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Treatise on Many-valued Logic [Kõva köide]

  • Formaat: Hardback, 616 pages, kõrgus x laius: 235x159 mm, kaal: 1107 g, 6 figures, 4 line drawings, references, indexes
  • Sari: Studies in Logic & Computation No. 9
  • Ilmumisaeg: 11-Aug-2001
  • Kirjastus: Research Studies Press
  • ISBN-10: 0863802621
  • ISBN-13: 9780863802621
Teised raamatud teemal:
Treatise on Many-valued LogicSuurem pilt
  • Formaat: Hardback, 616 pages, kõrgus x laius: 235x159 mm, kaal: 1107 g, 6 figures, 4 line drawings, references, indexes
  • Sari: Studies in Logic & Computation No. 9
  • Ilmumisaeg: 11-Aug-2001
  • Kirjastus: Research Studies Press
  • ISBN-10: 0863802621
  • ISBN-13: 9780863802621
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780863802621.html
Märksõnad:
For advanced undergraduate students of logic or computer science with a knowledge of elementary notions from classical logic and set theory, and lattices and other algebraic structures, Gottwald (logic and philosophy of science, U. of Leipzig, Germany) explains the theory underling many-valued logic, and surveys a broad class of applications. It is the growing applications that have driven recent interest in the logic, especially in computer science for automated theorem proving, approximate reasoning, multi-agent systems, switching theory, program verification, and other tricks. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Part I. Basic Notions
General Background
3(12)
Classical and Many-Valued Logic
3(3)
Preliminary Notions
6(9)
The Formalized Language and its Interpretations
15(14)
Propositional Syntax
15(2)
Propositional Semantics
17(4)
First-Order Syntax
21(3)
Many-Valued Predicates
24(2)
First-Order Semantics
26(3)
Logical Validity and Entailment
29(26)
Designated Truth Degrees
29(2)
The Propositional Situation
31(7)
The First-Order Situation
38(2)
Elementary Model Theory
40(15)
Outline of the History of Many-Valued Logic
55(8)
Part II. General Theory
Particular Connectives and Truth Degree Sets
63(44)
Conjunction Connectives
65(19)
Negation Connectives
84(4)
Disjunction Connectives
88(3)
Implication Connectives
91(13)
The J-Connectives
104(3)
Axiomatizability
107(30)
The Axiomatizability Problem
107(1)
Axiomatizing Propositional Systems
108(12)
Axiomatizing First-Order Systems
120(8)
Axiomatizing the Entailment Relation
128(9)
Sequent and Tableau Calculi
137(24)
Tableau Calculi for Many-Valued Logic
138(11)
Sequent Calculi for Many-Valued Logic
149(12)
Some Further Topics
161(18)
Functional Completeness
161(10)
Decidability of Propositional Systems
171(2)
Product Systems
173(6)
Part III. Particular Systems of Many-Valued Logic
The Lukasiewicz Systems
179(88)
The Propositional Systems
179(35)
Important tautologies of the Lukasiewicz systems
181(4)
Characterizing the number of truth degrees
185(8)
Axiomatizability
193(6)
Decidability of the system L∞
199(2)
Representability of truth degree functions
201(13)
Algebraic Structures for Lukasiewicz Systems
214(35)
MV-algebras
215(19)
MV-algebras and axiomatizations of the L-systems
234(8)
Wajsberg algebras
242(5)
Lukasiewicz algebras
247(2)
The First-Order Systems
249(18)
Important logically valid formulas
250(3)
Theoretical results for the L-systems
253(6)
The infinitely many-valued L-system
259(8)
The Godel Systems
267(24)
The Propositional Systems
267(17)
The First-Order Systems
284(7)
Product Logic
291(22)
The Propositional System
291(17)
The First-Order System
308(5)
The Post Systems
313(14)
The Original Presentation
313(5)
The Present Form
318(9)
t-Norm Based Systems
327(18)
The Propositional Systems
327(11)
The First-Order Systems
338(7)
Axiomatizing t-Norm Based Logics
345(40)
The Propositional Systems
345(29)
Some particular cases
345(1)
A global approach
346(6)
Monoidal logic
352(10)
Monoidal t-norm logic
362(5)
Basic t-norm logic
367(3)
Completeness under continuous t-norms
370(4)
The First-Order Systems
374(11)
Some Three-and Four-Valued Systems
385(16)
Three-Valued Systems
385(8)
Four-Valued Systems
393(8)
Systems with Graded Identity
401(18)
Graded Identity Relations
401(2)
Identity: the Absolute Point of View
403(3)
Identity: the Liberal Point of View
406(7)
Identity and Extent of Existence
413(6)
Part IV. Applications of Many-Valued Logic
The Problem of Applications
419(4)
Fuzzy Sets, Vague Notions, and Many-Valued Logic
423(48)
Vagueness of Notions and Fuzzy Sets
423(2)
Basic Theory of Fuzzy Sets
425(13)
Elementary set algebraic operations
426(3)
Graded inclusion of fuzzy sets
429(2)
Particular fuzzy sets
431(2)
Generalized set algebraic operations
433(2)
Fuzzy cartesian products
435(2)
The extension principle
437(1)
Fuzzy Relations
438(4)
The Full Image Under a Relation
442(3)
Special Types of Fuzzy Relations
445(15)
Fuzzy equivalence relations
446(2)
Fuzzy partitions of fuzzy sets
448(4)
Transitive hulls
452(2)
Fuzzy ordering relations
454(6)
Graded Properties of Fuzzy Relations
460(11)
Fuzzy Logic
471(22)
Many-Valued Logic with Graded Consequences
472(1)
The Semantic Approach
473(2)
The Syntactic Approach
475(2)
Axiomatizing Fuzzy Logic
477(3)
Partial Soundness of Inference Rules
480(4)
Formalizing the problem
480(2)
Partially sound rules in many-valued and fuzzy logics
482(2)
Some Theoretical Results
484(2)
The Algebraic Approach
486(7)
Treating Presuppositions with Many-Valued Logic
493(10)
The Phenomenon of Presuppositions
493(3)
Three-Valued Approaches
496(3)
Four-Valued Approaches
499(4)
Truth Degrees and Alethic Modalities
503(22)
Interpreting Modal Logic as Many-Valued Logic
503(9)
Graded Modalities
512(13)
Approximating Intuitionistic and Other Logics
525(10)
Many-Valued Approaches toward Intuitionistic Logic
525(2)
Approximating Logics by Many-Valued Logics
527(8)
Independence Proofs
535(22)
The Propositional Case
535(3)
The First-Order Case
538(19)
Consistency Considerations for Set Theory
557(10)
References 567(28)
Subject Index 595(6)
Index of Names 601(2)
Index of Symbols 603