A treatise on many-valued logics / Siegfried Gottwald.
Series Studies in logic and computation ; 9Editor: Baldock, Hertfordshire, England : Research Studies Press, c2001Descripción: xii, 604 p. ; 24 cmISBN: 0863802621Tema(s): Many-valued logicOtra clasificación: 03-02 (03B50 03B52)Part I. Basic Notions 1. General Background [3] 1.1 Classical and Many-Valued Logic [3] 1.2 Preliminary Notions [6] 2. The Formalized Language and its Interpretations [15] 2.1 Propositional Syntax [15] 2.2 Propositional Semantics [17] 2.3 First-Order Syntax [21] 2.4 Many-Valued Predicates [24] 2.5 First-Order Semantics [26] 3. Logical Validity and Entailment [29] 3.1 Designated Truth Degrees [29] 3.2 The Propositional Situation [31] 3.3 The First-Order Situation [38] 3.4 Elementary Model Theory [40] 4. Outline of the History of Many-Valued Logic [55] Part II. General Theory 5. Particular Connectives and Truth Degree Sets [63] 5.1 Conjunction Connectives [65] 5.2 Negation Connectives [84] 5.3 Disjunction Connectives [88] 5.4 Implication Connectives [91] 5.5 The J-Connectives [104] 6- Axiomatizability [107] 6-1 The Axiomatizability Problem [107] 6.2 Axiomatizing Propositional Systems [108] 6.3 Axiomatizing First-Order Systems [120] 6.4 Axiomatizing the Entailment Relation [128] 7. Sequent and Tableau Calculi [137] 7.1 Tableau Calculi for Many-Valued Logic [133] 7.2 Sequent Calculi for Many-Valued Logic [149] 8. Some Further Topics [181] 8.1 Functional Completeness [161] 8.2 Decidability of Propositional Systems [171] 8.3 Product Systems [173] Part III. Particular Systems of Many-Valued Logic 9. The Lukasiewicz Systems [179] 9.1 The Propositional Systems [179] 9.1.1 Important tautologies of the Lukasiewicz systems [181] 9.1.2 Characterizing the number of truth degrees [185] 9.1.3 Axiomatizability [193] 9.1.4 Decidability of the system L∞ [199] 9.1.5 Representability of truth degree functions [201] 9.2 Algebraic Structures for Lukasiewicz Systems [214] 9.2.1 MV-algebras [215] 9.2.2 MV-algebras and axiomatizations of the L-systems [234] 9.2.3 Wajsberg algebras [242] 9.2.4 Lukasiewicz algebras [247] 9.3 The First-Order Systems [249] 9.3.1 Important logically valid formulas [250] 9.3.2 Theoretical results for the L-systems [253] 9.3.3 The infinitely many-valued L-system [259] 10. The Gödel Systems [267] 10.1 The Propositional Systems [267] 10.2 The First-Order Systems [284] 11. Product Logic [291] 11.1 The Propositional System [291] 11.2 The First-Order System [308] 12. The Post Systems [313] 12.1 The Original Presentation [313] 12.2 The Present Form [318] 13. t-Norm Based Systems [327] 13.1 The Propositional Systems [327] 13.2 The First-Order Systems [338] 14. Axiomatizing t-Norm Based Logics [345] 14.1 The Propositional Systems [345] 14.1.1 Some particular cases [345] 14.1.2 A global approach [346] 14.1.3 Monoidal logic [352] 14.1.4 Monoidal t-norm logic [362] 14.1.5 Basic t-norm logic [367] 14.1.6 Completeness under continuous t-norms [370] 14.2 The First-Order Systems [374] 15. Some Three- and Four-Valued Systems [385] 15.1 Three-Valued Systems [385] 15.2 Four-Valued Systems . [393] 16. Systems with Graded Identity [401] 16.1 Graded Identity Relations [401] 16.2 Identity: the Absolute Point of View [403] 16.3 Identity: the Liberal Point of View [406] 16.4 Identity and Extent of Existence [413] Part IV. Applications of Many-Valued Logic 17. The Problem of Applications [419] 18. Fuzzy Sets, Vague Notions, and Many-Valued Logic [423] 18.1 Vagueness of Notions and Fuzzy Sets [423] 18.2 Basic Theory of Fuzzy Sets [425] 18.2.1 Elementary set algebraic operations [426] 18.2.2 Graded inclusion of fuzzy sets [429] 18.2.3 Particular fuzzy sets [431] 18.2.4 Generalized set algebraic operations [433] 18.2.5 Fuzzy cartesian products [435] 