ontology-mediated query answering Harnessing knowledge to get more from data Meghyn Bienvenu ( LaBRI - CNRS & University of Bordeaux )
ontology-mediated query answering (omqa) domain knowledge Why use an ontology? ∙ extend the vocabulary (making queries easier to formulate) ∙ provide a unified view of multiple data sources ∙ obtain more answers to queries (by exploiting domain knowledge) 2/42 ??? data incomplete ontology user query database (logical theory) (ground facts)
ontology-mediated query answering (omqa) Why use an ontology? ∙ obtain more answers to queries (by exploiting domain knowledge) ∙ provide a unified view of multiple data sources ∙ extend the vocabulary (making queries easier to formulate) 2/42 ??? data patient data medical knowledge user query “Melanie has listeriosis” “Listeriosis & Lyme disease “Find all patients with “Paul has Lyme disease” are bacterial infections” bacterial infections” expected answers : Melanie, Paul
ontology-mediated query answering (omqa) Why use an ontology? ∙ obtain more answers to queries (by exploiting domain knowledge) ∙ provide a unified view of multiple data sources ∙ extend the vocabulary (making queries easier to formulate) 2/42 ??? data patient data medical knowledge user query “Melanie has listeriosis” “Listeriosis & Lyme disease “Find all patients with “Paul has Lyme disease” are bacterial infections” bacterial infections” expected answers : Melanie, Paul
today’s talk Two main objectives: ∙ give a brief introduction to OMQA ∙ show connections between OMQA and theoretical CS Structure of the talk: ∙ Introductory material ∙ description logic (DL) ontologies, OMQA problem, query rewriting ∙ Understanding query rewriting ∙ natural questions related to size and existence of rewritings ∙ links to circuit complexity, automata, CSP 3/42
introduction to omqa & query rewriting
our focus: description logic ontologies Ontologies typically described using logic-based formalisms In this talk: ontologies formulated in description logics (DLs) ∙ family of decidable fragments of first-order logic (FO) ∙ range from fairly simple to highly expressive ∙ complexity of query answering well understood ∙ lots of practical work on algorithms and implementations ∙ basis for OWL web ontology language (W3C standard) Today, we’ll mainly focus on three particular DLs: 5/42 ∙ ALC , EL , DL-Lite R
dl basics Building blocks of DLs : ∙ concept names (unary predicates, classes) ∙ role names (binary predicates, properties) teaches ∙ individual names (constants) Build complex concepts and roles using constructors. For example: ∙ Non-professors: Prof ∙ Profs who teach a Master’s course: Prof teaches MCourse ∙ Taught by: teaches Note : set of available constructors depends on the particular DL ! 6/42 Prof , Course marie , inf100
dl basics Building blocks of DLs : ∙ concept names (unary predicates, classes) ∙ role names (binary predicates, properties) teaches ∙ individual names (constants) Build complex concepts and roles using constructors. For example: Note : set of available constructors depends on the particular DL ! 6/42 Prof , Course marie , inf100 ∙ Non-professors: ¬ Prof ∙ Profs who teach a Master’s course: Prof ⊓ ∃ teaches . MCourse ∙ Taught by: teaches −
dl knowledge bases Knowledge base (KB) = ABox (data) + TBox (ontology) ABox contains facts about specific individuals TBox contains general knowledge about the domain of interest ∙ finite set of axioms (types of axioms depends on the DL) ∙ concept inclusions most common form of axiom ∙ C D , with C D complex concepts ∙ intuitive meaning: “ everything that is a C is also a D ” ∙ examples on later slides 7/42 ∙ finite set of concept assertions A ( a ) and role assertions r ( a , b ) ∙ example assertions: Prof ( marie ) , teaches ( marie , inf 100 )
dl knowledge bases Knowledge base (KB) = ABox (data) + TBox (ontology) ABox contains facts about specific individuals TBox contains general knowledge about the domain of interest ∙ finite set of axioms (types of axioms depends on the DL) ∙ concept inclusions most common form of axiom ∙ intuitive meaning: “ everything that is a C is also a D ” ∙ examples on later slides 7/42 ∙ finite set of concept assertions A ( a ) and role assertions r ( a , b ) ∙ example assertions: Prof ( marie ) , teaches ( marie , inf 100 ) ∙ C ⊑ D , with C , D complex concepts
