Temporal Query Answering in DL-Lite
     over Inconsistent Data (Extended Abstract)?

                    Camille Bourgaux and Anni-Yasmin Turhan

                  Technische Universität Dresden, Dresden, Germany

    This extended abstract presents our work on inconsistency-tolerant temporal
query answering [3] which is motivated by ontology-based situation recognition
for context-aware systems. In such applications complex systems are observed
over time and critical situations are recognized based on information gathered
from different sources. We consider the setting of temporal query answering pre-
sented in [2] where a temporal knowledge base (TKB) consists of a global TBox
and a sequence of ABoxes that represents the data at different time points, and
a temporal conjunctive query (TCQ) combines conjunctive queries with oper-
ators of propositional linear temporal logic (without negation). We extend to
this setting three inconsistency-tolerant semantics that have been introduced
for querying inconsistent description logic knowledge bases [4, 1]. These three
semantics are based upon the notion of a repair, which is a maximal consistent
subset of the data. For TKBs, we define repairs as component-wise maximal
consistent sequences of subsets of the ABoxes. The AR semantics considers the
queries that hold in every repair, the more cautious IAR semantics queries the
intersection of the repairs, and the less cautious brave semantics returns every
answer that holds in some repair. We show that when there is no rigid predi-
cate, existing algorithms for TCQ answering and for IAR query answering can
be combined to perform IAR temporal query answering and that this method
can sometimes be used for AR and provides in any case an approximation of
the AR answers. We investigate the computational properties of the three se-
mantics for DL-LiteR TKBs, considering both data complexity and combined
complexity, and distinguishing three different cases regarding the rigid symbols
that are allowed (no rigid predicates, only rigid concepts, or rigid concepts and
roles). We show that only brave semantics in the cases where rigid predicates are
allowed has a higher data complexity than in the atemporal case (NP-complete
instead of polynomial). We also complete the complexity picture for the classical
semantics by showing that the cases with rigid predicates can often be reduced
to the case without rigid predicates by adding a set of assertions computable in
polynomial time to every ABox of the TKB.
1.    Bienvenu, M. and Rosati, R. “Tractable Approximations of Consistent Query An-
      swering for Robust Ontology-based Data Access”. In: Proceedings of IJCAI. 2013.
2.    Borgwardt, S., Lippmann, M., and Thost, V. “Temporalizing Rewritable Query
      Languages over Knowledge Bases”. In: Journal Web Sem. 33 (2015), pp. 50–70.
3.    Bourgaux, C. and Turhan, A.-Y. “Temporal Query Answering in DL-Lite over
      Inconsistent Data”. LTCS-Report 17-06, Chair for Automata Theory, TU Dresden.
      See https://lat.inf.tu-dresden.de/research/reports.html. 2017.
4.    Lembo, D. et al. “Inconsistency-Tolerant Query Answering in Ontology-Based
      Data Access”. In: Journal Web Sem. 33 (2015), pp. 3–29.

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     Supported by the DFG in CRC 912 (HAEC) and the DAAD.