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Multi-temporal RDF Ontology Versioning

This workshop focuses on the multi-temporal versioning of RDF ontologies, particularly in the legal domain. It discusses temporal RDF data models, database models, and the benefits of using temporal elements for memory saving.

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Multi-temporal RDF Ontology Versioning

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  1. Third International Workshop on Ontology Dynamics - IWOD 2009(in conj. with ISWC 2009 – Chantilly VA, October 2009) Multi-temporal RDF Ontology Versioning Fabio Grandi Alma Mater Studiorum - Università degli Studi di Bologna

  2. Introduction • Some application fields require the maintenance of past versions of an ontology after changes • For instance, in the legal domain: • Ontologies evolve as a natural consequence of the dynamics involved in normative systems • Agents must often deal with a past perspective (e.g. a Court judging today on some fact committed in the past) • Moreover, several time dimensions are usually important for applications in such domains IWOD 2009 - F. Grandi - Multi-temporal RDF Ontology Versioning

  3. Multi-temporalversioning • Time dimensions of interest in the legal domain: • Validity timeis the time a norm is in force in the real world • Efficacy timeis the time a norm can be applied to a concrete case;while such cases exist, the norm continues its efficacy though no longer in force • Transaction timeis the time a norm is stored in the computer system • Publication timeis the time a norm is published on the Official Journal IWOD 2009 - F. Grandi - Multi-temporal RDF Ontology Versioning

  4. Temporal RDF Data Models • Temporal RDF data models have been recently proposed, the proposals remarkably include: [Gutierrez, Hurtado & Vaisman, 2007] [Pugliese, Udrea & Subrahmanian, 2008] [Tappolet & Bernstein, 2009] • Interval timestamping of RDF triples is adopted • A single time dimension (valid time) is usually considered • Index structures (e.g. tGRIN and keyTree) have been proposed for efficient processing of temporal queries IWOD 2009 - F. Grandi - Multi-temporal RDF Ontology Versioning

  5. A Multi-temporal RDF Database Model • N-dimensionaltime domain: • T = T1 x T2x … x TNTi = [0,UC)i • Multi-temporal RDF triple: • ( s,p,o | T )sis a subjectpis a predicateoisanobjectT Tis a timestamp • Multi-temporal RDF database: • RDF-TDB = { ( s,p,o | T ) | T T } IWOD 2009 - F. Grandi - Multi-temporal RDF OntologyVersioning

  6. Multi-temporal RDF Triples • A temporal triple ( s,p,o | T ) assigns a temporalpertinencetoan RDF triple ( s,p,o ) • The non-temporal triple ( s,p,o )is the value (or the contents) of the temporal triple ( s,p,o | T ) • The temporalpertinenceTis a subset of the time domain T representedby a temporalelement IWOD 2009 - F. Grandi - Multi-temporal RDF Ontology Versioning

  7. TemporalElements • A temporalelement[Gadia 98] isa disjointunionoftemporalintervals • Multi-temporalintervals are obtainedas the Cartesianproductofoneintervalforeachtemporaldimension • T = U1≤j≤mIj = U1≤j≤m [tjs, tje)1 x [tjs, tje)2 x … x [tjs, tje)N • Ij ∩ Ik= Ø forall1≤j<k≤m IWOD 2009 - F. Grandi - Multi-temporal RDF OntologyVersioning

  8. IntegrityConstraint • No value-equivalentdistincttriplesexist: ( s,p,o | T ), ( s,p,o | T  )  RDF-TDB:s=s  p=p  o=o  T=T • The constraintismadepossibleby the adoptionoftemporalelementtimestamping • Temporal elements lead to space saving, whenever the temporal pertinence of a triple is not a convex interval IWOD 2009 - F. Grandi - Multi-temporal RDF Ontology Versioning

  9. Memory Saving with Temporal Elements • For example, even with a monodimensional time domain, the two value-equivalent triples with interval time-stamping ( t2 < t3 ):( s,p,o | [t1, t2) ) and ( s,p,o | [t3, t4)) can bemergedinto a single triple withelementtime-stamping: ( s,p,o | [t1, t2) U [t3, t4)) where the same space is required for the timestamps in both cases (i.e. the space needed by 4 time points) and the contents of the triple is stored twice in the former case and only once in the latter • Different triple versions are stored only once with a complex timestamp instead of storing multiple copies (value-equivalent triples) with a simple timestamp IWOD 2009 - F. Grandi - Multi-temporal RDF OntologyVersioning

