Datalog-Based Data Access over Ontology Knowledge Bases Unit 4 – Systems Thomas Eiter Institut für Informationsysteme, TU Wien ICCL Summer School 2013, August 29-30, 2013 Austrian Science Fund (FWF) grants P20841, P24090 1/36
Datalog over Ontologies / Unit 4 1. Introduction Unit Outline 1. Introduction 2. Clipper 3. DReW – Datalog Rewriting System 4. Conclusion T. Eiter / TU Wien ICCL 2013 29/08/2013 2/36
Datalog over Ontologies / Unit 4 1. Introduction Some Systems / Tools General queries can be reduced to Boolean queries: Q ( � X ) ❀ Q ( � c ) This is not much practical Systems handling non-ground queries, as in databases, are needed Predominant: rewriting to relational DBMS FO-Rewriting Systems Datalog-Rewriting Systems Q UONTO / P RESTO R EQUIEM / EL O WLGRES C LIPPER R EQUIEM / DL -Lite A SPIDE /OWL-2-DLVex, A SPIDE /R EQUIEM M OR ( dl -progs/ DL -Lite ) DReW ( dl -programs) T. Eiter / TU Wien ICCL 2013 29/08/2013 3/36
Datalog over Ontologies / Unit 4 2. Clipper C LIPPER Reasoner C LIPPER is a reasoner for CQ answering over Horn- SHIQ ontologies Homepage: http://www.kr.tuwien.ac.at/research/systems/clipper at GitHub: https://github.com/ghxiao/clipper Based on Datalog rewriting (unit 3) Implemented in Java Ontology parser: OWL-API Datalog backend: DLV (inside C LIPPER ); Clingo may be used as well (compute rewriting, via command line) T. Eiter / TU Wien ICCL 2013 29/08/2013 4/36
Datalog over Ontologies / Unit 4 2. Clipper Query Answering Algorithm Recall: three steps to construct Datalog program Algorithm Horn- SHIQ -CQ Input : normal Horn- SHIQ KB K = ( T , A ) , conjunctive query Q Output : query answers Ξ( T ) ← Saturate ( T ) ; rew T ( Q ) ← Rewrite ( Q , Ξ( T )) ; cr ( T ) ← CompletionRules ( T ) ; P ← A ∪ cr ( T ) ∪ rew T ( q ) ; u ) ∈ Datalog-eval ( P ) } ; ans ← { � u | q ( � ✄ call Datalog reasoner Note: recursive rules might occur in CR ( T ) predicate arities in P are bounded by 2. hence rewriting P is necessarily exponential in the worst case (unless E XP T IME = NP) T. Eiter / TU Wien ICCL 2013 29/08/2013 5/36
Datalog over Ontologies / Unit 4 2. Clipper System Architecture ABox A P ← A ∪ cr ( T ) ∪ rew T ( q ) Ontology (2) Prepro- Saturation (4) O T Datalog cessing Engine P ans (3) (DLV, Query Clingo) w T ( Q ) Query Q (1) Q Prepro- e r Rewriting cessing (1) Conjunctive Query (3) Existential axioms in Ξ( T ) (2) Normalized TBox (4) Axioms cr T for ABox completion rules Version 0.1: CQs with simple roles only (no transitive roles) Use SPARQL syntax T. Eiter / TU Wien ICCL 2013 29/08/2013 6/36
Datalog over Ontologies / Unit 4 2. Clipper Usage T. Eiter / TU Wien ICCL 2013 29/08/2013 7/36
Datalog over Ontologies / Unit 4 2. Clipper Usage, cont’d T. Eiter / TU Wien ICCL 2013 29/08/2013 8/36
Datalog over Ontologies / Unit 4 2. Clipper Properties Comparison with state-of-the-art systems P RESTO and R EQUIEM [E_ et al. 2012a,2012b] C LIPPER shows promising results Nice downscaling behavior, on less expressive ontologies (falling into DL -Lite ) Prototype with transitive roles may be available soon! Possible extensions (projected) • weakly DL-safe rules (algorithm developed, implementation pending) • other DLs, like regular EL ++ and Horn- SRIQ , datatypes • more expressive queries, like regular path queries Big issue: lack of realistic test cases! T. Eiter / TU Wien ICCL 2013 29/08/2013 9/36
