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Description Logic, Theory Combination, and All That pp 187–211Cite as

The What-To-Ask Problem for Ontology-Based Peers

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11560))

Abstract

The issue of cooperation, integration, and coordination between information peers has been addressed over the years both in the context of the Semantic Web and in several other networked environments, including data integration, Peer-to-Peer and Grid computing, service-oriented computing, distributed agent systems, and collaborative data sharing. One of the main problems arising in such contexts is how to exploit the mappings between peers in order to answer queries posed to one peer. We address this issue for peers managing data through ontologies and in particular focus on ontologies specified in logics of the DL-Lite family. Our goal is to present some basic, fundamental results on this problem. In particular, we focus on a simplified setting based on just two interoperating peers, and we investigate how to solve the so-called “What-To-Ask” problem: find a way to answer queries posed to a peer by relying only on the query answering service available at the queried peer and at the other peer. We show both a positive and a negative result. Namely, we first prove that a solution to this problem always exists when the ontology is specified in \(\textit{DL-Lite}_{\mathcal {R}} \), and we provide an algorithm to compute it. Then, we show that for the case of \(\textit{DL-Lite}_{\mathcal {F}} \) the problem may have no solution. We finally illustrate that a solution to our problem can still be found even for more general networks of peers, and for any language of the DL-Lite family, provided that we interpret mappings according to an epistemic semantics, rather than the usual first-order semantics.

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Notes

  1. 1.

    For simplicity of presentation, we have assumed here that conjunctive queries contain neither constants nor repeated variables among \(x_1,\ldots ,x_n\), but all our results extend to the case where this restrictions do not apply.

  2. 2.

    Whenever we refer to \(M_\ell \) as part of an ontology, we consider its FOL formulation.

  3. 3.

    This formally corresponds to computing the union of the two sets of answers.

  4. 4.

    Note that, differently from classical UML semantics, we do not consider as disjoint those classes that in the class diagram do not have a common ancestor.

  5. 5.

    For an analysis on the inconsistency problem in the context of database and ontology integration see, for example, [9, 11, 36, 47].

  6. 6.

    We use the symbol ‘\(_{-}\)’ to denote non-shared variables that are existentially quantified.

  7. 7.

    We do not reformulate \(q_2\) since it is contained in \(q_3\).

  8. 8.

    We use \(\psi ^x_c\) to denote the formula obtained from \(\psi \) by substituting each free occurrence of the variable x with the constant c.

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Authors and Affiliations

  1. Free University of Bozen-Bolzano, Bolzano, Italy

    Diego Calvanese

  2. Sapienza Università di Roma, Rome, Italy

    Giuseppe De Giacomo, Domenico Lembo, Maurizio Lenzerini & Riccardo Rosati

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  1. Diego Calvanese
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  2. Giuseppe De Giacomo
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  3. Domenico Lembo
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  4. Maurizio Lenzerini
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  5. Riccardo Rosati
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Correspondence to Diego Calvanese .

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Editors and Affiliations

  1. University of Bremen, Bremen, Germany

    Carsten Lutz

  2. University of Manchester, Manchester, UK

    Uli Sattler

  3. University of Iowa, Iowa City, IA, USA

    Cesare Tinelli

  4. TU Dresden, Dresden, Germany

    Anni-Yasmin Turhan

  5. University of Liverpool, Liverpool, UK

    Frank Wolter

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Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R. (2019). The What-To-Ask Problem for Ontology-Based Peers. In: Lutz, C., Sattler, U., Tinelli, C., Turhan, AY., Wolter, F. (eds) Description Logic, Theory Combination, and All That. Lecture Notes in Computer Science(), vol 11560. Springer, Cham. https://doi.org/10.1007/978-3-030-22102-7_9

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