Model and proof theory of constructive ALC: constructive description logics
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Bamberg
Univ. of Bamberg Press
2015
|
| Series: | Schriften aus der Fakultät Wirtschaftsinformatik und Angewandte Informatik der Otto-Friedrich-Universität Bamberg
20 |
| Subjects: | |
| Online Access: | Volltext Inhaltsverzeichnis |
| Item Description: | Zsfassung in dt. Sprache |
| Physical Description: | XIII, 326 S. Ill. |
| ISBN: | 9783863093204 |
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MARC
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| 100 | 1 | |a Scheele, Stephan M. |e Verfasser |0 (DE-588)107394123X |4 aut | |
| 245 | 1 | 0 | |a Model and proof theory of constructive ALC |b constructive description logics |c von Stephan M. Scheele |
| 264 | 1 | |a Bamberg |b Univ. of Bamberg Press |c 2015 | |
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Record in the Search Index
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| adam_text | Contents
List of Figures xff!
1 Introduction 1
11 Motivation: Wlu»n Const nut ivenes«* mat tors.......................... 3
1.2 Ainu« and Contribution*................................................... 7
1.3 Synojisis of the Thesis................................................ 10
1.4 Publications....................................................... . Ц
2 Background 13
2.1 Description Logic....................................................... 13
2.1.1 The Basic Language *4£C........................................... 13
2.1.2 DL Knowledge Base................................................. 15
2.1.3 Standard Inference Problems....................................... 18
2.1.4 Language* Extensions of ACC ...................................... 18
2.1.5 Relation to Modal Logit s......................................... 19
2.2 Constructive Logit ...................................................... 26
2.2.1 Intuitionistic Propositional and First-Order Logic................ 28
2.2.2 Intuitionistic Modal Logic........................................ 33
3 Constructive Description Logics - State of the Art 41
3.1 Constructive D«*scription Logics: What. Why к How? ..................... 41
3.2 Intuitionistic Semantics via Translation into IQC........................ 42
3.2.1 Intuitionistic ACC {IACC)......................................... 42
3.2.2 Intuit ionistic ACC Kuroda Logic (КАСС)........................... 43
3.3 Intuitionistic Semantics via Translation into FS IK...................... 45
3.4 Constructive Inconsistency-tolerant Description Logics ................. 46
3.5 Computational Interprets ions of Description Logie*.................... 48
3.5.1 Information Term Semantics for ACC iBCVC)......................... 48
3.5.2 Ty|x»-t hiHiretir Interpretation of cACC (ACK„)................... 50
3 6 Minor ( oust rue five Approfu hes to Description Logics................. 51
3.6.1 Proof-tln oretii Approach by Martin Hofmann....................... 51
ix
3.6.2 IntuitionistK Approach to Query Answering in DLs............. 51
52
3.7 Our Approach............................................................
4 Constructive Semantics for ACC 53
4.1 Kripke Seinantirs and the Choice of cACC.......................... 53
4.1.1 Variants of Kripke Semantics ................................ ^
4 12 Variants of Birelational Kripke Semantics..................... 56
4.1.3 The System cACC..............................................
4.2 Syntax and Semantics of cACC...................................... **0
4.2.1 Syntax....................................................... 60
4.2.2 Semantics.................................................... ^1
4.2.3 Terminological Knowledge..................................... 71
4 2.4 Representation of Dynamic and Incomplete Knowledge........... 74
4 2.5 Disjunction Property......................................... $0
4.2,6 Finite Model Property........................................ 87
4.3 Summary ........................................................... 04
5 Constructive Proof Systems for cACC 99
5 l HiU**tt-stvle Axiomatisation...................................... 99
5 I T HilluTt Calculus for cACC.................................... 99
5 12 Modal Deduct ion Theorem.....................................Ill
5 13 Soundness and Completeness ....................................116
5 2 (ient/cn Sequent Calculus Gl for cACC.............................122
5 2 1 Soundness and Completeness ....................................130
5 2 2 Decidability of Gl.............................................150
5 2 3 Equivalence of Gentten and Hilbert systems.....................151
5 3 Towards Intermediate Logics between cACC and ACC....................169
5 3 1 Infallible Kripke Semantics Axiom FS3/1K3......................169
5 3 2 Tim Principle of Disjunctive Distribution ֊ Axiom FS4/IK4 ... 182
5 3 3 Tlie Principle of the Excluded Middle..........................190
5 3 4 Obtaining classical ACC........................................195
5.4 Summary.............................................................. ^
• Thm Rslfttlon of cACC to Cfmical Description Logics 197
1 Embedding tAJX into classical Description Logics...................197