Datalog over Ontologies / Unit 4 3. DReW 3.1 Uniform Evaluation DReW System Loose Coupling - revisited Advantage: dl-atom 1 Ontology • clean semantics, can use legacy systems Rules • fairly easy to incorporate further knowledge formats dl-atom 2 Rule Ontology (e.g. RDF) Reasoner Reasoner Hybrid Reasoner • supportive to privacy, information hiding Drawback : impedance mismatch, performance • dl -program evaluation needs multiple calls of a dl -reasoner • Calls are expensive ∗ optimizations (caching, pruning ...) • exponentially many calls may be unavoidable • Even polynomially many calls might be too costly T. Eiter / TU Wien ICCL 2013 29/08/2013 10/36
Datalog over Ontologies / Unit 4 3. DReW 3.1 Uniform Evaluation Uniform Evaluation Method Convert the evaluation problem into one for a single reasoning engine Logic L L -formulas Reasoner Transform dl-program Π into an (equivalent) knowledge base in formalism L for evaluation ( uniform evaluation ) • L = FO Logic (SQL): MOR ; acyclic Π over DL -Lite , using an RDBMS • L = Datalog ¬ : DReW ; Π over Datalog-rewritable ontologies Note: uniform evaluation is different from tight integration in a unifying logic T. Eiter / TU Wien ICCL 2013 29/08/2013 11/36
Datalog over Ontologies / Unit 4 3. DReW 3.1 Uniform Evaluation Issues “Uniform Evaluation” raises some issues: 1) Cost of a transformation . E.g., • Reduction of CQs over DL-Lite ontologies to first-order (FO) Logic [Calvanese et al. , 2007] non-recursive Datalog [Gottlob and Schwentick, 2011], [Kontchakov et al. , 2010] • Reduction of SHIQ to D ATALOG ∨ [Hustadt et al. , 2007]. 2) Existence of a transformation (possibly under constraints) • Embedding of a formalism into another • Properties (e.g. modularity [Janhunen, 1999]) • Embedding of dl -programs e.g. into MKNF [Motik and Rosati, 2010], Equilibrium Logic [Fink and Pearce, 2010] 3) Complexity of the target formalism 4) Feasibility of transformations for practical concerns T. Eiter / TU Wien ICCL 2013 29/08/2013 12/36
Datalog over Ontologies / Unit 4 3. DReW 3.2 Reasoning via Datalog Rewriting Uniform Datalog Evaluation of dl -Programs Idea: for Datalog-rewritable ontologies, we may replace dl -atoms c ) with Datalog programs evaluating the atoms DL [ λ ; Q ]( � the result is computed in an atom Q λ ( � c ) rewrite the dl -rules to ordinary rules, by replacing dl -atoms evaluate the resulting logic program using a Datalog engine / ASP solver Important: uniform query rewriting, must work for all λ Demonstrate the method on the Network example T. Eiter / TU Wien ICCL 2013 29/08/2013 13/36