18.2.6 The extension principle [437] 18.3 Fuzzy Relations [438] 18.4 The Full Image Under a Relation [442] 18.5 Special Types of Fuzzy Relations [445] 18.5.1 Fuzzy equivalence relations [446] 18.5.2 Fuzzy partitions of fuzzy sets [448] 18.5.3 Transitive hulls [452] 18.5.4 Fuzzy ordering relations [454] 18.6 Graded Properties of Fuzzy Relations [460] 19. Fuzzy Logic [471] 19.1 Many-Valued Logic with Graded Consequences [472] 19.2 The Semantic Approach [473] 19.3 The Syntactic Approach [475] 19.4 Axiomatizing Fuzzy Logic [477] 19.5 Partial Soundness of Inference Rules [480] 19.5.1 Formalizing the problem [480] 19.5.2 Partially sound rules in many-valued and fuzzy logics [482] 19.6 Some Theoretical Results [484] 19.7 The Algebraic Approach [486] 20. Treating Presuppositions with Many-Valued Logic [493] 20.1 The Phenomenon of Presuppositions [493] 20.2 Three-Valued Approaches [496] 20.3 Four-Valued Approaches [499] 21. Truth Degrees and Alethic Modalities [503] 21.1 Interpreting Modal Logic as Many-Valued Logic [503] 21.2 Graded Modalities [512] 22. Approximating Intuitionistic and Other Logics [525] 22.1 Many-Valued Approaches toward Intuitionistic Logic [525] 22.2 Approximating Logics by Many-Valued Logics [527] 23. Independence Proofs [535] 23.1 The Propositional Case [535] 23.2 The First-Order Case [538] 24. Consistency Considerations for Set Theory [557] References [567] Subject Index [595] Index of Names [601] Index of Symbols [603]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode |
|---|---|---|---|---|---|---|---|
Libros
|
Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 03 G687 (Browse shelf) | Available | A-8320 |
Browsing Instituto de Matemática, CONICET-UNS shelves, Shelving location: Libros ordenados por tema Close shelf browser
| 03 G655 Recursive number theory : | 03 G655m-2 Mathematical logic / | 03 G655r Recursive analysis / | 03 G687 A treatise on many-valued logics / | 03 G755 Advanced logic for applications / | 03 G895 Fonctions récursives / | 03 H157 An introduction to modern logic : |
Incluye referencias bibliográficas (p. [567]-593) e índice.
Part I. Basic Notions --
1. General Background [3] --
1.1 Classical and Many-Valued Logic [3] --
1.2 Preliminary Notions [6] --
2. The Formalized Language and its Interpretations [15] --
2.1 Propositional Syntax [15] --
2.2 Propositional Semantics [17] --
2.3 First-Order Syntax [21] --
2.4 Many-Valued Predicates [24] --
2.5 First-Order Semantics [26] --
3. Logical Validity and Entailment [29] --
3.1 Designated Truth Degrees [29] --
3.2 The Propositional Situation [31] --
3.3 The First-Order Situation [38] --
3.4 Elementary Model Theory [40] --
4. Outline of the History of Many-Valued Logic [55] --
Part II. General Theory --
5. Particular Connectives and Truth Degree Sets [63] --
5.1 Conjunction Connectives [65] --
5.2 Negation Connectives [84] --
5.3 Disjunction Connectives [88] --
5.4 Implication Connectives [91] --
5.5 The J-Connectives [104] --
6- Axiomatizability [107] --
6-1 The Axiomatizability Problem [107] --
6.2 Axiomatizing Propositional Systems [108] --
6.3 Axiomatizing First-Order Systems [120] --
6.4 Axiomatizing the Entailment Relation [128] --
7. Sequent and Tableau Calculi [137] --
7.1 Tableau Calculi for Many-Valued Logic [133] --
7.2 Sequent Calculi for Many-Valued Logic [149] --
8. Some Further Topics [181] --
8.1 Functional Completeness [161] --
8.2 Decidability of Propositional Systems [171] --
8.3 Product Systems [173] --
Part III. Particular Systems of Many-Valued Logic --
9. The Lukasiewicz Systems [179] --
9.1 The Propositional Systems [179] --
9.1.1 Important tautologies of the Lukasiewicz systems [181] --
9.1.2 Characterizing the number of truth degrees [185] --
9.1.3 Axiomatizability [193] --
