Extensions of first order logic:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
1996
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge tracts in theoretical computer science
19 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXII, 388 S. |
| ISBN: | 0521354358 |
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Datensatz im Suchindex
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| adam_text | EXTENSIONS OF FIRST ORDER LOGIC MARIA MANZANO UNIVERSITY OF BARCELONA
CAMBRIDGE UNIVERSITY PRESS TABLE OF CONTENTS PREFACE XV CHAPTER I:
STANDARD SECOND ORDER LOGIC. 1 1.- INTRODUCTION. 1 1.1. GENERAL IDEA. 1
1.2. EXPRESSIVE POWER. 2 1.3. MODEL-THEORETIC COUNTERPARTS OF
EXPRESSIVENESS. 4 1.4. INCOMPLETENESS. 5 2.- SECOND ORDER GRAMMAR. 6
2.1. DEFINITION (SIGNATURE AND ALPHABET). 9 2.2. EXPRESSIONS: TERMS,
PREDICATES AND FORMULAS. 11 2.3. REMARKS ON NOTATION. 13 2.4. INDUCTION.
14 2.5. FREE AND BOUND VARIABLES. 17 2.6. SUBSTITUTION. 18 3.-
STANDARD STRUCTURES. 22 3.1. DEFINITION OF STANDARD STRUCTURES. 22 3.2.
RELATIONS BETWEEN STANDARD STRUCTURES ESTABLISHED WITHOUT THE FORMAL
LANGUAGE. 23 4.- STANDARD SEMANTICS. 30 4.1. ASSIGNMENT. 30 4.2.
INTERPRETATION. 31 4.3. CONSEQUENCE AND VALIDITY. 33 VLLL 6.- INDUCTION
MODELS AND PRIMITIVE RECURSION IN INDUCTION MODELS. 140 6.1. ADDITION
AND MULTIPLICATION IN INDUCTION MODELS. 140 6.2. EXPONENTIAL OPERATION
ON INDUCTION MODELS. 143 6.4. UNIVERSAL OPERATIONS. 144 CHAPTER IV:
FRAMES AND GENERAL STRUCTURES. 148 1.- INTRODUCTION. 148 1.1. FRAMES AND
GENERAL STRUCTURES. 148 1.2. STANDARD/NONSTANDARD VIEW. 149 1.3. THE
CONCEPT OF SUBSET. 150 1.4. SUMMARY. 152 2.- SECOND ORDER FRAMES. 154
2.1. DEFINITION OF FRAMES. 154 2.2. SEMANTICS ON FRAMES. 155 2.3.
SOUNDNESS AND COMPLETENESS IN FRAMES. 157 2.4. UNDEFINABILITY OF
IDENTITY IN FRAMES. 159 2.5. FRAMES AND LAMBDAS. 160 2.6. DEFINABLE SETS
AND RELATIONS IN A GIVEN FRAME. 161 3.- GENERAL STRUCTURES. 164 3.1.
DEFINITION OF GENERAL STRUCTURES. 165 3.2. SEMANTICS BASED ON GENERAL
STRUCTURES. 167 3.3. GENERAL STRUCTURES AND LAMBDAS. 167 3.4. SOUNDNESS
AND COMPLETENESS IN GENERAL STRUCTURES. 168 4.- ALGEBRAIC DEFINITION OF
GENERAL STRUCTURES. 171 4.1. FUNDAMENTAL RELATIONS OF A STRUCTURE. 171
4.2. ALGEBRAIC DEFINITION OF GENERAL STRUCTURES. 172 5.- LOGICS OBTAINED
BY WEAKENING THE SCHEMA OF COMPREHENSION. 173 6.- WEAK SECOND ORDER
LOGIC. 6.1. GENERAL IDEA. 174 IX 6.2. METAPROPERTIES OF WEAK SECOND
ORDER LOGIC. 175 CHAPTER V: TYPE THEORY. 18 0 1.- INTRODUCTION. 180 1.1.
GENERAL IDEA. 180 1.2. PARADOXES AND THEIR SOLUTION IN TYPE THEORY. 182
1.3. THREE PRESENTATIONS OF TYPE THEORY. 186 2.- A RELATIONAL THEORY OF
FINITE TYPES. 187 2.1. DEFINITION (SIGNATURE AND ALPHABET). 187 2.2.
EXPRESSIONS. 188 2.3. EQUALITY. 189 2.4. FREE VARIABLES AND
SUBSTITUTION. 189 2.5. DEDUCTIVE CALCULUS. 190 2.6. THE RELATIONAL
STANDARD STRUCTURE AND THE RELATIONAL STANDARD HIERARCHY OF TYPES. 190
2.7. RTT WITH LAMBDA. 192 2.8. INCOMPLETENESS OF STANDARD TYPE THEORY.
193 2.9. RELATIONAL GENERAL STRUCTURES AND RELATIONAL FRAMES. 193 R 3.-
ALGEBRAIC DEFINITION OF RELATIONAL GENERAL STRUCTURES. 197 3.1.
