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E-raamat: Fork Alegebras in Algebra, Logic and Computer Science [World Scientific e-raamat]

(Univ De Buenos Aires, Argentina)
  • Formaat: 232 pages
  • Sari: Advances In Logic 2
  • Ilmumisaeg: 01-Aug-2002
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-13: 9789812777928
Teised raamatud teemal:
  • World Scientific e-raamat
  • Hind: 104,41 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
  • Formaat: 232 pages
  • Sari: Advances In Logic 2
  • Ilmumisaeg: 01-Aug-2002
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-13: 9789812777928
Teised raamatud teemal:
Fork algebras are a formalism based on the relational calculus, with interesting algebraic and metalogical properties. Their representability is especially appealing in computer science, since it allows a closer relationship between their language and models. This book gives a careful account of the results and presents some applications of Fork algebras in computer science, particularly in system specification and program construction. Many applications of Fork algebras in formal methods can be applied in many ways, and the book covers all the essentials in order to provide the reader with a better understanding.
Preface vii
Introduction and Motivations
1(4)
Software Specification, Binary Relations and Fork
1(4)
Algebras of Binary Relations and Relation Algebras
5(14)
History and Definitions
5(7)
Arithmetical Properties
12(7)
Proper and Abstract Fork Algebras
19(18)
On the Origin of Fork Algebras
19(2)
Definition of the Classes
21(5)
Arithmetical Properties
26(11)
Representability and Independence
37(12)
Representability of Abstract Fork Algebras
38(5)
Independence of the Axiomatization of Fork
43(6)
Interpretability of Classical First-Order Logic
49(24)
Basic Definitions
49(2)
Interpreting FOLE
51(22)
Algebraization of Non-Classical Logics
73(66)
Basic Definitions and Properties
75(1)
The Fork Logic FL
76(2)
Modal Logics
78(2)
Representation of Constraints in FL
80(1)
Interpretability of Modal Logics in FL
81(5)
A Proof Theoretical Approach
86(5)
Interpretability of Propositional Dynamic Logic in FL
91(11)
The Fork Logic FL'
102(2)
Syntax of FL'
102(1)
Semantics of FL'
102(2)
A Rasiowa--Sikorski Calculus for FL'
104(11)
The Deduction System for FL'
105(2)
Soundness and Completeness of the Calculus FLC
107(5)
Examples of Proofs in the Calculus FLC
112(3)
A Relational Proof System for Intuitionistic Logic
115(11)
Intuitionistic Logic
115(2)
Interpretability of Intuitionistic Logic in FL'
117(4)
A Fork Logic Calculus for Intuitionistic Logic
121(3)
Example
124(2)
A Relational Proof System for Minimal Intuitionistic Logic
126(6)
Relational Reasoning in Intermediate Logics
132(7)
Method 1
132(1)
Method 2
133(4)
Method 3
137(2)
A Calculus for Program Construction
139(68)
Introduction
139(2)
Filters and Sets
141(2)
The Relational Implication
143(6)
Representability and Expressiveness in Program Construction
149(1)
A Methodology for Program Construction
150(8)
Examples
158(34)
First Example
159(8)
Finding the Minimum Element in a List
167(1)
Finding the Minimum Common Ancestor
168(6)
Second Example
174(10)
Finding the Contiguous Sublists of Maximum Sum
184(3)
Finding the Longest Plateau
187(5)
A D&C Algorithm for MAXSTA
192(11)
Comparison with Previous Work
203(4)
Bibliography 207(8)
Index 215