Goal directed reasoning in clausal logic with equality:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
München
CS Press
1996
|
| Series: | Dissertationen zur Informatik
2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zugl.: München, Techn. Univ., Diss., 1996 |
| Physical Description: | VI, 141 S. |
| ISBN: | 3931757021 |
Staff View
MARC
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| 100 | 1 | |a Moser, Maximilian J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Goal directed reasoning in clausal logic with equality |c Maximilian J. Moser |
| 246 | 1 | 3 | |a Goal-directed reasoning in clausal logic with equality |
| 264 | 1 | |a München |b CS Press |c 1996 | |
| 300 | |a VI, 141 S. | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Dissertationen zur Informatik |v 2 | |
| 500 | |a Zugl.: München, Techn. Univ., Diss., 1996 | ||
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Record in the Search Index
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| adam_text |
CONTENTS
1
INTRODUCTION
1
1.1
REASONING
IN
CLAUSAL
LOGIC
WITH
EQUALITY
.
1
1.2
THE
BOTTOM-UP
APPROACH
.
2
1.3
THE
GOAL-DIRECTED
APPROACH
.
4
1.4
OVERVIEW
AND
MAIN
RESULTS
.
6
2
PRELIMINARIES
11
2.1
SYNTAX
.
11
2.1.1
TERMS,
POSITIONS,
SUBTERMS
.
12
2.1.2
LITERALS
AND
EQUATIONS
.
13
2.1.3
CLAUSES
AND
FORMULAE
WITH
EQUALITY
.
14
2.1.4
SUBSTITUTIONS
.
14
2.2
SEMANTICS
.
16
2.2.1
INTERPRETATIONS
.
16
2.2.2
HERBRAND
INTERPRETATIONS
.
18
2.2.3
CALCULI
AND
SEMANTICS
.
19
2.3
ORDERINGS
AND
CONVERGENT
REWRITE
SYSTEMS
.
19
2.3.1
CONVERGENT
REWRITE
SYSTEMS
.
20
2.3.2
ORDERINGS
.
21
2.4
CONSTRAINTS
.
24
2.4.1
SYNTAX
AND
SEMANTICS
.
24
2.4.2
CONSTRAINED
CLAUSES
.
25
3
FORMULAE,
MATRICES
AND
PATH
SETS
27
3.1
FORMULAE
IN
CLAUSAL
LOGIC
WITH
EQUALITY
.
27
3.2
MATRICES
AND
PATHS
.
29
3.2.1
MATRICES
.
29
3.2.2
PATHS
AND
PATH
SETS
FOR
MATRICES
.
32
3.2.3
COVERING
PATH
SETS
.
34
3.2.4
SEMANTICS
OF
PATH
SETS
.
37
3.3
THEOREM
PROVING
AND
PATHS
-
RELATED
WORK
.
39
3.4
UNITARY
PATH
DERIVATIONS
AND
REFUTATIONS
.
41
3.4.1
RIGID
VERSUS
UNITARY
.
41
3.4.2
UNITARY
PATH
SETS
.
44
4
SATURATION
AND
EXISTENCE
OF
UNITARY
PATH
SETS
47
4.1
PROOF
SETTING
.
48
4.1.1
THE
MODEL
CONSTRUCTION
TECHNIQUE
.
48
4.1.2
PATH
SET
COMPLEXES
.
49
4.1.3
OUTLINE
OF
THE
SATURATION
.
52
4.2
INFERENCES
ON
PATH
SETS
.
53
4.2.1
DELAYED
VERSUS
IMMEDIATE
INFERENCES
.
54
4.2.2
REFLECTION
-
DELAYED
.
55
4.2.3
REFLECTION
-
IMMEDIATE
.
57
4.2.4
FACTORED
OVERLAP
-
DELAYED
.
59
4.2.5
FACTORED
OVERLAP
-
IMMEDIATE
.
61
4.2.6
CORRECTNESS
.
65
4.3
SATURATED
PATH
SET
COMPLEXES
.
67
4.3.1
PATH
SET
COMPLEXES
AND
PRODUCED
EQUATIONS
.
68
4.3.2
COMPLETENESS
.
71
4.4
DISCUSSION
OF
VARIANTS
.
75
4.4.1
MIXED
PATH
SET
COMPLEXES
BY
DELAYED
INFERENCES
.
75
4.4.2
COLLAPSED
AND
INSTANT
PATH
SET
COMPLEXES
.
75
4.4.3
NEGATIVE
PATH
SET
COMPLEXES
.
78
4.5
MODIFICATIONS
AND
REFINEMENTS
.
79
4.5.1
NON-FACTORED
OVERLAP
.
79
4.5.2
SIMPLIFICATION,
SUBSUMPTION
AND
TAUTOLOGY
DELETION
.
82
4.6
RELATED
WORK
ON
BOTTOM-UP
SATURATION
.
84
4.6.1
OTHER
BOTTOM-UP
CALCULI
.
84
4.6.2
EQUALITY
ELIMINATION
.
87
5
FROM
UNITARY
PATH
SETS
TO
TABLEAUX
89
5.1
A
MODEL
ELIMINATION
CALCULUS
WITH
ORDERED
PARAMODULATION
.
90
5.1.1
THE
CALCULUS
.
90
5.1.2
AN
EXAMPLE
.
94
5.1.3
CORRECTNESS
.
97
5.2
COMPLETENESS
.
