Exploring Controlled English OBDA Camilo Thorne, Diego Calvanese KRDB Centre Free University of Bozen-Bolzano Via della Mostra 4 39100 - Italy CNL 2009, Maretimmo, 9/6/09 (1)
The The Problem Problem Ontology-based systems [Staab&Studer 2004] aim at accessing and querying (possibly from the web) repositories of heterogenous data. Examples: data integration systems, knowledge portals, ontology-based systems for semantically annotated data, etc. [Staab&Studer] We denote such systems as ontology-based data access systems (OBDASs) [Cal- vanese et al. 2005] In such scenarios, an ontology layer on top of a data layer provides a global conceptual model of potentially incomplete sources over which formal queries (SQL, SPARQL, etc.) are formulated Q The semantics of such systems can be (conceptual Ontology characterized in terms of layer) FO interpretations Querying takes place under DB (data layer) the open world assumption (OWA) Exploring Exploring Controlled Controlled English English OBDA OBDA (2) (2)
Ontology Ontology Ontology Languages Languages Languages We will focus on ontologies represented in fragments of the W3C ontology language OWL Significant fragments of OWL correspond to widely used conceptual modelling for- malisms such as UML class diagrams Exploring Exploring Controlled Controlled English English OBDA OBDA (3) (3)
Ontology Ontology Ontology Languages Languages Languages We will focus on ontologies represented in fragments of the W3C ontology language OWL Significant fragments of OWL correspond to widely used conceptual modelling for- malisms such as UML class diagrams !"#$%&'' 0../ The Employee ontology !"#"$%&'()*+,+$ ' characterizes the domain 3'4'$%#5 of employees, specifying -../ (i) the classes, relations and ()*)+', /,%0'12 ' attributes (= the terminology) ' ' into which the domain is structured 0..0 123!453)*6'7589#+*+: ")*)+'5 (ii) the constraints (IS-A, -,').()*)+', /,%0'12.()*)+', 0..0 participation, cardinality) ' ' ' ' all (incomplete) sources satisfy Exploring Exploring Controlled Controlled English English OBDA OBDA (3) (3)
Controlled Controlled Controlled Controlled Languages Languages Languages Languages To improve the usability of interfaces to ontologies and OBDASs controlled languages [Bernstein et al. 2005, Sowa 2004] have been proposed They have been shown to outperform (in such terms) interfaces based on keywords or visual query languages [Bernstein et al. 2007] They provide a trade-off between the rigor of formal ontology/query languages and NL This is related to work on NLIs to databases [Androstopoulos 1995] and CL interfaces to databases [Wintner et al. 2006] Q (NL layer) CL interface (conceptual Ontology layer) DB (data layer) Exploring Exploring Controlled Controlled English English OBDA OBDA (4) (4)
Controlled Controlled Controlled Controlled Languages Languages Languages Languages To improve the usability of interfaces to ontologies and OBDASs controlled languages [Bernstein et al. 2005, Sowa 2004] have been proposed They have been shown to outperform (in such terms) interfaces based on keywords or visual query languages [Bernstein et al. 2007] They provide a trade-off between the rigor of formal ontology/query languages and NL This is related to work on NLIs to databases [Androstopoulos 1995] and CL interfaces to databases [Wintner et al. 2006] Q Declarations translate compositionally into (NL layer) CL interface ontologies and questions into formal queries Their semantic complexity [Pratt 2003] reduces to (conceptual Ontology layer) the computational properties of the OBDASs DB (data ⇒ We should study the computational layer) complexity of CLs w.r.t. OBDA Exploring Exploring Controlled Controlled English English OBDA OBDA (4) (4)
Ontology Ontology Ontology Ontology Ontology Languages Languages Languages Languages Languages Semantic Web Language Description Logics ( OWL ) + CL ¡owl:Class rdf:about=”#Employee”¿ ¡rdfs:subClassOf¿ ¡owl:Restriction¿ Employee ⊑ ∃ develops : Project ¡owl:onProperty rdf:resource=”#develops”/¿ ¡owl:someValuesFrom Every employee develops rdf:resource=”#Project”/¿ some project ¡/owl:Restriction¿ ¡/rdfs:SubclassOf¿ ¡/owl:Class¿ OWL is a machine-readable language (embedded in RDF and XML) CLs are human-readable , yet as unambigous as DLs Exploring Exploring Controlled Controlled English English OBDA OBDA (5) (5)
