G-hybrid Knowledge Bases Stijn Heymans, Livia Predoiu, Cristina - PowerPoint PPT Presentation

G-hybrid Knowledge Bases Stijn Heymans, Livia Predoiu, Cristina Feier, Jos de Bruijn and Davy Van Nieuwenborgh Digital Enterprise Research Institute (DERI) University of Innsbruck, Austria and Theoretical Computer Science Lab Vrije Universiteit Brussel, Belgium and Knowledge Representation and Knowledge Management Research Group University of Mannheim, Germany published at ALPSWS 2006

DL vs. LP ◮ Description Logics: ◮ Open Domains (First-order like) ◮ Suitable for Conceptual Modeling (Ontologies) ◮ Well-investigated (decidability, algorithms). ◮ Standardized: OWL. ⇒ Semantic Web Reasoning ◮ Logic Programming: ◮ Flexible Rule-based presentation, ◮ Nonmonotonic Reasoning is possible. ⇒ Semantic Web Reasoning possible (see W3C rule language proposals) but some disadvantages .

Problems and Solutions for LP on the SW ◮ no open domains: hampers conceptual reasoning. ⇒ Extensions of LP with open domains, e.g, open Answer Set Programming (decidability is issue) ◮ nonmonotonism is a challenge. ⇒ Scoped Negation ( Polleres et al. ) Instead of extending LP, let DL and LP coexist and interact: g-hybrid knowledge bases .

Definition g-hybrid KBs Definition Given Description Logic DL , a g-hybrid knowledge base is a pair (Σ , P ) where Σ is a DL knowledge base and P is a guarded program.

Example g-hybrid KBs DLRO −{≤} knowledge base Σ : socialDrinker ⊑ ∃ [$ 1 ]( drinks ⊓ ($ 3 / 3 : { wine } )) . Guarded Program P: ← problematic ( X ) socialDrinker ( X ) , knowsFromAA ( X , Y ) ← knowsFromAA ( john , michael ) ← socialDrinker ( john ) (Σ , P ) is a g-hybrid knowledge base.

Semantics g-hybrid KBs ⊑ ∃ [$ 1 ]( drinks ⊓ ($ 3 / 3 : { wine } )) . socialDrinker problematic ( X ) ← socialDrinker ( X ) , knowsFromAA ( X , Y ) knowsFromAA ( john , michael ) ← socialDrinker ( john ) ← ◮ D ≡ { john , michael , wine , x } , ◮ · I : ◮ socialDrinker I = { john } , ◮ drinks I = { ( john , x , wine ) } , ◮ wine I = wine . ◮ M ≡ { knowsfromAA ( john , michael ) , problematic ( john ) } .

Semantics g-hybrid KBs (2) socialDrinker ⊑ ∃ [$ 1 ]( drinks ⊓ ($ 3 / 3 : { wine } )) . problematic ( X ) ← socialDrinker ( X ) , knowsFromAA ( X , Y ) knowsFromAA ( john , michael ) ← socialDrinker ( john ) ← ◮ ( D , · I ) is a model of the DL knowledge base, ◮ M is an answer set of ground projection : problematic ( john ) ← knowsFromAA ( john , john ) problematic ( john ) ← knowsFromAA ( john , x ) problematic ( john ) ← knowsFromAA ( john , michael ) problematic ( john ) ← knowsFromAA ( john , wine ) knowsFromAA ( john , michael ) ← ◮ ( D , · I , M ) is a model of the g-hybrid knowledge base.

Decidability g-hybrid KBs ◮ Satisfiability checking. ◮ Decidable in case DL part is DLRO −{≤} by a reduction to guarded programs under the open answer set semantics .

socialDrinker ⊑ ∃ [$ 1 ]( drinks ⊓ ($ 3 / 3 : { wine } )) ← socialDrinker ( X ) , not ( ∃ [$ 1 ]( drinks ⊓ ($ 3 / 3 : { wine } )))( X ) socialDrinker ( X ) ∨ not socialDrinker ( X ) ← drinks ( X , Y , Z ) ∨ not drinks ( X , Y , Z ) ← ⊤ 1 ( X ) ∨ not ⊤ 1 ( X ) ← ⊤ 3 ( X , Y , Z ) ∨ not ⊤ 3 ( X , Y , Z ) ←

socialDrinker ⊑ ∃ [$ 1 ]( drinks ⊓ ($ 3 / 3 : { wine } )) ← drinks ( X , Y , Z ) , not ⊤ 3 ( X , Y , Z ) ← not ⊤ 1 ( X ) { wine } ( wine ) ← ($ 3 / 3 : { wine } )( X , Y , Z ) ← ⊤ 3 ( X , Y , Z ) , { wine } ( Z ) ( drinks ⊓ ($ 3 / 3 : { wine } ))( X , Y , Z ) ← drinks ( X , Y , Z ) , ($3 / 3 : { wine } )( X , Y , Z ) ( ∃ [$ 1 ]( drinks ⊓ ($ 3 / 3 : { wine } )))( X ) ← ( drinks ⊓ ($3 / 3 : { wine } ))( X , Y , Z )

Decidability g-hybrid KBs Theorem Satisfiability checking w.r.t. g-hybrid knowledge bases where the DL part is a DLRO −{≤} knowledge base is 2- exptime -complete.

Relation of DLRO −{≤} with OWL DL ( SHOIN ( D )) − No data types. − No Number restrictions. − No transitive roles. + n -ary relations. + Expressive Role expressions. Common fragment: ALCHOI .

DL + log Knowledge Bases (Rosati) (Σ , P ) is a DL + log knowledge base if for every rule in P : ◮ the negative part of the body does not contain DL-atoms ( DL-positiveness ), ◮ each variable in the rule occurs in some positive body atom ( Datalog safeness ), and ◮ each head variable occurs in a positive non-DL body atom ( weak safeness ). Difference regarding semantics: Rosati assumes standard names assumption .

Balance DL + log and g-hybrid KBs ◮ Disjunction of positive atoms in head is allowed in DL + log . ◮ Rules in g-hybrid KBs are guarded instead of Datalog safe. ◮ g-hybrid KBs do not require weak safeness. ◮ g-hybrid KBs do not require DL-positiveness. ◮ Decidability for satisfiability checking w.r.t DL + log knowledge bases is guaranteed if query containment is decidable for the DL.

Conclusions and Future Research ◮ Definition of integrating framework for DLs and LP, ◮ Decidability based on a reduction to Open Answer Set Programming, ◮ no standard names assumption, DL-positiveness, Datalog safeness, weak safeness requirement. Instead guardedness . ◮ Limitations: ◮ Lack of support for DLs with number restrictions, ◮ No implemented system available.