Proof reconstruction in classical and non-classical logics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Berlin
Akad. Verl.-Ges. Aka
2000
|
| Series: | Dissertationen zur künstlichen Intelligenz
239 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 218 S. 21 cm |
| ISBN: | 3898382397 |
Staff View
MARC
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| 100 | 1 | |a Schmitt, Stephan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Proof reconstruction in classical and non-classical logics |c Stephan Schmitt |
| 264 | 1 | |a Berlin |b Akad. Verl.-Ges. Aka |c 2000 | |
| 300 | |a XII, 218 S. |b 21 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Dissertationen zur künstlichen Intelligenz |v 239 | |
| 502 | |a Zugl.: Darmstadt, Techn. Univ., Diss., 1999 | ||
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Record in the Search Index
| _version_ | 1816443721140404224 |
|---|---|
| adam_text |
CONTENTS
INTRODUCTION
1
1
UNIFORM
REPRESENTATIONS
OF
NON-CLASSICAL
PROOF
CALCULI
11
1.1
SYNTAX,
LOGICS,
AND
UNIFORM
NOTATION
.
11
1.1.1
SYNTAX
.
11
1.1.2
LOGICS
.
14
1.1.3
UNIFORM
NOTATION
.
15
1.2
GENTZEN-LIKE
SEQUENT
CALCULI
.
18
1.2.1
CLASSICAL
LOGIC
.
18
1.2.2
MODAL
AND
INTUITIONISTIC
LOGICS
.
21
1.2.3
LINEAR
LOGIC
.
26
1.3
SPECIAL
SEQUENT
SYSTEMS
.
27
1.3.1
PREFIXED
SEQUENT
CALCULI
.
27
1.3.2
A
FOCUSING
SEQUENT
CALCULUS
FOR
MLL
.
32
1.4
MATRIX
CHARACTERIZATIONS
FOR
NON-CLASSICAL
LOGICS
.
34
1.4.1
CLASSICAL,
INTUITIONISTIC
AND
MODAL
LOGICS
.
35
1.4.2
THE
FRAGMENT
MLL
OF
LINEAR
LOGIC
.
45
1.5
SUMMARY:
INVARIANT
AND
VARIANT
PARTS
.
50
2
A
UNIFORM
CHARACTERIZATION
OF
PROOF
RECONSTRUCTION
53
2.1
RELATING
MATRIX
PROOFS
TO
SEQUENT
PROOFS
.
53
2.1.1
A
FIRST
RECONSTRUCTION
ALGORITHM
.
54
2.1.2
DEVIATIONS
BETWEEN
PROOF
REPRESENTATIONS
.
56
2.2
THE
SEMANTICAL
GAP
.
64
2.2.1
THE
EXISTENCE
OF
PROOF
PARAMETERS
.
65
2.2.2
GLOBAL
PREFIX
SUBSTITUTIONS
AND
SEQUENT
PROOFS
.
66
2.2.3
THE
SEMANTICAL
GAP
IS
INSURMOUNTABLE
.
68
2.3
UNIFORM
PRINCIPLES
FOR
PROOF
RECONSTRUCTION
.
70
2.3.1
THE
UNIFORMITY
PRINCIPLE
.
71
2.3.2
MODIFYING
PREFIXED
SEQUENT
CALCULI
.
74
2.3.3
ADDITIONAL
PRINCIPLES
FOR
GENTZEN-LIKE
SEQUENT
CALCULI
.
76
2.4
SUMMARY
.
86
3
UNIFORM
ALGORITHMS
FOR
PROOF
RECONSTRUCTION
87
3.1
PROOF
RECONSTRUCTION
IN
SPECIAL
SEQUENT
SYSTEMS
.
87
3.1.1
RECONSTRUCTING
PREFIXED
SEQUENT
PROOFS
.
88
3.1.2
CORRECTNESS,
COMPLETENESS
AND
COMPLEXITY
.
93
3.1.3
RECONSTRUCTING
FOCUSING
SEQUENT
PROOFS
IN
MLL
.
97
3.1.4
CORRECTNESS,
COMPLETENESS,
AND
COMPLEXITY
FOR
MLL
.
105
XII
C
ONTENTS
3.2
PROOF
RECONSTRUCTION
IN
GENTZEN-LIKE
SEQUENT
CALCULI
.
109
3.2.1
RECONSTRUCTION
IN
MODAL
AND
INTUITIONISTIC
LOGICS
.
110
3.2.2
REDUNDANCY
DELETION
AFTER
^-SPLITS
.
