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Supporting the Evolution of SHIQ Ontologies Using Inductive Logic Programming Techniques

This paper discusses the integration of Inductive Logic Programming (ILP) with SHIQ ontologies to enhance their evolution through machine learning. By automating the management of knowledge bases, the approach utilizes prior knowledge and organizes hypotheses into a partially ordered space. The study covers the representation of knowledge using DL+log, reasoning, and learning concepts and roles in the context of SHIQ+log. The proposed methodology aims at achieving effective generalizations of observations while addressing the complexities of combining different logical frameworks.

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Supporting the Evolution of SHIQ Ontologies Using Inductive Logic Programming Techniques

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  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

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