From Conjunctive Queries to Instance Queries in Ontology-Mediated Querying

IJCAI, pp. 1810-1816, 2018.

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extended ABoxesinstance queryconstraint satisfaction problemsdisjunctive datalogconstraint satisfactionMore(20+)
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An important step into this direction has been made by Kikot and Zolin who identify a large class of conjunctive queries that are rewritable into instance queries: a conjunctive queries is rewritable into an ALCI-instance queries if it is connected and every cycle passes through ...

Abstract:

© 2018 International Joint Conferences on Artificial Intelligence. All right reserved. We consider ontology-mediated queries (OMQs) based on expressive description logics of the ALC family and (unions) of conjunctive queries, studying the rewritability into OMQs based on instance queries (IQs). Our results include exact characterizations ...More

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Introduction
  • An ontology-mediated query (OMQ) is a database-style query enriched with an ontology that contains domain knowledge, aiming to deliver more complete answers [Calvanese et al, 2009; Bienvenu et al, 2014; Bienvenu and Ortiz, 2015].
  • P behaves like a monadic second-order variable due to the open-world assumption made for OMQs: the authors are free to interpret P in any possible way and when making P true at an object the authors are forced to make ∃r.P true if and only if the object is involved in a reflexive r-loop
  • It is an interesting question, raised in [Zolin, 2007; Kikot and Zolin, 2013; Kikot et al, 2013], to precisely characterize the class of CQs that are rewritable into IQs. An important step into this direction has been made by Kikot and Zolin [2013] who identify a large class of CQs that are rewritable into IQs: a CQ is rewritable into an ALCI-IQ if it is connected and every cycle passes through the answer variable; for rewritability into an ALC-IQ, one requires that all variables are reachable from the answer variable in a directed sense.
  • It remained open whether these classes are depleting, that is, whether they capture all CQs that are IQ-rewritable
Highlights
  • An ontology-mediated query (OMQ) is a database-style query enriched with an ontology that contains domain knowledge, aiming to deliver more complete answers [Calvanese et al, 2009; Bienvenu et al, 2014; Bienvenu and Ortiz, 2015]
  • While conjunctive queries and unions of conjunctive queries are widely known query languages that play a fundamental role in database systems and theory, instance queries are more closely linked to description logic
  • The conjunctive queries r(x, x), which asks to return all objects from the data that are involved in a reflexive r-loop, can be rewritten into the equivalent ALC-instance queries P → ∃r.P (x)
  • An important step into this direction has been made by Kikot and Zolin [2013] who identify a large class of conjunctive queries that are rewritable into instance queries: a conjunctive queries is rewritable into an ALCI-instance queries if it is connected and every cycle passes through the answer variable; for rewritability into an ALC-instance queries, one requires that all variables are reachable from the answer variable in a directed sense
  • Characterizing ontology-mediated queries from (ALCI, unions of conjunctive queries) that are rewritable into (ALCI, instance queries) is related to characterizing MMSNP sentences that are equivalent to a constraint satisfaction problems, and we study the latter problem
  • The main aim of this paper is to study the rewritability of ontology-mediated queries from (L, (U)conjunctive queries) into ontology-mediated queries from (L, instance queries), considering as L the basic expressive description logic ALC as well as extensions of ALC with inverse roles, role hierarchies, the universal role, and functional roles
Conclusion
  • The authors have made a leap forward in understanding the relation between (U)CQs and IQs in ontology-mediated querying.
  • Interesting open problems include a characterization of IQrewritability for DLs with functional roles when the TBox is non-empty and characterizations for DLs with transitive roles.
  • The remarks after Theorem 4 and 10 mention further problems left open.
  • It would be worthwhile to continue the effort from [Kikot et al, 2013] to understand the value of IQ-rewritings for the purposes of efficient practical implementation
Summary
  • Introduction:

    An ontology-mediated query (OMQ) is a database-style query enriched with an ontology that contains domain knowledge, aiming to deliver more complete answers [Calvanese et al, 2009; Bienvenu et al, 2014; Bienvenu and Ortiz, 2015].
  • P behaves like a monadic second-order variable due to the open-world assumption made for OMQs: the authors are free to interpret P in any possible way and when making P true at an object the authors are forced to make ∃r.P true if and only if the object is involved in a reflexive r-loop
  • It is an interesting question, raised in [Zolin, 2007; Kikot and Zolin, 2013; Kikot et al, 2013], to precisely characterize the class of CQs that are rewritable into IQs. An important step into this direction has been made by Kikot and Zolin [2013] who identify a large class of CQs that are rewritable into IQs: a CQ is rewritable into an ALCI-IQ if it is connected and every cycle passes through the answer variable; for rewritability into an ALC-IQ, one requires that all variables are reachable from the answer variable in a directed sense.
  • It remained open whether these classes are depleting, that is, whether they capture all CQs that are IQ-rewritable
  • Conclusion:

    The authors have made a leap forward in understanding the relation between (U)CQs and IQs in ontology-mediated querying.
  • Interesting open problems include a characterization of IQrewritability for DLs with functional roles when the TBox is non-empty and characterizations for DLs with transitive roles.
  • The remarks after Theorem 4 and 10 mention further problems left open.
  • It would be worthwhile to continue the effort from [Kikot et al, 2013] to understand the value of IQ-rewritings for the purposes of efficient practical implementation
Funding
  • Cristina Feier and Carsten Lutz were supported by ERC Consolidator Grant 647289 CODA
  • Frank Wolter was supported by EPSRC UK grant EP/M012646/1
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