54 research outputs found
First-order rewritability of temporal ontology-mediated queries
Aiming at ontology-based data access over temporal, in particular streaming data, we design a language of ontology-mediated queries by extending OWL 2 QL and SPARQL with temporal operators, and investigate rewritability of these queries into two-sorted first-order logic with < and PLUS over time
Ontology-mediated query answering over temporal data: a survey
We discuss the use of various temporal knowledge representation formalisms for ontology-mediated query answering over temporal data. In particular, we analyse ontology and query languages based on the linear temporal logic LTL, the multi-dimensional Halpern-Shoham interval temporal logic HSn, as well as the metric temporal logic MTL. Our main focus is on the data complexity of answering temporal ontology-mediated queries and their rewritability into standard first-order and datalog queries
First-Order Rewritability and Complexity of Two-Dimensional Temporal Ontology-Mediated Queries
Aiming at ontology-based data access to temporal data, we design
two-dimensional temporal ontology and query languages by combining logics from
the (extended) DL-Lite family with linear temporal logic LTL over discrete time
(Z,<). Our main concern is first-order rewritability of ontology-mediated
queries (OMQs) that consist of a 2D ontology and a positive temporal instance
query. Our target languages for FO-rewritings are two-sorted FO(<) -
first-order logic with sorts for time instants ordered by the built-in
precedence relation < and for the domain of individuals - its extension FOE
with the standard congruence predicates t \equiv 0 mod n, for any fixed n > 1,
and FO(RPR) that admits relational primitive recursion. In terms of circuit
complexity, FOE- and FO(RPR)-rewritability guarantee answering OMQs in uniform
AC0 and NC1, respectively.
We proceed in three steps. First, we define a hierarchy of 2D DL-Lite/LTL
ontology languages and investigate the FO-rewritability of OMQs with atomic
queries by constructing projections onto 1D LTL OMQs and employing recent
results on the FO-rewritability of propositional LTL OMQs. As the projections
involve deciding consistency of ontologies and data, we also consider the
consistency problem for our languages. While the undecidability of consistency
for 2D ontology languages with expressive Boolean role inclusions might be
expected, we also show that, rather surprisingly, the restriction to Krom and
Horn role inclusions leads to decidability (and ExpSpace-completeness), even if
one admits full Booleans on concepts. As a final step, we lift some of the
rewritability results for atomic OMQs to OMQs with expressive positive temporal
instance queries. The lifting results are based on an in-depth study of the
canonical models and only concern Horn ontologies
A decidable temporal DL-Lite logic with undecidable first-order and datalog-rewritability of ontology-mediated atomic queries
We design a logic in the temporal DL-Lite family (with non-Horn role inclusions and restricted temporalised roles), for which answering ontology-mediated atomic queries (OMAQs) can be done in ExpSpace
and even in PSpace for ontologies without existential quantification in the rule heads but determining FO-rewritability or (linear) Datalog-rewritability of OMAQs is undecidable. On the other hand, we
show (by reduction to monadic disjunctive Datalog) that deciding FO-rewritability of OMAQs in the non-temporal fragment of our logic can be done in 3NExpTime
Deciding FO-rewritability of Regular Languages and Ontology-Mediated Queries in Linear Temporal Logic
Our concern is the problem of determining the data complexity of answering an ontology-mediated query (OMQ) formulated in linear temporal logic LTL over (Z,<) and deciding whether it is rewritable to an FO(<)-query, possibly with some extra predicates. First, we observe that, in line with the circuit complexity and FO-definability of regular languages, OMQ answering in AC0, ACC0 and NC1 coincides with FO(<,≡)-rewritability using unary predicates x ≡ 0 (mod n), FO(<,MOD)-rewritability, and FO(RPR)-rewritability using relational primitive recursion, respectively. We prove that, similarly to known PSᴘᴀᴄᴇ-completeness of recognising FO(<)-definability of regular languages, deciding FO(<,≡)- and FO(<,MOD)-definability is also PSᴘᴀᴄᴇ-complete (unless ACC0 = NC1). We then use this result to show that deciding FO(<)-, FO(<,≡)- and FO(<,MOD)-rewritability of LTL OMQs is ExᴘSᴘᴀᴄᴇ-complete, and that these problems become PSᴘᴀᴄᴇ-complete for OMQs with a linear Horn ontology and an atomic query, and also a positive query in the cases of FO(<)- and FO(<,≡)-rewritability. Further, we consider FO(<)-rewritability of OMQs with a binary-clause ontology and identify OMQ classes, for which deciding it is PSᴘᴀᴄᴇ-, Π2p- and coNP-complete
Deciding FO-rewritability of ontology-mediated queries in linear temporal logic
Our concern is the problem of determining the data complexity of answering an ontology-mediated query (OMQ) given in linear temporal logic LTL over (Z,<) and deciding whether it is rewritable to an FO(<)-query, possibly with extra predicates.
First, we observe that, in line with the circuit complexity and FO-definability of regular languages, OMQ answering in AC0, ACC0 and NC1 coincides with FO(<,\equiv)-rewritability using unary predicates x \equiv 0 mod n), FO(<,MOD)-rewritability, and FO(RPR)-rewritability using relational primitive recursion, respectively.
We then show that deciding FO(<)-, \FO(<,\equiv)- and FO(<,MOD)-rewritability of LTL OMQs is ExpSpace-complete, and that these problems become PSpace-complete for OMQs with a linear Horn ontology and an atomic query, and also a positive query in the cases of FO(<)- and FO(<,\equiv)-rewritability.
Further, we consider FO(<)-rewritability of OMQs with a binary-clause ontology and identify OMQ classes, for which deciding it is PSpace-, Pi_2^p- and coNP-complete
- …