exists d 1 d 2 C Satisfaction in an interpretation satisfies B a a B satisfies C D dl semantics C Model of a KB = interpretation that satisfies all statements in entails (written ) = every model of satisfies D r with d 2 C (like FO logic semantics) ∙ extend ∙ to complex concepts and roles, for example: D C D r C d 1 8/42 Interpretation I (“possible world”) ∙ domain of objects ∆ I (possibly infinite set) ∙ interpretation function · I that maps ∙ concept name A ⇝ set of objects A I ⊆ ∆ I ∙ role name r ⇝ set of pairs of objects r I ⊆ ∆ I × ∆ I ∙ individual name a ⇝ object a I ∈ ∆ I
dl semantics B satisfies of ) = every model (written entails = interpretation that satisfies all statements in Model of a KB D C D satisfies C a satisfies B a Satisfaction in an interpretation (like FO logic semantics) 8/42 Interpretation I (“possible world”) ∙ domain of objects ∆ I (possibly infinite set) ∙ interpretation function · I that maps ∙ concept name A ⇝ set of objects A I ⊆ ∆ I ∙ role name r ⇝ set of pairs of objects r I ⊆ ∆ I × ∆ I ∙ individual name a ⇝ object a I ∈ ∆ I ∙ extend · I to complex concepts and roles, for example: ∙ ( C ⊓ D ) I = C I ∩ D I ( ∃ r . C ) I = { d 1 | exists ( d 1 , d 2 ) ∈ r I with d 2 ∈ C I }
dl semantics Satisfaction in an interpretation 8/42 (like FO logic semantics) Interpretation I (“possible world”) ∙ domain of objects ∆ I (possibly infinite set) ∙ interpretation function · I that maps ∙ concept name A ⇝ set of objects A I ⊆ ∆ I ∙ role name r ⇝ set of pairs of objects r I ⊆ ∆ I × ∆ I ∙ individual name a ⇝ object a I ∈ ∆ I ∙ extend · I to complex concepts and roles, for example: ∙ ( C ⊓ D ) I = C I ∩ D I ( ∃ r . C ) I = { d 1 | exists ( d 1 , d 2 ) ∈ r I with d 2 ∈ C I } I satisfies B ( a ) ⇔ a I ∈ B I I satisfies C ⊑ D ⇔ C I ⊆ D I Model of a KB K = interpretation that satisfies all statements in K K entails α (written K | = α ) = every model I of K satisfies α
Complex concepts are formed as follows: description logic alc where A is a concept name, r a role name. TBox : set of concept inclusions C D 9/42 In ALC , we have the following concept constructors: ∙ top concept ⊤ (acts as a “wildcard”, denotes set of all things) ∙ bottom concept ⊥ (denotes empty set) ∙ conjunction ( ⊓ ), disjunction ( ⊔ ), negation ( ¬ ) ∙ restricted forms of existential and universal quantification ( ∃ , ∀ ) C , D := ⊤ | ⊥ | A | ¬ C | C ⊓ D | C ⊔ D | ∃ r . C | ∀ r . C
Complex concepts are formed as follows: description logic alc where A is a concept name, r a role name. 9/42 In ALC , we have the following concept constructors: ∙ top concept ⊤ (acts as a “wildcard”, denotes set of all things) ∙ bottom concept ⊥ (denotes empty set) ∙ conjunction ( ⊓ ), disjunction ( ⊔ ), negation ( ¬ ) ∙ restricted forms of existential and universal quantification ( ∃ , ∀ ) C , D := ⊤ | ⊥ | A | ¬ C | C ⊓ D | C ⊔ D | ∃ r . C | ∀ r . C ALC TBox : set of concept inclusions C ⊑ D
examples of tbox axioms Professors and MCFs are disjoint classes of faculty Every Master’s student is supervised by some faculty member Master’s students are students who only take Master-level courses FO translation: 10/42 Prof ⊑ Faculty Mcf ⊑ Faculty Prof ⊑ ¬ Mcf MStudent ⊑ ∃ supervisedBy . Faculty MStudent ⊑ Student ⊓ ∀ takesCourse . MCourse ∀ x ( MStudent ( x ) → ( Student ( x ) ∧ ∀ y takesCourse ( x , y ) → MCourse ( y ))
description logic el Advantage w.r.t. : reasoning much simpler ( PTIME vs. EXPTIME ) Despite lower expressivity, very useful in practice ∙ used for large-scale biomedical ontologies (example: SNOMED) ∙ importance witnessed by OWL 2 EL profile 11/42 In EL , complex concepts are constructed as follows: C , D := ⊤ | A | C ⊓ D | ∃ r . C EL TBox = set of inclusions C ⊑ D , with C , D as above
∙ used for large-scale biomedical ontologies (example: SNOMED) description logic el ∙ importance witnessed by OWL 2 EL profile 11/42 In EL , complex concepts are constructed as follows: C , D := ⊤ | A | C ⊓ D | ∃ r . C EL TBox = set of inclusions C ⊑ D , with C , D as above Advantage w.r.t. ALC : reasoning much simpler ( PTIME vs. EXPTIME ) Despite lower expressivity, EL very useful in practice
Some DL-Lite R axioms : description logic dl-lite ∙ Everything that is taught is a course: taughtBy taughtBy , teaches teaches ∙ Teaches inverse of taughtBy: Course teaches ∙ Every professor teaches something: Prof teaches where 12/42 We present the dialect DL-Lite R (which underlies OWL 2 QL profile ). DL-Lite R TBoxes contain two types of axioms: ∙ concept inclusions B 1 ⊑ B 2 , B 1 ⊑ ¬ B 2 ∙ role inclusions S 1 ⊑ S 2 , S 1 ⊑ ¬ S 2 S := r | r − B := A | ∃ S
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