ODBASE'08 dl-lite explanations

Explanations for DL-LiteAlexander Borgida 2

Diego Calvanese 1

Mariano Rodríguez-Muro 1

1

1 Free University of Bozen Bolzano2 Rutgers University

ODBASE 08 - Monterrey, México

Thursday, August 8, 13

Outline

• Explanations

• DL-Lite and Explanations for DL-Lite

• Explanations for traditional services

• Explanations for conjunctive queries

• Conclusions and future work

2 ODBASE 08 - Monterrey, México


Explanations



ExplanationsWhy explanations?




What are explanations?





• Explanations are formal proofs, constructed from premises using rules of inference.






3

Features of an explanation:






3

Features of an explanation:

• Style

• Length

• Presentation



Explanations (cont.)




Audience: KB developer, End user





4

1. Style. Understandable inference rules (NOT refutation or resolution)





4


2. Length: 'shorter' preferred





4


2. Length: 'shorter' preferred

3. Presentation: Complete proof vs Iterative process. as indicated by the user. Possibly eliminating 'obvious' parts (not addressed here)



DL-Litef

Concept constructs

B ::= A | ƎP | ƎP-

C::= B | ¬B | C1 ⊓ C2

TBox Assertions

B ⊑ C(funct P) (funt P-)

ABox Assertions

A(a) R(a,b)



DL-Litef

Is-A HierarchiesClass disjointness

Role-typing

Participation constraints

Non-participation constraints

Functionality restrictions

A1 ⊑ A2

A1 ⊑ ¬A2

ƎP ⊑ A1

ƎP- ⊑ A1

A1 ⊑ ƎP A1 ⊑ ƎP-

A1 ⊑ ¬ƎP A1 ⊑ ¬ƎP-

(funct P) (funct P-)



DL-Litef

A1 ⊑ A2

A1 ⊑ ¬A2

ƎP ⊑ A1

ƎP- ⊑ A1

A1 ⊑ ƎP A1 ⊑ ƎP-

A1 ⊑ ¬ƎP A1 ⊑ ¬ƎP-


A1 ⊑ A2

disjoint(A1,A2)

domain(P) ⊑ A1

range(P) ⊑ A1

A1 ⊑ domain(P) A1 ⊑ range(P)disjoint(A1, domain(P)) disjoint(A1, range(P))




Reasoning services



Reasoning services

• Standard Inferences

• TBox reasoning (concept consistency, subsumption)

• ABox reasoning (KB satisfiability, Instance checking*)



Reasoning services




✦ Finite model reasoning



Reasoning services





• Conjunctive Query Answering



Reasoning services





• Conjunctive Query Answering

• Successful queries

• Failed queries



B C

A

D

Concept Subsumption



B C

A

D

Concept Subsumption

• Hierarchy Traversing



B C

A

D

Concept Subsumption


A ⊑ D ⊓ C



B C

A

D

Concept Subsumption


A ⊑ D ⊓ CA ⊑ CA ⊑ B

B ⊑ D



B C

A

D

Concept Subsumption


A ⊑ D ⊓ CA ⊑ CA ⊑ B

B ⊑ D

• Minimal size explanations



B1

C2

C1

A

C3

B2

B3

disjoint

n j

9

A is unsatisfiable



B1

C2

C1

A

C3

B2

B3

disjoint

n j

9

Explanation length

n + j = 6

A is unsatisfiable



B1

C2

C1

A

E3

E2

E1D1

C3

E4

B2

B3

disjoint

disjoint

n j k l

10

A is unsatisfiable



B1

C2

C1

A

E3

E2

E1D1

C3

E4

B2

B3

disjoint

disjoint

Explanation length

k + l = 5

Explanation length

n + j = 6

n j k l

10

A is unsatisfiable



KB is inconsistent

11

1. PhD ⊑ Student2. disjoint(Professor, Student)3. range(supervisedBy) ⊑ Professor4. PhD(al)5. supevisedBy(tim, al)



KB is inconsistent

11


al is a Student

al is a Professor

no Student can be a Professor ➔ 2



KB is inconsistent

11


al is a Student!every PhD is also a Student ➔ 1!al is a PhD ➔ 4

al is a Professor




KB is inconsistent

11



al is a Professoreverything in the range of supervisedBy is also a Professor ➔ 3al is in range of supervisedBy




KB is inconsistent

11



al is a Professoreverything in the range of supervisedBy is also a Professor ➔ 3al is in range of supervisedBy

tim supervisedBy al ➔ 5




Query Answering




⋮Student(bob)Student(juan)supervisedBy(tom, bob)Student(al)supervisedBy(tim, al)teaches(al, ben)teaches(sam, ben)teaches(sam, john)teaches(sam, karl)

⋮

CQs in regular DBsq(x) :- Student(x), supervisedBy(y,x), teaches(x,z)




⋮


q(al)




⋮


q(al)

Student(al), x=alsupervisedBy(tim, al), y=timteaches(al, ben), z = ben



1.PhD ⊑ Student2.PhD ⊑ dom(supervisedBy)3.range(supervisedBy) ⊑ Professor4.Professor ⊑ domain(teaches)5.PhD(al)

q(x) :- Student(x), supervisedBy(x,y), teaches(y,z)





q(al)



al supervisedBy @1!!


@1 teaches @2

al is a Student


q(al)



al supervisedBy @1!!


@1 teaches @2

al is a Studentevery PhD is also a Student ➔ 1al is a PhD ➔ 5


q(al)



al supervisedBy @1!!al is in the domain of supervisedBy


@1 teaches @2



q(al)




every PhD is also in the domain of supervisedBy ➔ 2al is a PhD ➔ 5


@1 teaches @2



q(al)






@1 teaches @2every Professor is in the domain of teaches ➔ 4 @1 is a Professor



q(al)







@1 is in the range of supervisedByeverything in the range of supervisedBy is a Professor ➔ 3



q(al)







@1 is in the range of supervisedByeverything in the range of supervisedBy is a Professor ➔ 3



q(al)



Query Answering



Query Answering


• Failed queries



Query Answering


• Failed queries

• Due to missing information



Query Answering


• Failed queries

• Due to missing information

• Due to unsatisfiability



1.PhD ⊑ Student2.range(supervisedBy) ⊑ Professor3.disjoint(Professor,Student)

q(x):- PhD(x), supervisedBy(y, x)

q inconsistent



@1 is a Professor

@1 is a Student



q inconsistent

q(@1) :- PhD(@1), supervisedBy(@2, @1)




@1 is a Professor

@1 is a Student@1 is a PhD every PhD is also a Student ➔ 1



q inconsistent





@1 is a Professor




q inconsistent





@1 is a Professor@2 supervisedBy @1everything in the range of supervisedBy is a Professor ➔ 2




q inconsistent





@1 is a Professor@2 supervisedBy @1everything in the range of supervisedBy is a Professor ➔ 2




q inconsistent





Conclusions

• We addressed DL-Lite explanations can be given for traditional reasoning services (shortness of proof).

• Finite model case.

• Explaining conjunctive queries when reasoning is present by a) exploiting existing DL-Lite query rewriting algorithm and b) Prolog-based program.

• We looked into the problem of explaining failed answers to queries.



Future Work

• Explanation of failed answers to CQs over DL-Lite ontologies.

• Integration of prototype with the QuOnto Reasoner.

• Explanation in Ontology Based Data Access (presence of mappings).

• Field testing of the algorithms.



Technology

ODBASE'08 dl-lite explanations