exact query reformulation with first order ontologies and

play

Exact Query Reformulation with First-order Ontologies and Databases - PowerPoint PPT Presentation

Oct 26, 2023 •310 likes •1.31k views

Exact Query Reformulation with First-order Ontologies and Databases Nhung Ngo Free University of Bolzano A joint work with Enrico Franconi and Volga Kernet Nov 13, 2013 Motivation DBox Query Determinacy Exact Safe-range Query Reformulation

Exact Query Reformulation with First-order Ontologies and Databases Nhung Ngo Free University of Bolzano A joint work with Enrico Franconi and Volga Kernet Nov 13, 2013
Motivation DBox Query Determinacy Exact Safe-range Query Reformulation Application: Query Answering over an Expressive DL and DBox Conclusion
Query Answering Under Contraints and Databases ◮ Given a FOL fragment L ◮ Constraints: a set of L-sentences K B ◮ Database: a finite set of facts D B over a relational signature P DB ◮ Query: a (open) L -formula
Query Answering Under Contraints and Databases ◮ Given a FOL fragment L ◮ Constraints: a set of L-sentences K B ◮ Database: a finite set of facts D B over a relational signature P DB ◮ Query: a (open) L -formula
Query Answering Under Contraints and Databases ◮ Given a FOL fragment L ◮ Constraints: a set of L-sentences K B ◮ Database: a finite set of facts D B over a relational signature P DB ◮ Query: a (open) L -formula
Query Answering Under Contraints and Databases ◮ Given a FOL fragment L ◮ Constraints: a set of L-sentences K B ◮ Database: a finite set of facts D B over a relational signature P DB ◮ Query: a (open) L -formula
Ontology-based Data Access ◮ Given a description logic fragment D L ◮ TBox: a set of TBox assertions T ◮ Databases: a set of ABox assertions A ◮ Query: a concept query
Ontology-based Data Access ◮ Given a description logic fragment D L ◮ TBox: a set of TBox assertions T ◮ Databases: a set of ABox assertions A ◮ Query: a concept query
Ontology-based Data Access ◮ Given a description logic fragment D L ◮ TBox: a set of TBox assertions T ◮ Databases: a set of ABox assertions A ◮ Query: a concept query
Ontology-based Data Access ◮ Given a description logic fragment D L ◮ TBox: a set of TBox assertions T ◮ Databases: a set of ABox assertions A ◮ Query: a concept query
Ontology-based Data Access ◮ Given a description logic fragment D L ◮ TBox: a set of TBox assertions T ◮ Databases: a set of ABox assertions A ◮ Query: a concept query
ABox ◮ An ABox is a finite set of ground atomic facts, syntactically Example A = { Employee(Jon), Project(Winter) } is an ABox ◮ The semantics of ABoxes is given by first-order structures. ◮ An ABox does not correspond to a first-order structure!
ABox ◮ An ABox is a finite set of ground atomic facts, syntactically Example A = { Employee(Jon), Project(Winter) } is an ABox ◮ The semantics of ABoxes is given by first-order structures. ◮ An ABox does not correspond to a first-order structure!
ABox ◮ An ABox is a finite set of ground atomic facts, syntactically Example A = { Employee(Jon), Project(Winter) } is an ABox ◮ The semantics of ABoxes is given by first-order structures. ◮ An ABox does not correspond to a first-order structure!
ABox ◮ An ABox is a finite set of ground atomic facts, syntactically Example A = { Employee(Jon), Project(Winter) } is an ABox ◮ The semantics of ABoxes is given by first-order structures. ◮ An ABox does not correspond to a first-order structure!
ABox Semantics Definition A first-order structure I is a model of an ABox A if I ⊇ A An ABox is an incomplete database i.e., an ABox represents a class of databases. Example Given the ABox A = { Employee(Jon), Project(Winter) } ◮ {{ Employee(Jon), Project(Winter) } is a model of A ◮ {{ Employee(Jon), Employee(Rob), Project(Winter) } ◮ {{ Employee(Jon), Employee(Rob), Project(River) } is not a model of A
ABox Semantics Definition A first-order structure I is a model of an ABox A if I ⊇ A An ABox is an incomplete database i.e., an ABox represents a class of databases. Example Given the ABox A = { Employee(Jon), Project(Winter) } ◮ {{ Employee(Jon), Project(Winter) } is a model of A ◮ {{ Employee(Jon), Employee(Rob), Project(Winter) } ◮ {{ Employee(Jon), Employee(Rob), Project(River) } is not a model of A
ABox Semantics Definition A first-order structure I is a model of an ABox A if I ⊇ A An ABox is an incomplete database i.e., an ABox represents a class of databases. Example Given the ABox A = { Employee(Jon), Project(Winter) } ◮ {{ Employee(Jon), Project(Winter) } is a model of A ◮ {{ Employee(Jon), Employee(Rob), Project(Winter) } ◮ {{ Employee(Jon), Employee(Rob), Project(River) } is not a model of A