  10. An Example • The memory saving obtained with temporal elements grows with the dimensionality of the time domain! • The memory saving is also emphasized by the triple size with respect to the timestamp size • In very large RDF benchmark datasets, the average triple sizeranges from 80140 bytes (DBpedia, UScensus, LUBM, BSBM)to more than 600 bytes (UniProtKB) • The timestamp (date+time) data size in SQL is 68 bytes • In the example which follows we assume a bitemporal domain (valid + transaction time) IWOD 2009 - F. Grandi - Multi-temporal RDF OntologyVersioning

  11. Representation of the Evolution of a Triple t0t1 t2 UC (s, p, o1 ) With temporal elements (3 triples needed)( s, p, o1 | [t0,t1)x[t0,UC) U [t1,UC)x[t0,t1) )( s, p, o2 | [t1,t2)x[t1,UC) U [t2,UC)x[t1,t2) )( s, p, o3 | [t2,UC)x[t2,UC) ) • Withtemporalintervals(5 needed) • ( s, p, o1 | [t0,t1)x[t0,UC) )( s, p, o1 | [t1,UC)x[t0,t1) ) ( s, p, o2 | [t1,t2)x[t1,UC) )( s, p, o2 | [t2,UC)x[t1,t2) )( s, p, o3 | [t2,UC)x[t2,UC) ) (s, p, o2 ) (s, p, o3 ) t0 t1 t2UC IWOD 2009 - F. Grandi - Multi-temporal RDF OntologyVersioning

  12. Memory Saving Figures • Percentage space saving with temporal element vs interval timestamping. Avg. number of versions per triple in colums, triple size in bytes in rows. We assume 8-byte timestamps. • For instance, with 120-byte triples with 5 versions per triple on average, we have a 39,22% space saving.With 1 billion of triples, this means an RDF-TDB size of • 721 GB with temporal elements • 1.14 TB with temporal intervals IWOD 2009 - F. Grandi - Multi-temporal RDF Ontology Versioning

  13. QueryOperators • The onlyretrievaloperatorweconsider in this workis a snaphotextractionoperator, which can beusedtoextractanontologyversionfrom a multi-versionontologyrepresentedas a temporal RDF database • Given a timepointt= (t1, t2,…, tN)  T wedefine the RDF database snapshotvalid at tasRDF-TDB(t) = { ( s,p,o ) | ( s,p,o | T )  RDF-TDB  t  T} • The result is a (non-temporal) RDF graph, which can be used to represent the ontology version valid at t IWOD 2009 - F. Grandi - Multi-temporal RDF OntologyVersioning

  14. ModificationOperators – Insertion • Assumingan (N-1)-dimensionaltemporalelementtv (foranymodification, transactiontime[now, UC)isimplied), the insertionoperation INSERT DATA { s,p,o} VALID tv can bedefined via itseffects on the database stateasfollows (using a triple calculus) RDF-TDB  = RDF-TDB U { ( s,p,o | T ) |  ( s,p,o | T )  RDF-TDB  T = coalesce( TU tv x [now, UC) )} U { ( s,p,o | tv x [now, UC) ) | ¬ ( s,p,o | T )  RDF-TDB } IWOD 2009 - F. Grandi - Multi-temporal RDF OntologyVersioning

  15. Maintenanceoftemporalelements • In ordertoensure the results are stilltemporalelements,union and differenceoperationsmustbecarefullydefined • In particular, ifTi (i=1,2) are temporalelementsdefinedasTi = U1≤j≤miIijwhereIijare multidimensionalintervalsthen the difference can becomputedasfollowsT1 \ T2 = U1≤j≤m1I1j\ T2 and isensuredtobe a temporalelementifI1j\ T2 is a temporalelementforeachj • Given the difference, the union can becomputedasfollowsT1 UT2= T1 U (T2 \ T1) IWOD 2009 - F. Grandi - Multi-temporal RDF OntologyVersioning

