Solvable cases of the decision problem
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| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
North-Holland Publ.
1968
|
| Ausgabe: | 3. print. |
| Schriftenreihe: | Studies in logic and the foundations of mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Ackermann, Wilhelm |d 1896-1962 |e Verfasser |0 (DE-588)116006080 |4 aut | |
| 245 | 1 | 0 | |a Solvable cases of the decision problem |c by W. Ackermann |
| 250 | |a 3. print. | ||
| 264 | 1 | |a Amsterdam |b North-Holland Publ. |c 1968 | |
| 300 | |a VIII, 114 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 0 | |a Studies in logic and the foundations of mathematics | |
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Datensatz im Suchindex
| _version_ | 1819784810278682624 |
|---|---|
| adam_text | CONTENTS
I. VALIDITY AND SATISFIABILITY IN FINITE DOMAINS 1
1. Well formed formulas 1
2. Valuation of well formed formulas in a finite domain.
Validity and satisfiability 4
II. THE DECISION PROBLEM 9
1. Valuation in arbitrary domains. Universal validity ... 9
2. Equivalences 12
3. /S formulas. Elimination of the prepositional variables . . 15
4. Normal forms 19
5. Three forms of the decision problem 22
III. SOLUTION OF THE DECISION PROBLEM FOR
EQUALITY FORMULAS 24
1. Solution of the form II of the decision problem .... 24
2. Another criterion for the universal validity of equality
formulas 26
IV. SOLUTION OF THE DECISION PROBLEM FOR WELL
FORMED FORMULAS CONTAINING ONLY MONADIC
PREDICATE VARIABLES 34
1. Solution of the form II of the decision problem for wffs
which do not contain bound predicate variables and the
sign of equality 34
2. Elimination theorems 37
3. General solution of the decision problem for wffs with
only monadic predicate variables 41
V. SOME GENERAL THEOREMS ABOUT THE VALIDITY
OF FORMULAS OF THE PREDICATE CALCULUS OF
FIRST ORDER INCLUDING EQUALITY 48
1. Skolem s normal form 48
2. Theorems about the validity of wffs not containing the sign
of equality 50
3. Theorems about the validity of wffs which may contain the
sign of equality 52
VI CONTENTS
VI. SOLUTION OF THE DECISION PROBLEM FOR WFFS
WITH SPECIAL PREFIXES 60
1. Remarks on the selection of special cases of the decision
problem 60
2. Solution for wffs having prefixes consisting solely of
universal quantifiers 62
3. Solution for wffs having prefixes consisting solely of
existential quantifiers 63
4. Reduction of the decision problem for wffs with certain
prefixes to that for wffs with simpler prefixes 67
5. Solution for wffs having prefixes such that all the universal
quantifiers precede all the existential ones 70
VII. FURTHER CLASSES OF PREFIXES FOR WHICH THE
DECISION PROBLEM CAN BE SOLVED 72
1. Solution for wffs having prefixes containing only one
existential quantifier 72
2. Solution for wffs having prefixes containing only two
existential quantifiers which are not separated by universal
quantifiers 75
VIII. GENERAL REMARKS ABOUT FURTHER INVESTI¬
GATIONS 83
1. Limitation of the range of the method hitherto used ... 83
2. Some other cases for which the decision problem has been
solved 85
3. A general theorem about the validity of wffs 90
IX. THE DECISION PROBLEM FOR WFFS WITH FUNCTION¬
AL VARIABLES 98
1. Introduction of wffs with functional variables 98
2. Special cases for which the decision problem is solved for wffs
with functional variables 100
BIBLIOGRAPHY 108
INDEX 113
|
| any_adam_object | 1 |
| author | Ackermann, Wilhelm 1896-1962 |
| author_GND | (DE-588)116006080 |
| author_facet | Ackermann, Wilhelm 1896-1962 |
| author_role | aut |
| author_sort | Ackermann, Wilhelm 1896-1962 |
| author_variant | w a wa |
| building | Verbundindex |
| bvnumber | BV021895971 |
| classification_rvk | SK 130 |
| ctrlnum | (OCoLC)256055231 (DE-599)BVBBV021895971 |
| discipline | Mathematik |
| edition | 3. print. |
| format | Book |
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| id | DE-604.BV021895971 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T19:46:30Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015111156 |
| oclc_num | 256055231 |
| open_access_boolean | |
| owner | DE-706 |
| owner_facet | DE-706 |
| physical | VIII, 114 S. |
| publishDate | 1968 |
| publishDateSearch | 1968 |
| publishDateSort | 1968 |
| publisher | North-Holland Publ. |
| record_format | marc |
| series2 | Studies in logic and the foundations of mathematics |
| spellingShingle | Ackermann, Wilhelm 1896-1962 Solvable cases of the decision problem Entscheidungsproblem (DE-588)4253928-6 gnd Unentscheidbarkeit (DE-588)4294363-2 gnd Lösung Chemie (DE-588)4036159-7 gnd Prädikatenkalkül (DE-588)4175518-2 gnd Entscheidungstheorie (DE-588)4138606-1 gnd |
| subject_GND | (DE-588)4253928-6 (DE-588)4294363-2 (DE-588)4036159-7 (DE-588)4175518-2 (DE-588)4138606-1 |
| title | Solvable cases of the decision problem |
| title_auth | Solvable cases of the decision problem |
| title_exact_search | Solvable cases of the decision problem |
| title_full | Solvable cases of the decision problem by W. Ackermann |
| title_fullStr | Solvable cases of the decision problem by W. Ackermann |
| title_full_unstemmed | Solvable cases of the decision problem by W. Ackermann |
| title_short | Solvable cases of the decision problem |
| title_sort | solvable cases of the decision problem |
| topic | Entscheidungsproblem (DE-588)4253928-6 gnd Unentscheidbarkeit (DE-588)4294363-2 gnd Lösung Chemie (DE-588)4036159-7 gnd Prädikatenkalkül (DE-588)4175518-2 gnd Entscheidungstheorie (DE-588)4138606-1 gnd |
| topic_facet | Entscheidungsproblem Unentscheidbarkeit Lösung Chemie Prädikatenkalkül Entscheidungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015111156&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ackermannwilhelm solvablecasesofthedecisionproblem |