FUNDAMENTAL RELATIONS. 198 3.2. DEFINITION OF RELATIONAL GENERAL
STRUCTURE BY ALGEBRAIC CLOSURE OF THE DOMAINS. 199 3.3. THEOREM. 200
3.4. SOME PARAMETRICALLY DEFINABLE RELATIONS ALSO INCLUDED IN THE
UNIVERSE OF RELATIONAL GENERAL STRUCTURES DEFINED BY ALGEBRAIC CLOSURE.
201 3.5. THEOREM. 203 4.- A FUNCTIONAL THEORY OF TYPES. 205 4.1.
DEFINITION (SIGNATURE AND ALPHABET). 205 4.2. EXPRESSIONS. 206 4.3.
FUNCTIONAL FRAMES, FUNCTIONAL GENERAL STRUCTURES AND FUNCTIONAL STANDARD
STRUCTURES. 207 4.4. FROM RTT TO FTT. 210 5.- EQUATIONAL PRESENTATION OF
THE FUNCTIONAL THEORY OF FINITE TYPES. 214 5.1. MAIN FEATURES OF ETT.
214 5.2. CONNECTORS AND QUANTIFIERS IN ETT. 215 5.3. THE SELECTOR
OPERATOR IN ETT. 218 5.4. A CALCULUS FOR ETT. 218 CHAPTER VI:
MANY-SORTED LOGIC. 220 1.- INTRODUCTION. 220 1.1. EXAMPLES. 220 1.2.
REDUCTION TO AND COMPARISON WITH FIRST ORDER LOGIC. 221 1.3. USES OF
MANY-SORTED LOGIC. 225 1.4. MANY-SORTED LOGIC AS A UNIFIER LOGIC. 226
2.- STRUCTURES. 227 2.1. DEFINITION (SIGNATURE). 229 2.2. DEFINITION
(STRUCTURE). 229 3.- FORMAL MANY-SORTED LANGUAGE. 231 3.1 ALPHABET. 231
3.2. EXPRESSIONS: FORMULAS AND TERMS. 231 3.3. REMARKS ON NOTATION. 232
3.4. ABBREVIATIONS. 233 3.5. INDUCTION. 233 3.6. FREE AND BOUND
VARIABLES. 234 4.- SEMANTICS. 234 4.1. DEFINITIONS. 235 4.2.
SATISFIABILITY, VALIDITY, CONSEQUENCE AND LOGICAL EQUIVALENCE. 236 XI
5.- SUBSTITUTION OF A TERM FOR A VARIABLE. 23 6 6.- SEMANTIC THEOREMS.
238 6.1. COINCIDENCE LEMMA. 238 6.2. SUBSTITUTION LEMMA. 238 6.3. EQUALS
SUBSTITUTION LEMMA. 239 6.4. ISOMORPHISM THEOREM. 239 7.- THE
COMPLETENESS OF MANY-SORTED LOGIC. 240 7.1. DEDUCTIVE CALCULUS. 241 7.2.
SYNTACTIC NOTIONS. 242 7.3. SOUNDNESS. 244 7.4. COMPLETENESS THEOREM
(COUNTABLE LANGUAGE). 245 7.5. COMPACTNESS THEOREM. 256 7.6.
LOWENHEIM-SKOLEM THEOREM. 256 8.- REDUCTION TO ONE-SORTED LOGIC. 257
8.1. THE SYNTACTICAL TRANSLATION (RELATIVIZATION OF QUANTIFIERS). 257
8.2. CONVERSION OF STRUCTURES. 258 CHAPTER VH: APPLYING MANY-SORTED
LOGIC. 236 1.- GENERAL PLAN. 263 1.1. AIMS. 263 1.2. REPRESENTATION
THEOREM. 264 1.3. MAIN THEOREM. 269 1.4. TESTING A GIVEN CALCULUS FOR
XL. 272 APPLYING MANY-SORTED LOGIC TO HIGHER ORDER LOGIC. 2.- HIGHER
ORDER LOGIC AS MANY-SORTED LOGIC. 2.0. PRELIMINARIES. 277 2.1. THE
FORMAL MANY-SORTED LANGUAGE MSL . 281 2.2. THE SYNTACTICAL TRANSLATION.