98
IV
5.2.1
PATH
SET
OPERATIONS
FOR
LEAF
LITERALS
.
99
5.2.2
THE
FOCUSING
PATH
SET
OPERATION
.
104
5.2.3
EXISTENCE
OF
TABLEAUX
.
106
5.3
REFINEMENTS
.
108
5.3.1
NEGATIVE
START
CLAUSE
.
108
5.3.2
ANCESTOR
LITERALS
IN
BRANCHES
.
110
5.3.3
RESTRICTING
LAZINESS
.
112
5.3.4
INDEPENDENCE
OF
THE
SELECTION
FUNCTION
.
116
5.4
A
MODEL
ELIMINATION
CALCULUS
WITH
LAZY
PARAMODULATION
.
119
5.5
RELATED
WORK
ON
GOAL-DIRECTED
CALCULI
.
121
5.5.1
ORIENTED
EQUATIONAL
PROGRAMMING
.
121
5.5.2
ADDING
EQUALITY
TO
SEMANTIC
TABLEAUX
.
122
6
CONCLUSION
125
BIBLIOGRAPHY
129
INDEX
135 |
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| author_facet | Moser, Maximilian J. |
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| author_sort | Moser, Maximilian J. |
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| callnumber-subject | QA - Mathematics |
| classification_tum | DAT 706d DAT 540d |
| ctrlnum | (OCoLC)37597467 (DE-599)BVBBV010877055 |
| discipline | Informatik |
| format | Book |
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| genre_facet | Hochschulschrift |
| id | DE-604.BV010877055 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-14T00:25:39Z |
| institution | BVB |
| isbn | 3931757021 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007272521 |
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| open_access_boolean | |
| owner | DE-12 DE-91 DE-BY-TUM |
| owner_facet | DE-12 DE-91 DE-BY-TUM |
| physical | VI, 141 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | CS Press |
| record_format | marc |
| series | Dissertationen zur Informatik |
| series2 | Dissertationen zur Informatik |
| spelling | Moser, Maximilian J. Verfasser aut Goal directed reasoning in clausal logic with equality Maximilian J. Moser Goal-directed reasoning in clausal logic with equality München CS Press 1996 VI, 141 S. txt rdacontent n rdamedia nc rdacarrier Dissertationen zur Informatik 2 Zugl.: München, Techn. Univ., Diss., 1996 Automatic theorem proving Logic, Symbolic and mathematical Klausellogik (DE-588)4293051-0 gnd rswk-swf Automatisches Beweisverfahren (DE-588)4069034-9 gnd rswk-swf Gleichheit (DE-588)4021231-2 gnd rswk-swf Zielfunktion (DE-588)4190793-0 gnd rswk-swf Gleichungstheorie (DE-588)4226572-1 gnd rswk-swf Logischer Schluss (DE-588)4139983-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Logischer Schluss (DE-588)4139983-3 s Zielfunktion (DE-588)4190793-0 s DE-604 Klausellogik (DE-588)4293051-0 s Gleichheit (DE-588)4021231-2 s Automatisches Beweisverfahren (DE-588)4069034-9 s Gleichungstheorie (DE-588)4226572-1 s Dissertationen zur Informatik 2 (DE-604)BV011113485 2 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007272521&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Moser, Maximilian J. Goal directed reasoning in clausal logic with equality Dissertationen zur Informatik Automatic theorem proving Logic, Symbolic and mathematical Klausellogik (DE-588)4293051-0 gnd Automatisches Beweisverfahren (DE-588)4069034-9 gnd Gleichheit (DE-588)4021231-2 gnd Zielfunktion (DE-588)4190793-0 gnd Gleichungstheorie (DE-588)4226572-1 gnd Logischer Schluss (DE-588)4139983-3 gnd |
| subject_GND | (DE-588)4293051-0 (DE-588)4069034-9 (DE-588)4021231-2 (DE-588)4190793-0 (DE-588)4226572-1 (DE-588)4139983-3 (DE-588)4113937-9 |
| title | Goal directed reasoning in clausal logic with equality |
| title_alt | Goal-directed reasoning in clausal logic with equality |
| title_auth | Goal directed reasoning in clausal logic with equality |
| title_exact_search | Goal directed reasoning in clausal logic with equality |
| title_full | Goal directed reasoning in clausal logic with equality Maximilian J. Moser |
| title_fullStr | Goal directed reasoning in clausal logic with equality Maximilian J. Moser |
| title_full_unstemmed | Goal directed reasoning in clausal logic with equality Maximilian J. Moser |
| title_short | Goal directed reasoning in clausal logic with equality |
| title_sort | goal directed reasoning in clausal logic with equality |
| topic | Automatic theorem proving Logic, Symbolic and mathematical Klausellogik (DE-588)4293051-0 gnd Automatisches Beweisverfahren (DE-588)4069034-9 gnd Gleichheit (DE-588)4021231-2 gnd Zielfunktion (DE-588)4190793-0 gnd Gleichungstheorie (DE-588)4226572-1 gnd Logischer Schluss (DE-588)4139983-3 gnd |
| topic_facet | Automatic theorem proving Logic, Symbolic and mathematical Klausellogik Automatisches Beweisverfahren Gleichheit Zielfunktion Gleichungstheorie Logischer Schluss Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007272521&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011113485 |
| work_keys_str_mv | AT mosermaximilianj goaldirectedreasoninginclausallogicwithequality |