Datalog over Ontologies / Unit 4 3. DReW 3.2 Reasoning via Datalog Rewriting Network Example Ontology O : Π = ( O , P ) ≥ 1 . wired ⊑ Node ⊤ ⊑ ∀ wired . Node x 1 ? n 1 wired = wired − ; X n 5 n 1 � = n 2 � = n 3 � = n 4 � = n 5 n 2 wired ( n 1 , n 2 ) wired ( n 2 , n 3 ) wired ( n 2 , n 4 ) wired ( n 2 , n 5 ) wired ( n 3 , n 4 ) wired ( n 3 , n 5 ) . n 4 ≥ 4 . wired ⊑ HighTrafficNode n 3 x 2 ? newnode ( x 1 ) . newnode ( x 2 ) . Rules P overloaded ( X ) ← DL [ wired ⊎ connect ; HighTrafficNode ]( X ) . connect ( X , Y ) ← newnode ( X ) , DL [ Node ]( Y ) , not overloaded ( Y ) , not excl ( X , Y ) . excl ( X , Y ) ← connect ( X , Z ) , DL [ Node ]( Y ) , Y � = Z . excl ( X , Y ) ← connect ( Z , Y ) , newnode ( Z ) , newnode ( X ) , Z � = X . excl ( x 1 , n 4 ) . T. Eiter / TU Wien ICCL 2013 29/08/2013 14/36
Datalog over Ontologies / Unit 4 3. DReW 3.2 Reasoning via Datalog Rewriting Network Example, cont’d 1. Rewriting the ontology The DL component O is in OWL 2 RL resp. LDL + , which is Datalog-rewritable (so are the dl -atoms). We transform O to the Datalog program Φ LDL + ( O ) : wired − ( Y , X ) ← wired ( X , Y ) wired ( Y , X ) ← wired − ( X , Y ) ⊤ ( X ) ← wired ( X , Y ) ⊤ ( Y ) ← wired ( X , Y ) ⊤ ( X ) ← wired − ( X , Y ) ⊤ ( Y ) ← wired − ( X , Y ) % axiom ≥ 1 . wired ⊑ Node Node ( Y ) ← wired ( X , Y ) % axiom ⊤ ⊑ ∀ wired . Node Node ( Y ) ← wired ( X , Y ) , ⊤ ( X ) % axiom ≥ 4 . wired ⊑ HighTrafficNode HighTrafficNode ( X ) ← wired ( X , Y 1 ) , wired ( X , Y 2 ) , wired ( X , Y 3 ) , wired ( X , Y 4 ) , Y 1 � = Y 2 , Y 1 � = Y 3 , . . . , Y 3 � = Y 4 . wired ( n 1 , n 2 ) wired ( n 2 , n 3 ) wired ( n 2 , n 4 ) , wired ( n 2 , n 5 ) . wired ( n 3 , n 4 ) . wired ( n 3 , n 5 ) . T. Eiter / TU Wien ICCL 2013 29/08/2013 15/36
Datalog over Ontologies / Unit 4 3. DReW 3.2 Reasoning via Datalog Rewriting Network Example, cont’d 2. Duplicating for dl -inputs dl -atoms in Π : DL [ Node ]( Y ) , DL [ wired ⊎ connect ; HighTrafficNode ]( X ) the dl -queries in are just instance queries, so given by Node ( Y ) resp. HighTrafficNode ( X ) Each DL-atom sends up a different input λ to O and so entailments for the λ ’s might be different. To this purpose, we copy Φ LDL + ( O ) to new disjoint equivalent versions for each DL-input λ For the set Λ P = { λ 1 = ǫ, λ 2 = wired ⊎ connect } , we have • Φ LDL + ,λ 1 ( O ) = { Node λ 1 ( X ) ← wired λ 1 ( X , Y ) , . . . } and • Φ LDL + ,λ 2 ( O ) = { Node λ 2 ( X ) ← wired λ 2 ( X , Y ) , . . . } T. Eiter / TU Wien ICCL 2013 29/08/2013 16/36
Datalog over Ontologies / Unit 4 3. DReW 3.2 Reasoning via Datalog Rewriting Network Example, cont’d 3. Rewriting dl -rules to ordinary rules To rewrite DL-rules P into ordinary rules P ord , we simply replace each DL-atom DL [ λ ; Q ]( t ) by a new atom Q λ ( t ) . � � P ord newnode ( x 1 ) . newnode ( x 2 ) . overloaded ( X ) ← HighTrafficNode λ 2 ( X ) . connect ( X , Y ) ← newnode ( X ) , Node λ 1 ( Y ) , not overloaded ( Y ) , not excl ( X , Y ) . excl ( X , Y ) ← connect ( X , Z ) , Node λ 1 ( Y ) , Y � = Z . excl ( X , Y ) ← connect ( Z , Y ) , newnode ( Z ) , newnode ( X ) , Z � = X . excl ( x 1 , n 4 ) . T. Eiter / TU Wien ICCL 2013 29/08/2013 17/36
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