1. Analyzing Minerva1 AUTORI: Antonello Ercoli Alessandro Pezzullo CORSO: Seminari di Ingegneria del SW DOCENTE: Prof. Giuseppe De Giacomo

2. Analyzing Minerva2 Minerva Abstract: “…storage and inference system for large scale OWL ontologies on top of relational databases. The method combines Description Logic reasoners for the Tbox inference with logic rules for Abox inference… ”

3. Analyzing Minerva3 Goals of Minerva “…it aims to meet scalability requirements of real applications and provide pratical reasoning capability as well as high query performance…” “…the effective integration of ontology inference and storage is expected to improve reasoning effeciency, while querying without run-time inference guarantees satisfactory response time…” (ref. Minerva:A Scalable OWL Ontology Storage and Inference System)

4. Analyzing Minerva4 Our Goals Studying the architecture and understanding the functionalities of the system. Simulating its run-time functioning. Analizing the quality of the system, namely the Soundness and Completeness of inference  is it OWL-DL Sound and Complete?

5. Analyzing Minerva5 Architecture: A general schema

6. Analyzing Minerva6 The Component Diagram of Minerva

7. Analyzing Minerva7 The components Import Module: Consists of : An Owl parser  from OWL-document to EODM model Two translators  DB translator: Abox assertions into DB  TBOX translator: Tbox axioms into DL reasoner Inference results from DL reasoner to DB Inference Module: DL reasoner  complete subsumption relationship between classes and properties Rule Inference engine  Abox inference based on the DLP rules Storage Module: store both the original and inferred assertion by DL reasoner and rule inference engine Query Module: SPARQL for retrieving inferred results from the DB using SQL statements

8. Analyzing Minerva8 TBOX OWL-DL TBOX inference DL Reasoner: Pellet Racer Structural Subsumption Working Schema 1/2 Inferred results: named properties and classes subsumption relationships τ DHLDLP ABOX OWL-DL ABOX Inference Engine (IBM code) DB SPARQL SQL Original assertions

9. Analyzing Minerva9 Precomputation step  Inference and materialization of results in a back-end DB Query step  no-runtime inference: inferred results are retrieved directly from DB Working Schema 2/2

10. Analyzing Minerva10 Inference TBOX INFERENCE: sound & complete inference (Pellet e Racer) Structural Subsumption Algorithm  sound but not always complete ABOX INFERENCE: Rule engine conducts Abox inference based on DLP Rules  sound & complete with respect to the semantics of DHL TBOX OWL-DL TBOX inference DL Reasoner: Pellet Racer Structural Subsumption Inferred results: named properties and classes subsumption relationships τ DHLDLP ABOX OWL-DL ABOX Inference Engine (IBM code) Original assertions ?

11. Analyzing Minerva11 DLP (ref. Description Logic Programs: Combining Logic Programs with Description Logic): DHL: DLP & DHL 1/3

12. Analyzing Minerva12 DLP & DHL 2/3 “…DLP is the Horn fragment of OWL-DL...” ? “…Horn fragment refers to a syntactic fragment of FOL, while OWL-DL is commonly perceived as a semantic fragment of FOL..”  “…DLP is the syntactic Horn fragment (in the sense of FOL syntax) of something (namely OWL-DL) which isn’t in FOL syntax but can semantically be mapped to a syntactic fragment of FOL..” “…an OWL-DL statement is in DLP iff it can be written – semantically equivalently - as a set of Horn clauses in FOL...” (ref. Description Logic Programs: A Pratical Choice for the Modelling of Ontologies)

13. Analyzing Minerva13 Constructors which can be used freely in OWL ontology without running the risk of leaving DLP DLP & DHL 3/3 disjointWith ?allValuesFrom ?someValuesFrom ? hasValue ?unionOf ?complementOf ? oneOf ?

14. Analyzing Minerva14 τ -mapping Based on DLP-fusion: the bidirectional translation from premises and inferences from DHL-fragment on DL to DLP and viceversa It allows us to build rules on top of ontologies so we can use a rule inference engine and materialize inference results into DB

15. Analyzing Minerva15 DLP rules from DHL axioms The mapping converts all concept and property instances into facts of two predicates,TypeOf and Relationship, and ontology axioms into facts of some predefined predicates (e.g. SubClassOf and SubPropertyOf).

16. Analyzing Minerva16 Storage into RDBMS To support both original and inferred assertions by the DL reasoner and rule inference engine, Minerva designs a specific RDBMS Schema. Minerva categorizes table of DB schema into 4 types: atomic tables, TBox axioms tables, Abox fact tables and class constructor tables The focus of the DB Schema is that all predicates in the DLP rules have corresponding tables into DB  these rules can be easily translated into sequences of relational algebra operations, so we need simple SQL Select and Join operations among the previous tables.

17. Analyzing Minerva17 Querying: SPARQL SPARQL is a query language based on matching graph patterns  triple pattern: is like an RDF triple (resource, property, value) but with the possibility of variables in any position. Query answering algorithm: simple retrieval of the materialized data from DB Query Module: SPARQL query parser SQL translator

18. Analyzing Minerva18 Conclusion 1/3 Why DLP?: “…existing avalaible ontologies often use very few constructs outside the DLP language fragment..” (ref.Description Logic Programs: A Pratical Choice for the Modelling of Ontologies) “…DLP enjoys polynomial data complexity and exptime combined complexity…” (ref.Description Logic Programs: A Pratical Choice for the Modelling of Ontologies) “…Inferencing in def-LP is thus tractable (worst case polynomial time)…DLs are generally not tractable (typically ExpTime or even NExpTime complexity)...” (ref.Description Logic Programs: Combining Logic Programs with Description Logic)

19. Analyzing Minerva19 Why precomputation?: “…querying without runtime inference guarantees satisfactory response time..” (ref. Minerva:A Scalable OWL Ontology Storage and Inference System) “…The inferred results are materialized in the database so that queries can be evaluated efficiently. Our approach is to trade space for time...” (ref. Minerva:A Scalable OWL Ontology Storage and Inference System) Conclusion 2/3

20. Analyzing Minerva20 “…Based on the thoretically proved mapping from Description Logic to Logic Programs, we can claim that our system is sound and complete on DHL ontologies…” (ref. Minerva:A Scalable OWL Ontology Storage and Inference System) Conclusion 3/3