  16. ModificationOperators - Deletion • Assumingan (N-1)-dimensionaltemporalelementtvand a selection predicate pred(s,p,o), the deletionoperation DELETE { s,p,o} VALID tv WHERE pred(s,p,o) can bedefined via itseffects on the database state asfollows RDF-TDB  = RDF-TDB \ { ( s,p,o | T ) |  ( s,p,o | T )  RDF-TDB  pred(s,p,o)  T ∩ tv x [now, UC) ≠ Ø} U { ( s,p,o | T ) |  ( s,p,o | T )  RDF-TDB  pred(s,p,o)  T ∩ tv x [now, UC) ≠ Ø  T  = coalesce( T\ tv x [now, UC) )} IWOD 2009 - F. Grandi - Multi-temporal RDF OntologyVersioning

  17. ModificationOperators - Update • Assumingan (N-1)-dimensionaltemporalelementtv,the update operation UPDATE { s,p,o} SET { s’,p’,o’} VALID tv WHERE pred(s,p,o) isnot primitive, asit can bedefinedas a deleteoperationfollowedbyaninsertoperationasfollows DELETE { s,p,o} VALID tv WHERE pred(s,p,o);INSERT DATA { s’,p’,o’} VALID tv IWOD 2009 - F. Grandi - Multi-temporal RDF OntologyVersioning

  18. OperatorsforOntology Management • On the basisof the primitivesintroduced so far, alsohigh-level macro operatorsfor the management of a multi-version RDF ontologycan bedefinedCREATE_CLASS(Name,Validity)RENAME_CLASS(Class,NewName,Validity) DROP_CLASS(Class,Validity)ADD_SUBCLASS(SubClass,Class,Validity)DEL_SUBCLASS(SubClass,Class,Validity) CREATE_PROPERTY(Name,Range,Validity)RENAME_PROPERTY(Property,NewName,Validity) CHANGE_PROPERTY_RANGE(Property,NewRange,Validity) DROP_PROPERTY(Property,Validity)ADD_PROPERTY(Class,Property,Validity) DEL_PROPERTY(Class,Property,Validity)ADD_SUBPROPERTY(SubProperty,Property,Validity)DEL_SUBPROPERTY(SubProperty,Property,Validity) ………… IWOD 2009 - F. Grandi - Multi-temporal RDF OntologyVersioning

  19. Sample OperatorDefinitions • Forexample the definitionsof some of the property management operatorsis the following • ADD_PROPERTY(Class,Property,Range,Validity)INSERT DATA{ Propertyrdfs:domain Class ;rdfs:rangeRange . } VALID Validity • CHANGE_PROPERTY_RANGE(Property,NewRange,Validity)UPDATE { Propertyrdfs:range ?range }SET { Propertyrdfs:rangeNewRange } VALID Validity • DEL_PROPERTY(Class,Property,Validity)DELETE { Propertyrdfs:domain Class ;rdfs:range ?range . } VALID Validity IWOD 2009 - F. Grandi - Multi-temporal RDF OntologyVersioning

  20. Conclusions • We presented a temporal RDF database model whose distinctive features with respect to previously proposed models are • It is defined on a multi-dimensional time domain • It employs triple timestamping with temporal elements • The adoption of temporal elements in the multi-temporal setting best preserves the scalability property enjoyed by triple storage technologies as it minimizes the database growth (the absence of value-equivalent triples is an integrity constraint) • The data model has been equipped with manipulation operatorsfor the extraction of a temporal snapshot and for the maintenance of the database; moreover, also high-level operators can be defined to be used to manage a multi-version RDF ontology IWOD 2009 - F. Grandi - Multi-temporal RDF Ontology Versioning

  21. Future Work • Some design choices were motivated by application requirements of an ontology-based personalization service in the legal (or medical) domain. We plan to explore the applicability of the approach also in application fields with more generic requirements • We also plan to consider extensions of the proposed RDF database model, including the development of a complete multi-temporal SPARQL-like query language and the adoption of suitable multi-temporal index structures IWOD 2009 - F. Grandi - Multi-temporal RDF Ontology Versioning

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