ABox Semantics Definition A first-order structure I is a model of an ABox A if I ⊇ A An ABox is an incomplete database i.e., an ABox represents a class of databases. Example Given the ABox A = { Employee(Jon), Project(Winter) } ◮ {{ Employee(Jon), Project(Winter) } is a model of A ◮ {{ Employee(Jon), Employee(Rob), Project(Winter) } ◮ {{ Employee(Jon), Employee(Rob), Project(River) } is not a model of A
Certain Answers Definition Given: ◮ a TBox T , an ABox A and ◮ a concept query Q and an individual a Question: ( T , A ) | = Q ( a ) ? That is ∀ models I of ( T , A ) , is it the case that I | = Q ( a )
ABox vs Database ◮ Additional constraint as a standard view over data: ∀ x Bad-Project(x) ↔ Project(x) ∧ ¬∃ y Work-for(y,x) ◮ Database: Work-for = { <Jon, Winter>, <Rob, Winter> } Project = { Winter, River } ◮ Q ( x ) := Bad-Project(x) ⇒ { River } ◮ ABox: Work-for ⊇ { <Jon, Winter>, <Rob, Winter> } Project ⊇ { Winter, River } ◮ Q ( x ) := Bad-Project(x) ⇒ {} ABox does not scale down to standard DB answer
ABox vs Database ◮ Additional constraint as a standard view over data: ∀ x Bad-Project(x) ↔ Project(x) ∧ ¬∃ y Work-for(y,x) ◮ Database: Work-for = { <Jon, Winter>, <Rob, Winter> } Project = { Winter, River } ◮ Q ( x ) := Bad-Project(x) ⇒ { River } ◮ ABox: Work-for ⊇ { <Jon, Winter>, <Rob, Winter> } Project ⊇ { Winter, River } ◮ Q ( x ) := Bad-Project(x) ⇒ {} ABox does not scale down to standard DB answer
ABox vs Database ◮ Additional constraint as a standard view over data: ∀ x Bad-Project(x) ↔ Project(x) ∧ ¬∃ y Work-for(y,x) ◮ Database: Work-for = { <Jon, Winter>, <Rob, Winter> } Project = { Winter, River } ◮ Q ( x ) := Bad-Project(x) ⇒ { River } ◮ ABox: Work-for ⊇ { <Jon, Winter>, <Rob, Winter> } Project ⊇ { Winter, River } ◮ Q ( x ) := Bad-Project(x) ⇒ {} ABox does not scale down to standard DB answer
ABox vs Database ◮ Additional constraint as a standard view over data: ∀ x Bad-Project(x) ↔ Project(x) ∧ ¬∃ y Work-for(y,x) ◮ Database: Work-for = { <Jon, Winter>, <Rob, Winter> } Project = { Winter, River } ◮ Q ( x ) := Bad-Project(x) ⇒ { River } ◮ ABox: Work-for ⊇ { <Jon, Winter>, <Rob, Winter> } Project ⊇ { Winter, River } ◮ Q ( x ) := Bad-Project(x) ⇒ {} ABox does not scale down to standard DB answer
ABox vs Database ◮ Additional constraint as a standard view over data: ∀ x Bad-Project(x) ↔ Project(x) ∧ ¬∃ y Work-for(y,x) ◮ Database: Work-for = { <Jon, Winter>, <Rob, Winter> } Project = { Winter, River } ◮ Q ( x ) := Bad-Project(x) ⇒ { River } ◮ ABox: Work-for ⊇ { <Jon, Winter>, <Rob, Winter> } Project ⊇ { Winter, River } ◮ Q ( x ) := Bad-Project(x) ⇒ {} ABox does not scale down to standard DB answer
ABox vs Database ◮ Additional constraint as a standard view over data: ∀ x Bad-Project(x) ↔ Project(x) ∧ ¬∃ y Work-for(y,x) ◮ Database: Work-for = { <Jon, Winter>, <Rob, Winter> } Project = { Winter, River } ◮ Q ( x ) := Bad-Project(x) ⇒ { River } ◮ ABox: Work-for ⊇ { <Jon, Winter>, <Rob, Winter> } Project ⊇ { Winter, River } ◮ Q ( x ) := Bad-Project(x) ⇒ {} ABox does not scale down to standard DB answer
ABox vs Database ◮ Additional constraint as a standard view over data: ∀ x Bad-Project(x) ↔ Project(x) ∧ ¬∃ y Work-for(y,x) ◮ Database: Work-for = { <Jon, Winter>, <Rob, Winter> } Project = { Winter, River } ◮ Q ( x ) := Bad-Project(x) ⇒ { River } ◮ ABox: Work-for ⊇ { <Jon, Winter>, <Rob, Winter> } Project ⊇ { Winter, River } ◮ Q ( x ) := Bad-Project(x) ⇒ {} ABox does not scale down to standard DB answer
ABox vs Database ◮ ABox: Work-for ⊇ { <Jon, Winter> } Project ⊇ { Winter, River } ◮ Query as a standard view over database: Q ( x ) := Work-for(y,x) Q = Π 2 Work-for ◮ Q = EVAL (Π 2 Work-for ) ⇒ { Winter, River } ◮ Q = Π 2 ( EVAL ( Work-for )) ⇒ { Winter } Queries are not compositional wrt certain answer semantics!
ABox vs Database ◮ ABox: Work-for ⊇ { <Jon, Winter> } Project ⊇ { Winter, River } ◮ Query as a standard view over database: Q ( x ) := Work-for(y,x) Q = Π 2 Work-for ◮ Q = EVAL (Π 2 Work-for ) ⇒ { Winter, River } ◮ Q = Π 2 ( EVAL ( Work-for )) ⇒ { Winter } Queries are not compositional wrt certain answer semantics!
ABox vs Database ◮ ABox: Work-for ⊇ { <Jon, Winter> } Project ⊇ { Winter, River } ◮ Query as a standard view over database: Q ( x ) := Work-for(y,x) Q = Π 2 Work-for ◮ Q = EVAL (Π 2 Work-for ) ⇒ { Winter, River } ◮ Q = Π 2 ( EVAL ( Work-for )) ⇒ { Winter } Queries are not compositional wrt certain answer semantics!

Download Presentation

Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

More recommend