Supporting the Evolution of SHIQ ontologies with Inductive Logic Programming

1. Supporting the Evolution of SHIQ ontologies with Inductive Logic Programming Francesca A. LisiFloriana Espositolisi@di.uniba.it esposito@di.uniba.it Dipartimento di Informatica Università degli Studi di Bari Via Orabona, 4 - 70126 Bari - Italy IWOD@ISWC’08 Karlsruhe, October 27, 2008

2. Machine Learning can (partially) automate this task! LONER Ontology Evolution UNMARRIED(Mary) UNMARRIED(Joe) famous(Mary) famous(Paul) famous(Joe) F scientist(Joe) [A1] RICHuUNMARRIED v WANTS-TO-MARRY−.T K [R1] RICH(X)  famous(X), ¬scientist(X) [R2] happy(X)  famous(X), WANTS-TO-MARRY(Y,X) • LONER(Joe) • LONER(Mary) • LONER(Paul) Dr. Francesca A. Lisi

3. Logic Programming ILP Machine Learning Inductive Logic Programming • Use of prior knowledge • Hypotheses can be used for the management of a knowledge base • Use of Concept Learning notions • Hypotheses are organized into partially ordered space to be searched in order to find a good generalization of observations • Use of Horn Clausal Logic (HCL) • Hypotheses are often represented as Datalog clauses Dr. Francesca A. Lisi

4. ? Ontologies vs Logic Programming DLs vs CLs • Different expressive power (Borgida, 1996) • No relations of arbitrary arity or arbitrary joins between relations in DLs • No exist. quant. in CLs • Different semantics (Rosati, 2005) • OWA for DLs • CWA for CLs • Can they be combined? Yes, but integration can be easily undecidable if unrestricted FOL CLs DLs Datalog Dr. Francesca A. Lisi

5. Tbox T IDB Abox A EDB Ontologies vs Logic Programming Hybrid DL-CL KR systems • CARIN (Levy & Rousset, 1998) • Any DL+HCL • Unsafe • Decidable for some simple DL (e.g., ALCNR) • AL-log (Donini et al., 1998) • ALC+Datalog • Safe • Decidable • DL+log (Rosati, 2006) • Any DL+ Datalog • Weakly-safe • Decidable for some v.e. DL (e.g., SHIQ) Querying DL KB  Reasoner CL DB ¦ DL-CL KR System Dr. Francesca A. Lisi

6. Overview • Introduction • Representing in DL+log • Syntax • Semantics • Reasoning • Learning concepts/roles in SHIQ+log with ILP • Conclusions and future work Dr. Francesca A. Lisi

7. Representing with DL+log:syntax DL+log KB = DL KB extended with Datalog rules p1(X1)  ...  pn(Xn)  r1(Y1), ..., rm(Ym),s1(Z1),..., sk(Zk),u1(W1),..., uh(Wh) satisfying the following properties • Datalog safeness: every variable occurring in a rule must appear in at least one of the atoms r1(Y1), ..., rm(Ym), s1(Z1),..., sk(Zk) • DL weak safeness: every head variable of a rule must appear in at least one of the atoms r1(Y1), ..., rm(Ym) Dr. Francesca A. Lisi

8. Representing with DL+log:semantics • FOL-semantics • OWA for both DL and Datalog predicates • NM-semantics: extends stable model semantics of Datalog • OWA for DL-predicates • CWA for Datalog-predicates • In both semantics, entailment can be reduced to satisfiability • In Datalog, FOL-semantics equivalent to NM-semantics Dr. Francesca A. Lisi

9. Representing with DL+log:reasoning • CQ answering can be reduced to satisfiability • NM-satisfiability of DL+log KBs combines • Consistency in Datalog : A Datalog program is consistent if it has a stable model • Boolean CQ/UCQ containment problem in DLs: Given a DL-TBox T, a Boolean CQ Q1 and a Boolean UCQ Q2 over the alphabet of concept and role names, Q1 is contained in Q2 wrt T, denoted by T |= Q1 Q2, iff, for every model I of T, if Q1 is satisfied in I then Q2 is satisfied in I. • The decidability of reasoning in DL+log depends on the decidability of the Boolean CQ/UCQ containment problem in DL • SHIQ+log = most powerful decidable instantiation of DL+log! Dr. Francesca A. Lisi