Outline Outline Outline Outline Outline Outline 1. The Problem (i) Ontology languages (ii) Controlled Languages 1. OBDA and Query Answering (i) ALCI ontologies and conjunctive queries (ii) Certain answers and query answering (iii) DL-Lite ontologies 2. Controlled Languages (i) DL-English and Lite-English (ii) The { IS-A i } i ∈ [0 , 7] fragments 3. Computational Complexity (i) Expressing query answering (ii) Tree-shaped conjunctive queries (iii) Data complexity of QA 4. Conclusions and further work Exploring Exploring Controlled Controlled English English OBDA OBDA (6) (6)
Ontologies Ontologies Ontologies Ontologies Ontologies Ontologies Ontologies ALCI ALCI ALCI ALCI ALCI ALCI ALCI In ALCI , roles R and concepts C are formed according to the syntax P | P − → R ⊤ | A | ∃ R : C | ¬ C | C ⊓ C ′ → C Exploring Exploring Controlled Controlled English English OBDA OBDA (7) (7)
Ontologies Ontologies Ontologies Ontologies Ontologies Ontologies Ontologies ALCI ALCI ALCI ALCI ALCI ALCI ALCI In ALCI , roles R and concepts C are formed according to the syntax P | P − → R ⊤ | A | ∃ R : C | ¬ C | C ⊓ C ′ → C An assertion is an expression C ⊑ C ′ A terminology (TBox) T is a set of assertions An ontology is a pair �T , A� , where A is a set of ground facts (ABox) Exploring Exploring Controlled Controlled English English OBDA OBDA (7) (7)
Ontologies Ontologies Ontologies Ontologies Ontologies Ontologies Ontologies ALCI ALCI ALCI ALCI ALCI ALCI ALCI In ALCI , roles R and concepts C are formed according to the syntax P | P − → R ⊤ | A | ∃ R : C | ¬ C | C ⊓ C ′ → C An assertion is an expression C ⊑ C ′ A terminology (TBox) T is a set of assertions An ontology is a pair �T , A� , where A is a set of ground facts (ABox) Semantics is given by FO interpretations D := � ∆ , · D � A D = C ⊑ C ′ iff C D ⊆ C ′D ⊆ ∆ D | ⊤ D := ∆ { d | exists d ′ s.t. ( ∃ R : C ) D := D | = �T , A� iff � d, d ′ � ∈ R D and d ′ ∈ C D } i. D | = T ( ¬ C ) D ∆ − C D := ii. D | = A C D ∩ C ′D ( C ⊓ C ′ ) D := P D ⊆ ∆ × ∆ Exploring Exploring Controlled Controlled English English OBDA OBDA (7) (7) Mod ( �T , A� ) := {D | D | = �T , A�} ( R − ) D {� d, d ′ � | � d ′ , d � ∈ R D } :=
Conjun tive Conjun tive Conjun tive Conjun tive Conjun tive Conjun tive Conjun tive Conjun tive Queries Queries Queries Queries Queries Queries Queries Queries A conjunctive query (CQ) is a query of the form q ( � x ) ← ∃ � y Φ( � y ) x, � x is a sequence of n distinguished variables and ∃ � where q ( � x ) is the head , � y Φ( � x, � y ) is a conjunction of existentially quantified atoms called body Exploring Exploring Controlled Controlled English English OBDA OBDA (8) (8)
Conjun tive Conjun tive Conjun tive Conjun tive Conjun tive Conjun tive Conjun tive Conjun tive Queries Queries Queries Queries Queries Queries Queries Queries A conjunctive query (CQ) is a query of the form q ( � x ) ← ∃ � y Φ( � y ) x, � x is a sequence of n distinguished variables and ∃ � where q ( � x ) is the head , � y Φ( � x, � y ) is a conjunction of existentially quantified atoms called body They correspond to SQL SELECT-PROJECT-JOIN queries Exploring Exploring Controlled Controlled English English OBDA OBDA (8) (8)
Conjun tive Conjun tive Conjun tive Conjun tive Conjun tive Conjun tive Conjun tive Conjun tive Queries Queries Queries Queries Queries Queries Queries Queries A conjunctive query (CQ) is a query of the form q ( � x ) ← ∃ � y Φ( � y ) x, � x is a sequence of n distinguished variables and ∃ � where q ( � x ) is the head , � y Φ( � x, � y ) is a conjunction of existentially quantified atoms called body They correspond to SQL SELECT-PROJECT-JOIN queries EXAMPLE: Which manager is a project manager !"#$%&'' 0../ !"#"$%&'()*+,+$ that manages some project? ' 3'4'$%#5 ← Manager ( x ) ∧ ProjectManager ( x ) q ( x ) -../ ∧∃ y ( manages ( x, y ) ∧ Project ( y )) ()*)+', /,%0'12 ' ' ' SELECT Manager.MName 0..0 123!453)*6'7589#+*+: FROM Manager, ProjectManager, manages, Project ")*)+'5 WHERE Manager.MName = ProjectManager.MName -,').()*)+', /,%0'12.()*)+', 0..0 ' ' AND Manager.MName = manages.MName ' ' AND Project.PName = manages.PName Exploring Exploring Controlled Controlled English English OBDA OBDA (8) (8)
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