Proceedings of the 09th Asian Logic Conference: Mathematical Logic in Asia

CONTENTS ......Page 7
Preface ......Page 5
1. Introduction ......Page 9
2. Definitions and Preliminaries ......Page 10
3. Closure Relations ......Page 14
4. The Deduction-Detachment Theorem ......Page 17
5. DDT and Protoalgebraic Hilbert Systems ......Page 21
References ......Page 23
1. Background and preliminaries ......Page 25
2. One-element Rogers semilattices ......Page 27
References ......Page 38
1. Properties of 2-formulas ......Page 39
2. Main theorem ......Page 45
References ......Page 48
1. Introduction and Motivation ......Page 49
2. Preliminaries ......Page 50
3. Model Checking Game for SOEPDL ......Page 53
4. Reduction to CTL ......Page 55
References ......Page 57
1. Introduction ......Page 59
References ......Page 65
1. Introduction ......Page 66
2. Marker's construction ......Page 68
3. On one-to-one representation of E02-sets ......Page 70
4. N1-categorical theory with computable models ......Page 71
5. N0-categorical theory with computable model ......Page 73
6. Complexity of index sets ......Page 75
References ......Page 77
1. Preamble ......Page 78
2. l1 ......Page 79
3. lP (p > 1) ......Page 81
4. The O notation ......Page 83
5. O and loo ......Page 85
6. More about loo ......Page 88
7. c0 and Kanovei's questionr ......Page 90
References ......Page 96
1. Introduction ......Page 98
2. Preliminaries ......Page 103
3. Identification with Finite Negative Information ......Page 106
4. Some other Negative Information Models ......Page 107
5. Identification with Open Negative Information ......Page 108
6. Learning with Negative Counterexamples ......Page 111
7. Learning With Subset Queries ......Page 116
8. Random Negative Examples ......Page 118
References ......Page 119
Introduction ......Page 121
1. Structure of the nonstandard universe ......Page 123
2. Classes Ass2 and L[I]: effective sets ......Page 125
3. Effective cardinalities of internal sets ......Page 127
4. Effective cardinalities of sets of standard size ......Page 128
5. Exteriors and interiors ......Page 129
6. Effective cardinalities of Ess1 sets ......Page 131
7. Effective cardinalities of IIss1 sets ......Page 133
8. Effective sets in the form of quotients ......Page 137
9. Equivalence relations with standard size classes ......Page 138
10. Monadic partitions ......Page 140
11. The proof of the reducibility theorem ......Page 142
12. On small and large effective sets ......Page 146
13. Nonstandard version of the finite Ramsey theorem ......Page 150
References ......Page 151
1. Introduction ......Page 153
2. Specifications of computer arithmetics ......Page 154
3. Arithmetics design method ......Page 155
4. Digital number systems ......Page 159
5. Application: dataflow computations verification ......Page 161
6. Conclusion ......Page 162
References ......Page 163
2. Lesniewski's Systems ......Page 164
3. The Functional Completeness of Y-Prototheticr ......Page 168
4. The Functional Completeness of Y-Ontology ......Page 169
References ......Page 173
1. Introduction ......Page 174
2. Notation and Problem Statement ......Page 175
3. Reduction Calculus ......Page 176
4. A Reduction Algorithm for Tautology Test ......Page 179
5. Conclusion ......Page 181
References ......Page 182
1. Introduction ......Page 183
2. Non-vanishing I-algebras ......Page 184
3. Ordered semigroup ......Page 185
4. Local I-algebras ......Page 186
5. Finitely axiomatizable I-algebras ......Page 194
7. Nonaxiomatizability of local finitely axiomatizable and w-categorical I-algebras ......Page 196
References ......Page 197
1. Introduction ......Page 199
2. Fuzzification of Boolean-valued models ......Page 202
3. Generalized fuzzy models ......Page 204
4. Boolean-valued models with atomic Boolean algebras ......Page 207
References ......Page 210
1. Introduction ......Page 211
2. Permanents and determinants of Boolean matrices ......Page 212
3. Permanent expansion of Boolean matrices and its uniqueness ......Page 214
4. The group of invertible Boolean matrices and permanent expansion ......Page 216
5. Examples of nonnegative Boolean binary relations ......Page 218
6. Interiorities and their properties ......Page 219
References ......Page 221
1. Introduction ......Page 223
2. Effective Randomness Tests for Outer Measures ......Page 225
3. Nullsets and Kolmogorov complexity ......Page 231
4. A Hierarchy of Randomness Tests ......Page 234
References ......Page 239
1. Introduction ......Page 241
2. General Definitions, Notation, Preliminary Facts ......Page 245
3. Admissibility of Logical Consecutions, Preliminary Discussion ......Page 247
4. Decidability of Lt,y(Z) w.r.t. Admissible Consecutionsr ......Page 250
References ......Page 259
Isomorphisms and Definable Relations on Rings and Lattices ......Page 262
1. The lattice ......Page 263
2. The ring ......Page 266
3. The basic results ......Page 269
References ......Page 270
1. Induction ......Page 271
2. Laws ......Page 275
3. The Probability of Events and Sentences ......Page 276
4. The Probabilistic Laws on m ......Page 277
6. Probabilistic Maximum Specific Laws ......Page 279
7. The Solution of the Statistical Ambiguity Problem ......Page 281
References ......Page 283
1. Introduction ......Page 285
2. The category Rep ......Page 287
3. (Co)completeness of Rep ......Page 291
References ......Page 294
1. Introduction ......Page 296
2. Conceptual Semantic Systems ......Page 300
3. Temporal Conceptual Semantic Systems ......Page 302
4. An Example of a Temporal Conceptual Semantic System ......Page 304
5. Conclusion and Future Research ......Page 306
References ......Page 307
1. Introduction ......Page 310
2. MU-Formulas with Fixed Deficiency ......Page 312
3. Minimal Formulas with Simple Structures ......Page 313
4. Maximal MU Formulas ......Page 314
5. Marginal MU Formulas ......Page 316
6. Unique MU Formulas ......Page 317
7. MU Formulas with Disjunctive Splitting ......Page 320
8. MU Formulas Closed under Splitting ......Page 321
10. Homomorphisms Between MU Formulas ......Page 323
11. Generalizations ......Page 324
References ......Page 326