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Tables of Contents for Algebraic Foundations of Many-Valued Reasoning
Chapter/Section Title
Page #
Page Count
Introduction
1
6
Basic notions
7
24
MV-algebras
7
5
Homomorphisms and ideals
12
7
Subdirect representation theorem
19
1
MV-equations
20
4
Boolean algebras
24
3
MV-chains
27
2
Bibliographical remarks
29
2
Chang completeness theorem
31
20
The functor T
31
3
Good sequences
34
3
The partially ordered monoid MA
37
3
Chang's l-group GA
40
3
Chang completeness theorem
43
6
Bibliographical remarks
49
2
Free MV-algebras
51
26
McNaughton functions
51
5
The one-dimensional case
56
6
Decomposing McNaughton functions
62
2
Ideals in free MV-algebras
64
6
Simple MV-algebras
70
2
Semisimple MV-algebras
72
3
Bibliographical remarks
75
2
Lukasiewicz ∞-valued calculus
77
26
Many-valued propositional calculi
78
4
Wajsberg algebras
82
5
Provability
87
5
Lindenbaum algebra
92
2
All tautologies are provable
94
3
Syntactic and semantic consequence
97
4
Bibliographical remarks
101
2
Ulam's game
103
8
Questions and answers
103
1
Dynamics of states of knowledge
104
3
Operation on states of knowledge
107
2
Bibliographical remarks
109
2
Lattice-theoretical properties
111
28
Minimal prime ideals
112
3
Stonean ideals and archimedean elements
115
1
Hyperarchimedean algebras
116
5
Direct products
121
3
Boolean products of MV-algebras
124
5
Completeness
129
3
Atoms and Pseudocomplements
132
2
Complete distributivity
134
3
Bibliographical remarks
137
2
MV-algebras and l-groups
139
18
Inverting the functor Γ
139
7
Applications
146
4
The radical
150
1
Perfect MV-algebras
151
5
Bibliographical remarks
156
1
Varieties of MV-algebras
157
22
Basic definitions
157
3
Varieties from simple algebras
160
1
MV-chains of finite rank
161
6
Komori's classification
167
4
Varieties generated by a finite chain
171
2
The cardinality of Freenr
173
4
Bibliographical remarks
177
2
Advanced topics
179
18
McNaughton's theorem
180
5
Nonsingular fans and normal forms
185
2
Complexity of the tautology problem
187
4
MV-algebras and AF C*-algebras
191
2
Di Nola's representation theorem
193
1
Bibliographical remarks
194
3
Further Readings
197
6
More than two truth values
197
2
Current Research Topics
199
4
Product
199
1
States, Observables, Probability, Partitions
200
1
Deduction
201
1
Further constructions
201
2
Bibliography
203
22
Index
225