anytime reasoning by ontology approximation s.schlobach, e.blaauw, m.el kebir, a.ten teije, f.van...
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![Page 1: Anytime reasoning by Ontology Approximation S.Schlobach, E.Blaauw, M.El Kebir, A.ten Teije, F.van Harmelen, S.Bortoli, M.Hobbelman, K.Millian, Y.Ren, S.Stam,,](https://reader035.vdocuments.us/reader035/viewer/2022062619/551524a8550346a80c8b63fc/html5/thumbnails/1.jpg)
Anytime reasoning by Ontology Approximation S.Schlobach, E.Blaauw, M.El Kebir, A.ten Teije, F.van Harmelen, S.Bortoli, M.Hobbelman, K.Millian, Y.Ren, S.Stam,, P.Thomassen, R.van het Schip, W.van Willigem
Vrije Universiteit Amsterdam
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The right reasoning for the Semantic web? Scalability Anytime behaviour
time
results
currently
ideal
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Anytime classification: by Approximation Trying to find a way to find more simple
reasoning problems that solve parts of the problem in shorter time
Complexity of the subproblem
recall runtime
100%
100% recall
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Approaches to approximate reasoning Cadoli Schaerf: S-approximation.
²1 ) ² ) ²3
Where ²1 is incomplete, ²3 unsound approximation of the classical consequence ²
Stuckenschmidt, Wache: O ² Querys-approx
Our approach:Os-approx ² Query
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Approximate classification
Formally: consequence Á of an ontology: O={ax1,..,axn}² Á
iff (8 I, 8 1· i· n: I ² axi) ! I ² Á
Theorem: Assume (8 I, 8 1· i· n: I ² ax’i) ! I ² Á, where axi ² ax’i, then O² Á
Let us get the intuition by an example: We know: (ax) A v Bu Cu D ² Av Bu C (ax’) If now also: (ax’) Av Bu C ² A v C
Then (ax) Av Bu Cu D ² Av C follows always
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Approximate subsumption
BC
Ontology
A v B u Cu D
A
implies
A v Bu C
ApproximateOntology
D
Implies
Subsumption: Av B
Implies
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S-Approximation
Approximation due to ignoring parts of the symbols
The set S contains the elements that are NOT ignored.
Ignoring is done by: Semantically: interpreting a symbol as ? or ¢. Syntactically: replacing a symbol by > or ?.
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S-ApproximationOO{A,B,D}O{A,B}O{B}
Av Bu C
Bv D
Av Bu >
Bv D
Av Bu>
Bv >
?v Bu>
Bv >
? v A? v B? v C? v DA v BA v CA v DB v DA v >B v >C v >D v >
Recall: 2 (16%) 12 (100%)9 (75%)5 (42%)
? v A? v B? v C? v DA v BA v CA v DB v DA v >B v >C v >D v >
? v A? v B? v C? v DA v BA v CA v DB v DA v >B v >C v >D v >
? v A? v B? v C? v DA v BA v CA v DB v DA v >B v >C v >D v >
²² ² ²
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Results: recall graphically
4 Size of S321
Recall
100%
50%
Idealised curve
Real curve
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S-Approximation (different order) OO{A,C,D}O{C,D}O{D}
Av Bu C
Bv D
Av Cu >
?v D
? v Cu>
?v D
? v A? v B? v C? v DA v BA v CA v DB v DA v >B v >C v >D v >
Recall: 2 (16%) 12 (100%)8 (66 %)4 (33 %)
? v A? v B? v C? v DA v BA v CA v DB v DA v >B v >C v >D v >
? v A? v B? v C? v DA v BA v CA v DB v DA v >B v >C v >D v >
? v A? v B? v C? v DA v BA v CA v DB v DA v >B v >C v >D v >
²² ² ²
?v D
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Results: recall graphically
4 Size of S321
Recall
100%
50%
Idealised curve
Previous curve
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Results: runtime
4321
Runtime
100%
50%
Idealised curve
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S-approximation: selection strategies Selection strategies influence anytime
behaviour We tested three selection functions
LEAST: take least often occurring CN first MOST: take most often occurring CN first RANDOM
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Experiments: approximate classification of 8 public ontologies
Expressive – Classification is difficult
Inexpressive – Classification is cheap
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DICE and MORE
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DICE and Different strategies Bad result
Better result,
But MORE strategy wins!
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UNSPCS with MORE strategy
Bad result for UNSPC Similarly for other strategies
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Comparative results: difference
Lesson: approximation works for expressive ontologies with difficult classification problem.
Approximationworks
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Conclusion
Approximating ontology not query Evaluation shows that anytime behaviour
works for the most difficult ontologies Choosing most often occurring symbol