283 2.3. STRUCTURES. 283 XLL 2.4. THE EQUIVALENCE SOL-MSL D 288 APPLYING
MANY-SORTED LOGIC TO MODAL LOGIC. 3.- MODAL LOGIC. 291 3.1. SOME
HISTORY. 291 3.2. A FORMAL LANGUAGE FOR PML. 295 3.3. MODAL
PROPOSITIONAL LOGICS. 297 3.4. NORMAL MODAL LOGICS. 301 3.5. CONSISTENCY
OF ALL NORMAL MODAL LOGICS CONTAINED IN S5. 303 3.6. KRIPKE MODELS. 305
3.7. A FORMAL LANGUAGE FOR FOML. 309 3.8. SEMANTICS. 310 3.9. A
DEDUCTIVE CALCULUS FOR FOML(S5). 311 4.- PROPOSITIONAL MODAL LOGIC AS
MANY-SORTED LOGIC. 4.1. THE FORMAL MANY-SORTED LANGUAGE MSL . 312 4.2.
TRANSLATING FUNCTION. 313 4.3. GENERAL STRUCTURES AND FRAMES BUILT ON
PM-STRUCTURES. 314 4.4. THE MODO THEORY. 317 4.5. REVERSE CONVERSION.
320 4.6. TESTING THE CALCULUS. 323 5.- FIRST ORDER MODAL LOGIC AS
MANY-SORTED LOGIC. 327 5.1. THE FORMAL MANY-SORTED LANGUAGE MSL . 328
5.2. TRANSLATING FUNCTION. 328 5.3. THEOREMS ON SEMANTIC EQUIVALENCE
FOML-MSL. 329 5.4. METAPROPERTIES OF FOML-S5: COMPACTNESS, AND
LOWEHEIM-SKOLEM. 333 5.5. SOUNDNESS AND COMPLETENESS OF S5. 333 XLLL
APPLYING MANY-SORTED LOGIC TO DYNAMIC LOGIC. 6.- DYNAMIC LOGIC. 335 6.1.
GENERAL IDEA. 335 6.2. A FORMAL LANGUAGE FOR PDL. 336 6.3. SEMANTICS.
337 6.4. THE LOGIC PDL. 340 7.- PROPOSITIONAL DYNAMIC LOGIC AS
MANY-SORTED LOGIC. 342 7.1. THE FORMAL MANY-SORTED LANGUAGE MSL . 342
7.2. TRANSLATING FUNCTION. 343 7.3. STRUCTURES AND FRAMES BUILT ON
PD-STRUCTURES. 344 7.4. THE SOLO 2 THEORY. 347 BIBLIOGRAPHY 352 LIST OF
NOTATION 364 INDEX 369
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| genre_facet | Logik Stufe 1 |
| id | DE-604.BV010739410 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:58:03Z |
| institution | BVB |
| isbn | 0521354358 |
| language | English |
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| series2 | Cambridge tracts in theoretical computer science |
| spelling | Manzano, María Verfasser aut Extensions of first order logic María Manzano 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1996 XXII, 388 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in theoretical computer science 19 Stufe 1 (DE-588)4362503-4 gnd rswk-swf Prädikatenlogik (DE-588)4046974-8 gnd rswk-swf Extensionale Logik (DE-588)4346527-4 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Ordnung n (DE-588)4322729-6 gnd rswk-swf Logik Stufe 1 gnd rswk-swf Extensionale Logik (DE-588)4346527-4 s Logik Stufe 1 f DE-604 Mathematische Logik (DE-588)4037951-6 s Ordnung n (DE-588)4322729-6 s Prädikatenlogik (DE-588)4046974-8 s Stufe 1 (DE-588)4362503-4 s DE-188 Cambridge tracts in theoretical computer science 19 (DE-604)BV000754528 19 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007170794&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Manzano, María Extensions of first order logic Cambridge tracts in theoretical computer science Stufe 1 (DE-588)4362503-4 gnd Prädikatenlogik (DE-588)4046974-8 gnd Extensionale Logik (DE-588)4346527-4 gnd Mathematische Logik (DE-588)4037951-6 gnd Ordnung n (DE-588)4322729-6 gnd |
| subject_GND | (DE-588)4362503-4 (DE-588)4046974-8 (DE-588)4346527-4 (DE-588)4037951-6 (DE-588)4322729-6 |
| title | Extensions of first order logic |
| title_auth | Extensions of first order logic |
| title_exact_search | Extensions of first order logic |
| title_full | Extensions of first order logic María Manzano |
| title_fullStr | Extensions of first order logic María Manzano |
| title_full_unstemmed | Extensions of first order logic María Manzano |
| title_short | Extensions of first order logic |
| title_sort | extensions of first order logic |
| topic | Stufe 1 (DE-588)4362503-4 gnd Prädikatenlogik (DE-588)4046974-8 gnd Extensionale Logik (DE-588)4346527-4 gnd Mathematische Logik (DE-588)4037951-6 gnd Ordnung n (DE-588)4322729-6 gnd |
| topic_facet | Stufe 1 Prädikatenlogik Extensionale Logik Mathematische Logik Ordnung n Logik Stufe 1 |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007170794&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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