Representability in DL-Lite R Knowledge Base Exchange Marcelo Arenas - PowerPoint PPT Presentation

Knowledge Base Exchange Representability in DL - Lite R Conclusions Representability in DL-Lite R Knowledge Base Exchange Marcelo Arenas 1 Elena Botoeva 2 Diego Calvanese 2 Vladislav Ryzhikov 2 Evgeny Sherkhonov 3 1 Dept. of Computer Science, PUC Chile marenas@ing.puc.cl 2 KRDB Research Centre, Free Univ. of Bozen-Bolzano, Italy lastname @inf.unibz.it ISLA, University of Amsterdam, Netherlands e.sherkhonov@uva.nl Description Logics Workshop 7 June 2012, Rome Representability in DL-Lite R Knowledge Base Exchange Elena Botoeva 1/20

Knowledge Base Exchange Representability in DL - Lite R Conclusions Outline 1 Knowledge Base Exchange 2 Representability in DL - Lite R 3 Conclusions Representability in DL-Lite R Knowledge Base Exchange Elena Botoeva 2/20

Knowledge Base Exchange Representability in DL - Lite R Conclusions Outline 1 Knowledge Base Exchange 2 Representability in DL - Lite R 3 Conclusions Representability in DL-Lite R Knowledge Base Exchange Elena Botoeva 3/20

Knowledge Base Exchange Representability in DL - Lite R Conclusions Knowledge Base Exchange Problem given a mapping M and a source knowledge base (KB) K 1 , compute a target KB K 2 that is a solution for K 1 under M . Σ 1 Σ 1 Σ 2 Σ 2 target signature source signature Representability in DL-Lite R Knowledge Base Exchange Elena Botoeva 4/20

Knowledge Base Exchange Representability in DL - Lite R Conclusions Knowledge Base Exchange Problem given a mapping M and a source knowledge base (KB) K 1 , compute a target KB K 2 that is a solution for K 1 under M . M Σ 1 Σ 1 Σ 2 Σ 2 target signature source signature Representability in DL-Lite R Knowledge Base Exchange Elena Botoeva 4/20

Knowledge Base Exchange Representability in DL - Lite R Conclusions Knowledge Base Exchange Problem given a mapping M and a source knowledge base (KB) K 1 , compute a target KB K 2 that is a solution for K 1 under M . M Σ 1 Σ 1 Σ 2 Σ 2 target signature source signature T 1 A 1 D 1 B 1 C 1 A 1 source KB K 1 Representability in DL-Lite R Knowledge Base Exchange Elena Botoeva 4/20

Knowledge Base Exchange Representability in DL - Lite R Conclusions Knowledge Base Exchange Problem given a mapping M and a source knowledge base (KB) K 1 , compute a target KB K 2 that is a solution for K 1 under M . M Σ 1 Σ 1 Σ 2 Σ 2 target signature source signature T 1 T 2 A 1 D 1 A 2 B 1 C 1 B 2 C 2 A 1 A 2 target KB K 2 source KB K 1 Representability in DL-Lite R Knowledge Base Exchange Elena Botoeva 4/20

Knowledge Base Exchange: Example T 1 : matches Item FootWear OpenShoes Strappy Plateau hasMatchingOpenShoes HighHeel . . . Apparel Gown LightGown FormalGown CocktailGown EveningGown . . . A 1 : Strappy Plateau HighHeel LightGown turq _ gown brown _ sand wedge _ sand heel _ sand hasMatchingOpenShoes

Knowledge Base Exchange: Example T 1 : M : matches fitsWith Item Product FootWear Shoes OpenShoes Sandals Strappy Classic Plateau Platform hasMatchingOpenShoes HighHeel Heeled . . . fitsWithSandals Apparel Clothing Gown Dress LightGown SummerDress FormalGown WorkDress CocktailGown EveningDress EveningGown . . . A 1 : Strappy Plateau HighHeel LightGown turq _ gown brown _ sand wedge _ sand heel _ sand hasMatchingOpenShoes

Example: Universal Solution Definition K 2 is a universal solution for K 1 under M if Mod( K 2 ) = Mod( K 1 ∪ M ) | Σ 2 . Theorem If chase T 1 ( A 1 ) is finite, then chase T 1 ∪M, Σ 2 ( A 1 ) is a universal solution for �T 1 , A 1 � under M . A univ T 1 ∪ M : A 1 : : 2 Strappy Item Product FootWear Shoes OpenShoes Sandals Plateau Strappy Classic Plateau Platform HighHeel Heeled HighHeel Apparel Clothing Gown Dress LightGown SummerDress . . . LightGown

Example: Universal Solution Definition K 2 is a universal solution for K 1 under M if Mod( K 2 ) = Mod( K 1 ∪ M ) | Σ 2 . Theorem If chase T 1 ( A 1 ) is finite, then chase T 1 ∪M, Σ 2 ( A 1 ) is a universal solution for �T 1 , A 1 � under M . A univ T 1 ∪ M : A 1 : : 2 Strappy Classic Item Product FootWear Shoes OpenShoes Sandals Plateau Platform Strappy Classic Plateau Platform HighHeel Heeled HighHeel Heeled Apparel Clothing Gown Dress LightGown SummerDress . . . LightGown SummerDress

Example: Universal Solution Definition K 2 is a universal solution for K 1 under M if Mod( K 2 ) = Mod( K 1 ∪ M ) | Σ 2 . Theorem If chase T 1 ( A 1 ) is finite, then chase T 1 ∪M, Σ 2 ( A 1 ) is a universal solution for �T 1 , A 1 � under M . A univ T 1 ∪ M : A 1 : : 2 Strappy Classic Sandals Item Product FootWear Shoes OpenShoes Sandals Plateau Platform Strappy Classic Plateau Platform HighHeel Heeled HighHeel Heeled Apparel Clothing Gown Dress LightGown SummerDress . . . LightGown SummerDress Dress

