5 research outputs found
The Data Complexity of Ontology-Mediated Queries with Closed Predicates
In the context of ontology-mediated querying with description logics (DLs), we study the data complexity of queries in which selected predicates can be closed (OMQCs). We provide a non-uniform analysis, aiming at a classification of the complexity into tractable and non-tractable for ontologies in the lightweight DLs DL-Lite and EL, and the expressive DL ALCHI. At the level of ontologies, we prove a dichotomy between FO-rewritable and coNP-complete for DL-Lite and between PTime and coNP-complete for EL. The meta problem of deciding tractability is proved to be in PTime. At the level of OMQCs, we show that there is no dichotomy (unless NP equals PTime) if both concept and role names can be closed. If only concept names can be closed, we tightly link the complexity of query evaluation to the complexity of surjective CSPs. We also identify a class of OMQCs based on ontologies formulated in DL-Lite that are guaranteed to be tractable and even FO-rewritable
Living Without Beth and Craig: Definitions and Interpolants in Description Logics with Nominals and Role Inclusions
The Craig interpolation property (CIP) states that an interpolant for an
implication exists iff it is valid. The projective Beth definability property
(PBDP) states that an explicit definition exists iff a formula stating implicit
definability is valid. Thus, the CIP and PBDP transform potentially hard
existence problems into deduction problems in the underlying logic. Description
Logics with nominals and/or role inclusions do not enjoy the CIP nor PBDP, but
interpolants and explicit definitions have many potential applications in
ontology engineering and ontology-based data management. In this article we
show the following: even without Craig and Beth, the existence of interpolants
and explicit definitions is decidable in description logics with nominals
and/or role inclusions such as ALCO, ALCH and ALCHIO. However, living without
Craig and Beth makes this problem harder than deduction: we prove that the
existence problems become 2ExpTime-complete, thus one exponential harder than
validity. The existence of explicit definitions is 2ExpTime-hard even if one
asks for a definition of a nominal using any symbol distinct from that nominal,
but it becomes ExpTime-complete if one asks for a definition of a concept name
using any symbol distinct from that concept name.Comment: We have added results on description logics with role inclusions and
an ExpTime-completeness result for the explicit definability of concept
names. The title has been modified by adding role inclusions. This paper has
been accepted for AAAA 202
A data complexity and rewritability tetrachotomy of ontology-mediated queries with a covering axiom
Aiming to understand the data complexity of answering conjunctive queries mediated by an axiom stating that a class is covered by the union of two other classes, we show that deciding their first-order rewritability is PSPACE-hard and obtain a number of sufficient conditions for membership in AC0, L, NL, and P. Our main result is a complete syntactic AC0/NL/P/CONP tetrachotomy of path queries under the assumption that the covering classes are disjoint
Living Without Beth and Craig: Definitions and Interpolants in Description and Modal Logics with Nominals and Role Inclusions
The Craig interpolation property (CIP) states that an interpolant for an implication exists iff it is valid. The projective Beth definability property (PBDP) states that an explicit definition exists iff a formula stating implicit definability is valid. Thus, the CIP and PBDP reduce potentially hard existence problems to entailment in the underlying logic. Description (and modal) logics with nominals and/or role inclusions do not enjoy the CIP nor the PBDP, but interpolants and explicit definitions have many applications, in particular in concept learning, ontology engineering, and ontology-based data management. In this article we show that, even without Beth and Craig, the existence of interpolants and explicit definitions is decidable in description logics with nominals and/or role inclusions such as
,
and
and corresponding hybrid modal logics. However, living without Beth and Craig makes these problems harder than entailment: the existence problems become 2ExpTime-complete in the presence of an ontology or the universal modality, and coNExpTime-complete otherwise. We also analyze explicit definition existence if all symbols (except the one that is defined) are admitted in the definition. In this case the complexity depends on whether one considers individual or concept names. Finally, we consider the problem of computing interpolants and explicit definitions if they exist and turn the complexity upper bound proof into an algorithm computing them, at least for description logics with role inclusions.
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The Data Complexity of Ontology-Mediated Queries with Closed Predicates
In the context of ontology-mediated querying with description logics (DLs),
we study the data complexity of queries in which selected predicates can be
closed (OMQCs). We provide a non-uniform analysis, aiming at a classification
of the complexity into tractable and non-tractable for ontologies in the
lightweight DLs DL-Lite and EL, and the expressive DL ALCHI. At the level of
ontologies, we prove a dichotomy between FO-rewritable and coNP-complete for
DL-Lite and between PTime and coNP-complete for EL. The meta problem of
deciding tractability is proved to be in PTime. At the level of OMQCs, we show
that there is no dichotomy (unless NP equals PTime) if both concept and role
names can be closed. If only concept names can be closed, we tightly link the
complexity of query evaluation to the complexity of surjective CSPs. We also
identify a class of OMQCs based on ontologies formulated in DL-Lite that are
guaranteed to be tractable and even FO-rewritable