611 Translation of cACC into ACCr* ................................200
6 12 The Complexity of cACC........................................ 20g
613 Decidability and Finite Model Property........................ 915
6 2 The Fragment UC......................... ^
x
Con։ сіп»
6.2.1 Introduction to Tradable DLs............................ 217
6.2.2 Тік» Language UC ......................................... 219
6.2.3 Existentially Guarded 14 Co is Exi*TIXIE-Iiard for Сішгаї
scriptive Semantics.......................................... 220
6.2.4 Existentially Guarded 14C is in PTlME for Constructive De-
script ive Semantics..........................................220
6.3 Summary .......................................................... 226
7 Tableau·based Calculus for cACC 231
7.1 Constraint System ............................................... 231
7.2 Tableau Rules.......................................................236
7.2.1 Tableau Rules of............................................ 238
7.2.2 Fitting-style Representation of 247
7.3 Proof of Correct news...............................................249
7.3.1 Termination...................................................249
7.3.2 Soundness and Completeness ...................................253
7.4 Towards Construct і ve A Box Reasoning an Outlook...................268
7.5 Summary ..........................................................276 8
8 Conclusion 279
8.1 Contributions.......................................................280
8.2 Future Perspectives.................................................283
8.2.1 Theoretical As| ects.........................................284
8.2.2 Towards Applications.........................................286
Bibliography 291
Index
317
|
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| bvnumber | BV042694759 |
| classification_rvk | SK 130 |
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| ctrlnum | (OCoLC)915161591 (DE-599)BVBBV042694759 |
| discipline | Mathematik |
| format | Thesis Book |
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| language | English |
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| physical | XIII, 326 S. Ill. |
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| publishDate | 2015 |
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| series | Schriften aus der Fakultät Wirtschaftsinformatik und Angewandte Informatik der Otto-Friedrich-Universität Bamberg |
| series2 | Schriften aus der Fakultät Wirtschaftsinformatik und Angewandte Informatik der Otto-Friedrich-Universität Bamberg |
| spelling | Scheele, Stephan M. Verfasser (DE-588)107394123X aut Model and proof theory of constructive ALC constructive description logics von Stephan M. Scheele Bamberg Univ. of Bamberg Press 2015 XIII, 326 S. Ill. txt rdacontent n rdamedia nc rdacarrier Schriften aus der Fakultät Wirtschaftsinformatik und Angewandte Informatik der Otto-Friedrich-Universität Bamberg 20 Zsfassung in dt. Sprache Zugl.: Bamberg, Univ., Diss., 2015 Terminologische Logik (DE-588)4359506-6 gnd rswk-swf Konstruktive Logik (DE-588)4165104-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Konstruktive Logik (DE-588)4165104-2 s Terminologische Logik (DE-588)4359506-6 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:473-opus4-264607 978-3-86309-321-1 Schriften aus der Fakultät Wirtschaftsinformatik und Angewandte Informatik der Otto-Friedrich-Universität Bamberg 20 (DE-604)BV035260948 20 3,972 MB https://fis.uni-bamberg.de/handle/uniba/21626 Verlag kostenfrei Volltext Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028126374&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Scheele, Stephan M. Model and proof theory of constructive ALC constructive description logics Schriften aus der Fakultät Wirtschaftsinformatik und Angewandte Informatik der Otto-Friedrich-Universität Bamberg Terminologische Logik (DE-588)4359506-6 gnd Konstruktive Logik (DE-588)4165104-2 gnd |
| subject_GND | (DE-588)4359506-6 (DE-588)4165104-2 (DE-588)4113937-9 |
| title | Model and proof theory of constructive ALC constructive description logics |
| title_auth | Model and proof theory of constructive ALC constructive description logics |
| title_exact_search | Model and proof theory of constructive ALC constructive description logics |
| title_full | Model and proof theory of constructive ALC constructive description logics von Stephan M. Scheele |
| title_fullStr | Model and proof theory of constructive ALC constructive description logics von Stephan M. Scheele |
| title_full_unstemmed | Model and proof theory of constructive ALC constructive description logics von Stephan M. Scheele |
| title_short | Model and proof theory of constructive ALC |
| title_sort | model and proof theory of constructive alc constructive description logics |
| title_sub | constructive description logics |
| topic | Terminologische Logik (DE-588)4359506-6 gnd Konstruktive Logik (DE-588)4165104-2 gnd |
| topic_facet | Terminologische Logik Konstruktive Logik Hochschulschrift |
| url | https://fis.uni-bamberg.de/handle/uniba/21626 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028126374&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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