9.1.4 Decidability of the system L∞ [199] --
9.1.5 Representability of truth degree functions [201] --
9.2 Algebraic Structures for Lukasiewicz Systems [214] --
9.2.1 MV-algebras [215] --
9.2.2 MV-algebras and axiomatizations of the L-systems [234] --
9.2.3 Wajsberg algebras [242] --
9.2.4 Lukasiewicz algebras [247] --
9.3 The First-Order Systems [249] --
9.3.1 Important logically valid formulas [250] --
9.3.2 Theoretical results for the L-systems [253] --
9.3.3 The infinitely many-valued L-system [259] --
10. The Gödel Systems [267] --
10.1 The Propositional Systems [267] --
10.2 The First-Order Systems [284] --
11. Product Logic [291] --
11.1 The Propositional System [291] --
11.2 The First-Order System [308] --
12. The Post Systems [313] --
12.1 The Original Presentation [313] --
12.2 The Present Form [318] --
13. t-Norm Based Systems [327] --
13.1 The Propositional Systems [327] --
13.2 The First-Order Systems [338] --
14. Axiomatizing t-Norm Based Logics [345] --
14.1 The Propositional Systems [345] --
14.1.1 Some particular cases [345] --
14.1.2 A global approach [346] --
14.1.3 Monoidal logic [352] --
14.1.4 Monoidal t-norm logic [362] --
14.1.5 Basic t-norm logic [367] --
14.1.6 Completeness under continuous t-norms [370] --
14.2 The First-Order Systems [374] --
15. Some Three- and Four-Valued Systems [385] --
15.1 Three-Valued Systems [385] --
15.2 Four-Valued Systems . [393] --
16. Systems with Graded Identity [401] --
16.1 Graded Identity Relations [401] --
16.2 Identity: the Absolute Point of View [403] --
16.3 Identity: the Liberal Point of View [406] --
16.4 Identity and Extent of Existence [413] --
Part IV. Applications of Many-Valued Logic --
17. The Problem of Applications [419] --
18. Fuzzy Sets, Vague Notions, and Many-Valued Logic [423] --
18.1 Vagueness of Notions and Fuzzy Sets [423] --
18.2 Basic Theory of Fuzzy Sets [425] --
18.2.1 Elementary set algebraic operations [426] --
18.2.2 Graded inclusion of fuzzy sets [429] --
18.2.3 Particular fuzzy sets [431] --
18.2.4 Generalized set algebraic operations [433] --
18.2.5 Fuzzy cartesian products [435] --
18.2.6 The extension principle [437] --
18.3 Fuzzy Relations [438] --
18.4 The Full Image Under a Relation [442] --
18.5 Special Types of Fuzzy Relations [445] --
18.5.1 Fuzzy equivalence relations [446] --
18.5.2 Fuzzy partitions of fuzzy sets [448] --
18.5.3 Transitive hulls [452] --
18.5.4 Fuzzy ordering relations [454] --
18.6 Graded Properties of Fuzzy Relations [460] --
19. Fuzzy Logic [471] --
19.1 Many-Valued Logic with Graded Consequences [472] --
19.2 The Semantic Approach [473] --
19.3 The Syntactic Approach [475] --
19.4 Axiomatizing Fuzzy Logic [477] --
19.5 Partial Soundness of Inference Rules [480] --
19.5.1 Formalizing the problem [480] --
19.5.2 Partially sound rules in many-valued and fuzzy logics [482] --
19.6 Some Theoretical Results [484] --
19.7 The Algebraic Approach [486] --
20. Treating Presuppositions with Many-Valued Logic [493] --
20.1 The Phenomenon of Presuppositions [493] --
20.2 Three-Valued Approaches [496] --
20.3 Four-Valued Approaches [499] --
21. Truth Degrees and Alethic Modalities [503] --
21.1 Interpreting Modal Logic as Many-Valued Logic [503] --
21.2 Graded Modalities [512] --
22. Approximating Intuitionistic and Other Logics [525] --
22.1 Many-Valued Approaches toward Intuitionistic Logic [525] --
22.2 Approximating Logics by Many-Valued Logics [527] --
23. Independence Proofs [535] --
23.1 The Propositional Case [535] --
23.2 The First-Order Case [538] --
24. Consistency Considerations for Set Theory [557] --
References [567] --
Subject Index [595] --
Index of Names [601] --
Index of Symbols [603] --
MR, 2002g:03004
Click on an image to view it in the image viewer
There are no comments on this title.