114
3.2.3
COMPLETE
AND
CORRECT
RECONSTRUCTION
ALGORITHMS
.
129
3.2.4
THE
FRAGMENT
MLL
OF
LINEAR
LOGIC
.
136
3.3
COMPLEXITY
OF
PROOF
RECONSTRUCTION
.
138
3.3.1
POLYNOMIAL
SIMULATIONS
.
139
3.3.2
COMPLEXITY
OF
THE
RECONSTRUCTION
ALGORITHMS
.
142
3.4
SUMMARY
.
144
4
INTEGRATION
OF
PROOF
KNOWLEDGE
INTO
THE
RECONSTRUCTION
PROCESS
145
4.1
ANALYZING
THE
DECOMPOSITION
PROBLEM
.
146
4.1.1
MATRIX
REPRESENTATIONS
AND
WEAK
SEQUENT
PROOFS
.
146
4.1.2
USING
WEAK
SEQUENT
PROOFS
FOR
REDUNDANCY
DELETION
.
150
4.2
FL-PROOFS:
A
UNIFORM
FRAMEWORK
FOR
MATRIX
PROOFS
.
154
4.2.1
REPRESENTING
MATRIX
PROOFS
WITHIN
/3-PROOFS
.
154
4.2.2
APPROXIMATING
/3-PROOFS
TO
REDUCTION
ORDERINGS
.
158
4.3
SEARCH-FREE
PROOF
RECONSTRUCTION
.
163
4.3.1
INTEGRATING
FL-PROOFS
INTO
PROOF
RECONSTRUCTION
.
164
4.3.2
EXTRACTING
OPTIMAL
/3-PROOFS
FROM
REDUCTION
ORDERINGS
.
172
4.4
COMPUTING
OPTIMAL
/3-PROOFS
DURING
PROOF
SEARCH
.
176
4.4.1
RELATING
CONNECTION
ORDERINGS
TO
WEAK
SEQUENT
PROOFS
.
176
4.4.2
A
UNIFORM
CHARACTERIZATION
OF
EXTENSION
PROOFS
.
183
4.4.3
RELATING
EXTENSION
PROOFS
TO
OPTIMAL
/3-PROOFS
.
189
4.5
SUMMARY
.
191
CONCLUSIONS
AND
APPLICATIONS
195
LIST
OF
FIGURES
205
LIST
OF
TABLES
207
BIBLIOGRAPHY
209
CURRICULUM
VITAE
217 |
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| indexdate | 2024-11-22T17:15:22Z |
| institution | BVB |
| isbn | 3898382397 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009127564 |
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| owner_facet | DE-91G DE-BY-TUM DE-29T DE-521 DE-634 |
| physical | XII, 218 S. 21 cm |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Akad. Verl.-Ges. Aka |
| record_format | marc |
| series | Dissertationen zur künstlichen Intelligenz |
| series2 | Dissertationen zur künstlichen Intelligenz |
| spelling | Schmitt, Stephan Verfasser aut Proof reconstruction in classical and non-classical logics Stephan Schmitt Berlin Akad. Verl.-Ges. Aka 2000 XII, 218 S. 21 cm txt rdacontent n rdamedia nc rdacarrier Dissertationen zur künstlichen Intelligenz 239 Zugl.: Darmstadt, Techn. Univ., Diss., 1999 Automatisches Beweisverfahren (DE-588)4069034-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Automatisches Beweisverfahren (DE-588)4069034-9 s DE-604 Dissertationen zur künstlichen Intelligenz 239 (DE-604)BV005345280 239 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009127564&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schmitt, Stephan Proof reconstruction in classical and non-classical logics Dissertationen zur künstlichen Intelligenz Automatisches Beweisverfahren (DE-588)4069034-9 gnd |
| subject_GND | (DE-588)4069034-9 (DE-588)4113937-9 |
| title | Proof reconstruction in classical and non-classical logics |
| title_auth | Proof reconstruction in classical and non-classical logics |
| title_exact_search | Proof reconstruction in classical and non-classical logics |
| title_full | Proof reconstruction in classical and non-classical logics Stephan Schmitt |
| title_fullStr | Proof reconstruction in classical and non-classical logics Stephan Schmitt |
| title_full_unstemmed | Proof reconstruction in classical and non-classical logics Stephan Schmitt |
| title_short | Proof reconstruction in classical and non-classical logics |
| title_sort | proof reconstruction in classical and non classical logics |
| topic | Automatisches Beweisverfahren (DE-588)4069034-9 gnd |
| topic_facet | Automatisches Beweisverfahren Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009127564&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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