10. Overview • Introduction • Representing in DL+log • Learning concepts/roles in SHIQ+log with ILP • Problem statement • Ingredients for an ILP solution • Proof-of-concept application scenario • Conclusions and future work Dr. Francesca A. Lisi

11. Learning concepts/roles:problem statement Given: • a SHIQ+log¬ KB B composed of a SHIQ ontology and a Datalog¬ program • a new target SHIQ predicate name p • a set O of observations for p • a language L of hypotheses for p Goal: Induce a definition H belonging to L such that BH is correct w.r.t. O. Dr. Francesca A. Lisi

12. Learning concepts/roles:problem statement (2) UNMARRIED(Mary) UNMARRIED(Joe) famous(Mary) famous(Paul) famous(Joe) F scientist(Joe) [A1] RICHuUNMARRIED v WANTS-TO-MARRY−.T K [R1] RICH(X)  famous(X), ¬scientist(X) [R2] happy(X)  famous(X), WANTS-TO-MARRY(Y,X) LLONER • {famous/1, scientist/1, UNMARRIED/1} • LONER(X)  scientist(X,Y),UNMARRIED(X) LLIKES • {happy/1, RICH/1, WANTS-TO-MARRY/2} • LIKES(X,Y)  happy(X), RICH(Y) Dr. Francesca A. Lisi

13. Learning concepts/roles:ILP ingredients • Scope of induction: prediction/description • Logical setting: learning from interpretations • Language of hypotheses: linked and range-restricted SHIQ+log¬ rules • Coverage relation: boils down to CQ answering in SHIQ+log¬ • Generality order: boils down to CQ answering in SHIQ+log¬ Dr. Francesca A. Lisi

14. Learning concepts/roles:ILP ingredients (2) UNMARRIED(Mary) UNMARRIED(Joe) famous(Mary) famous(Paul) famous(Joe) F scientist(Joe) [A1] RICHuUNMARRIED v WANTS-TO-MARRY−.T K [R1] RICH(X)  famous(X), ¬scientist(X) [R2] happy(X)  famous(X), WANTS-TO-MARRY(Y,X) LONER(X)  scientist(X,Y),UNMARRIED(X) covers oJoe = (LONER(Joe),FJoe) because K  FJoe  H |= LONER(Joe) LIKES(X,Y)  happy(X), RICH(Y) covers o<Mary,Paul> = (LIKES(Mary,Paul),FMary  FPaul) because K FMary  FPaul  H |= LIKES(Mary,Paul) Dr. Francesca A. Lisi

15. H1LONER : LONER(A)  scientist(A) • H2LONER : LONER(X)  scientist(X), UNMARRIED(X) • H1LONERK H2LONER • H2LONERK H1LONER • H1LIKES : LIKES(A,B)  WANTS-TO-MARRY(A,B) • H4LIKES : LIKES(X,Y)  happy(X), RICH(Y) • H1LIKESK H4LIKES • H4LIKESK H1LIKES Learning concepts/roles:ILP ingredients (3) UNMARRIED(Mary) UNMARRIED(Joe) famous(Mary) famous(Paul) famous(Joe) F scientist(Joe) [A1] RICHuUNMARRIED v WANTS-TO-MARRY−.T K [R1] RICH(X)  famous(X), ¬scientist(X) [R2] happy(X)  famous(X), WANTS-TO-MARRY(Y,X) Dr. Francesca A. Lisi

16. Learning concepts/roles: ontology evolution scenario • Change capturing • Availability of new facts for an unknown p • Change representation • Use of rules for defining p • Semantic of changes • Attention to NAF literals • Change propagation • Change implementation • Change validation Dr. Francesca A. Lisi

17. Overview • Introduction • Representing in DL+log • Learning concepts/roles in SHIQ+log with ILP • Conclusions and future work Dr. Francesca A. Lisi

18. Conclusions • ILP can support the evolution of SHIQ ontologies • Preliminary study! • DL+log is good for representing changes • Parametric wrt the DL part • Decidable for many DLs, notably SHIQ • ILP in SHIQ+log¬ is feasible • Decidable coverage and generality relations • Valid for any decidable instantiation of DL+log with Datalog¬ Dr. Francesca A. Lisi

19. Related work Dr. Francesca A. Lisi

20. Future work • To study the impact of having Datalog both in the language of hypotheses and in the language for the BK • Nonmonotonic features to deal with incomplete knowledge • To define ILP algorithms starting from the ingredients identified in this paper. • To apply these algorithms to SHIQ ontologies Dr. Francesca A. Lisi