Example: Universal Solution Definition K 2 is a universal solution for K 1 under M if Mod( K 2 ) = Mod( K 1 ∪ M ) | Σ 2 . Theorem If chase T 1 ( A 1 ) is finite, then chase T 1 ∪M, Σ 2 ( A 1 ) is a universal solution for �T 1 , A 1 � under M . A univ T 1 ∪ M : A 1 : : 2 Strappy Classic Sandals Shoes Item Product FootWear Shoes OpenShoes Sandals Plateau Platform Strappy Classic Plateau Platform HighHeel Heeled HighHeel Heeled Apparel Clothing Gown Dress LightGown SummerDress . . . LightGown SummerDress Dress Clothing

Example: Universal Solution Definition K 2 is a universal solution for K 1 under M if Mod( K 2 ) = Mod( K 1 ∪ M ) | Σ 2 . Theorem If chase T 1 ( A 1 ) is finite, then chase T 1 ∪M, Σ 2 ( A 1 ) is a universal solution for �T 1 , A 1 � under M . A univ T 1 ∪ M : A 1 : : 2 Strappy Classic Sandals Shoes Product Item Product FootWear Shoes OpenShoes Sandals Plateau Platform Strappy Classic Plateau Platform HighHeel Heeled HighHeel Heeled Apparel Clothing Gown Dress LightGown SummerDress . . . LightGown SummerDress Dress Clothing

Example: Universal Solution Definition K 2 is a universal solution for K 1 under M if Mod( K 2 ) = Mod( K 1 ∪ M ) | Σ 2 . Theorem If chase T 1 ( A 1 ) is finite, then chase T 1 ∪M, Σ 2 ( A 1 ) is a universal solution for �T 1 , A 1 � under M . A univ T 1 ∪ M : A 1 : : 2 Strappy Classic Sandals Shoes Product matches fitsWith Item Product FootWear Shoes OpenShoes Sandals Plateau Platform s e Strappy Classic o h S Plateau Platform n e p HighHeel O Heeled g hasMatchingOpenShoes n fitsWithSandals HighHeel i h Heeled c t Apparel a Clothing M s Gown Dress a h LightGown SummerDress . . . LightGown SummerDress Dress Clothing

Example: Universal Solution Definition K 2 is a universal solution for K 1 under M if Mod( K 2 ) = Mod( K 1 ∪ M ) | Σ 2 . Theorem If chase T 1 ( A 1 ) is finite, then chase T 1 ∪M, Σ 2 ( A 1 ) is a universal solution for �T 1 , A 1 � under M . A univ T 1 ∪ M : A 1 : : 2 Strappy Classic Sandals Shoes Product fitsWithSandals matches fitsWith Item Product FootWear Shoes OpenShoes Sandals Plateau Platform s e Strappy Classic o h S Plateau Platform n e p HighHeel O Heeled g hasMatchingOpenShoes n fitsWithSandals HighHeel i h Heeled c t Apparel a Clothing M s Gown Dress a h LightGown SummerDress . . . LightGown SummerDress Dress Clothing

Example: Universal Solution Definition K 2 is a universal solution for K 1 under M if Mod( K 2 ) = Mod( K 1 ∪ M ) | Σ 2 . Theorem If chase T 1 ( A 1 ) is finite, then chase T 1 ∪M, Σ 2 ( A 1 ) is a universal solution for �T 1 , A 1 � under M . A univ T 1 ∪ M : A 1 : : 2 Strappy Classic Sandals Shoes Product fitsWithSandals fitsWith matches fitsWith Item Product FootWear Shoes OpenShoes Sandals Plateau Platform s e Strappy Classic o h S Plateau Platform n e p HighHeel O Heeled g hasMatchingOpenShoes n fitsWithSandals HighHeel i h Heeled c t Apparel a Clothing M s Gown Dress a h LightGown SummerDress . . . LightGown SummerDress Dress Clothing

Knowledge Base Exchange Representability in DL - Lite R Conclusions Example: Universal UCQ-solution Definition K 2 is a universal UCQ-solution for K 1 under M if for each UCQ q over Σ 2 , cert ( q , �T 1 ∪ M , A 1 � ) = cert ( q , K 2 ) . T 2 : A 2 : Classic fitsWith Product brown _ sand Shoes Sandals Platform Classic fitsWithSandals Platform wedge _ sand Heeled . . . fitsWithSandals Heeled Clothing Dress heel _ sand SummerDress WorkDress SummerDress EveningDress . . . turq _ gown Representability in DL-Lite R Knowledge Base Exchange Elena Botoeva 7/20

Knowledge Base Exchange Representability in DL - Lite R Conclusions Outline 1 Knowledge Base Exchange 2 Representability in DL - Lite R 3 Conclusions Representability in DL-Lite R Knowledge Base Exchange Elena Botoeva 8/20

Knowledge Base Exchange Representability in DL - Lite R Conclusions Representability Problem Problem given a mapping M and a source TBox T 1 , decide whether there exists a target TBox T 2 , such that for each ABox A 1 over Σ 1 , �T 2 , chase M , Σ 2 ( A 1 ) � is a universal UCQ-solution for �T 1 , A 1 � under M . M ⊆ M ∗ and T 1 ∪ M | M ∗ = M ∗ s.t. M Σ 1 Σ 1 Σ 2 Σ 2 target signature source signature T 1 A 1 D 1 B 1 C 1 source TBox Representability in DL-Lite R Knowledge Base Exchange Elena Botoeva 9/20