Anytime reasoning by Ontology Approximation S.Schlobach, E.Blaauw, M.El Kebir, A.ten Teije, F.van...
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Transcript of Anytime reasoning by Ontology Approximation S.Schlobach, E.Blaauw, M.El Kebir, A.ten Teije, F.van...
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
The right reasoning for the Semantic web? Scalability Anytime behaviour
time
results
currently
ideal
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
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
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
Approximate subsumption
BC
Ontology
A v B u Cu D
A
implies
A v Bu C
ApproximateOntology
D
Implies
Subsumption: Av B
Implies
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 ?.
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
Results: recall graphically
4 Size of S321
Recall
100%
50%
Idealised curve
Real curve
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
Results: recall graphically
4 Size of S321
Recall
100%
50%
Idealised curve
Previous curve
Results: runtime
4321
Runtime
100%
50%
Idealised curve
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
Experiments: approximate classification of 8 public ontologies
Expressive – Classification is difficult
Inexpressive – Classification is cheap
DICE and MORE
DICE and Different strategies Bad result
Better result,
But MORE strategy wins!
UNSPCS with MORE strategy
Bad result for UNSPC Similarly for other strategies
Comparative results: difference
Lesson: approximation works for expressive ontologies with difficult classification problem.
Approximationworks
Conclusion
Approximating ontology not query Evaluation shows that anytime behaviour
works for the most difficult ontologies Choosing most often occurring symbol