Conservative Rewritability of Description Logic TBoxes: First Results

We want to understand when a given TBox T in a description logic L can be rewritten into a TBox T' in a weaker description logic L' such that T' is a conservative extension of T. We consider two notions of conservative rewritability: model-conservative rewritability (T' entails T and all models of T can be expanded to models of T') and L-conservative rewritability (T' has the same L-consequences in the signature of T as T) and investigate conservative rewritability from ALCI to ALC, ALCQ to ALC, ALC to EL, and from ALC to DL-Lite_horn. We compare conservative rewritability and equivalent rewritability, give model-theoretic characterizations of conservative rewritability, prove complexity results for the rewritability problem, and provide some rewriting algorithms

Conservative Rewritability of Description Logic TBoxes: First Results

We want to understand when a given TBox T in a description logic L can be rewritten into a TBox T' in a weaker description logic L' such that T' is a conservative extension of T. We consider two notions of conservative rewritability: model-conservative rewritability (T' entails T and all models of T can be expanded to models of T') and L-conservative rewritability (T' has the same L-consequences in the signature of T as T) and investigate conservative rewritability from ALCI to ALC, ALCQ to ALC, ALC to EL, and from ALC to DL-Lite_horn. We compare conservative rewritability and equivalent rewritability, give model-theoretic characterizations of conservative rewritability, prove complexity results for the rewritability problem, and provide some rewriting algorithms

Horn rewritability vs PTime query evaluation for description logic TBoxes

We study the following question: if τ is a TBox that is formulated in an expressive DL L and all CQs can be evaluated in PTime w.r.t. τ, can τ be replaced by a TBox τ' that is formulated in the Horn-fragment of L and such that for all CQs and ABoxes, the answers w.r.t. τ and τ' coincide? Our main results are that this is indeed the case when L is the set of ALCHI or ALCIF TBoxes of quantifier depth 1 (which covers the majority of such TBoxes), but not for ALCHIF and ALCQ TBoxes of depth 1

Temporalising OWL 2 QL

We design a temporal description logic, TQL, that extends the standard ontology language OWL2QL, provides basic means for temporal conceptual modelling and ensures first-order rewritability of conjunctive queries for suitably defined data instances with validity time

Temporal description logic for ontology-based data access

Our aim is to investigate ontology-based data access over temporal data with validity time and ontologies capable of temporal conceptual modelling. To this end, we design a temporal description logic, TQL, that extends the standard ontology language OWL2QL, provides basic means for temporal conceptual modelling and ensures first-order rewritability of conjunctive queries for suitably defined data instances with validity time

THE DATA COMPLEXITY OF DESCRIPTION LOGIC ONTOLOGIES

We analyze the data complexity of ontology-mediated querying where the ontologies are formulated in a description logic (DL) of the ALC family and queries are conjunctive queries, positive existential queries, or acyclic conjunctive queries. Our approach is non-uniform in the sense that we aim to understand the complexity of each single ontology instead of for all ontologies formulated in a certain language. While doing so, we quantify over the queries and are interested, for example, in the question whether all queries can be evaluated in polynomial time w.r.t. a given ontology. Our results include a PTime/coNP-dichotomy for ontologies of depth one in the description logic ALCFI, the same dichotomy for ALC- and ALCI-ontologies of unrestricted depth, and the non-existence of such a dichotomy for ALCF-ontologies. For the latter DL, we additionally show that it is undecidable whether a given ontology admits PTime query evaluation. We also consider the connection between PTime query evaluation and rewritability into (monadic) Datalog

On decidability and tractability of querying in temporal EL

We study access to temporal data with TEL, a temporal extension of the tractable description logic EL. Our aim is to establish a clear computational complexity landscape for the atomic query answering problem, in terms of both data and combined complexity. Atomic queries in full TEL turn out to be undecidable even in data complexity. Motivated by the negative result, we identify well-behaved yet expressive fragments of TEL. Our main contributions are a semantic and sufficient syntactic conditions for decidability and three orthogonal tractable fragments, which are based on restricted use of rigid roles, temporal operators, and novel acyclicity conditions on the ontologies