
title_full_unstemmed	Algebraic methods in philosophical logic J. Michael Dunn and Gary M. Hardagree
title_short	Algebraic methods in philosophical logic
title_sort	algebraic methods in philosophical logic
topic	Algebra gtt Logica gtt Logique algébrique Modale logica gtt Partiële orde gtt Semantiek gtt Logik Semantik Algebraic logic Mathematische Logik (DE-588)4037951-6 gnd Nichtklassische Logik (DE-588)4197462-1 gnd Logik (DE-588)4036202-4 gnd Algebraische Methode (DE-588)4141841-4 gnd Klassische Logik (DE-588)4333219-5 gnd Vollständigkeit (DE-588)4284513-0 gnd
topic_facet	Algebra Logica Logique algébrique Modale logica Partiële orde Semantiek Logik Semantik Algebraic logic Mathematische Logik Nichtklassische Logik Algebraische Methode Klassische Logik Vollständigkeit
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009400917&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000013997
work_keys_str_mv	AT dunnjmichael algebraicmethodsinphilosophicallogic AT hardegreegarym algebraicmethodsinphilosophicallogic

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