We study description logics (DLs) supporting number restrictions on transitive roles. We first take a look at SOQ and SON with binary and unary coding of numbers, and provide algorithms for the satisfiability problem and tight complexity bounds ranging from EXPTIME to NEXPTIME. We then show that by allowing for counting only up to one (functionality), inverse roles and role inclusions can be added without losing decidability. We finally investigate DLs of the DL-Lite-family, and show that, in the presence of role inclusions, the core fragment becomes undecidable.

We consider existential rules (aka Datalog+) as a formalism for specifying ontologies. In recent years, many classes of existential rules have been exhibited for which conjunctive query (CQ) entailment is decidable. However, most of these classes cannot express transitivity of binary relations, a frequently used modelling construct. In this paper, we address the issue of whether transitivity can be safely combined with decidable classes of existential rules. First, we prove that transitivity is incompatible with one of the simplest decidable classes, namely aGRD (acyclic graph of rule dependencies), which clarifies the landscape of `finite expansion sets' of rules. Second, we show that transitivity can be safely added to linear rules (a subclass of guarded rules, which generalizes the description logic DL-Lite-R) in the case of atomic CQs, and also for general CQs if we place a minor syntactic restriction on the rule set. This is shown by means of a novel query rewriting algorithm that is specially tailored to handle transitivity rules. Third, for the identified decidable cases, we pinpoint the combined and data complexities of query entailment.

Two essential tasks in managing description logic knowledge bases are eliminating problematic axioms and incorporating newly formed ones. Such elimination and incorporation are formalised as the operations of contraction and revision in belief change. In this paper, we deal with contraction and revision for the DL-Lite family through a model-theoretic approach. Standard description logic semantics yields an infinite number of models for DL-Lite knowledge bases, thus it is difficult to develop algorithms for contraction and revision that involve DL models. The key to our approach is the introduction of an alternative semantics called type semantics which can replace the standard semantics in characterising the standard inference tasks of DL-Lite.

The problem The need to equip reasoning systems with explanation services of querying such KBs using database-style queries (in is widely acknowledged by the DL community (see particular, conjunctive queries) has been a major focus of Section 6 for discussion and references), and such facilities recent DL research. Since scalability is a key concern, much are all the more essential when using inconsistency-tolerant of the work has focused on lightweight DLs for which query semantics, as recently argued in (Arioua et al. 2014). Indeed, answering can be performed in polynomial time w.r.t. the the brave, AR, and IAR semantics allow one to classify size of the ABox. The DL-Lite family of lightweight DLs query answers into three categories of increasing reliability, (Calvanese et al. 2007) is especially popular due to the fact and a user may naturally wonder why a given tuple was assigned that query answering can be reduced, via query rewriting, to to, or excluded from, one of these categories.

Ontology Learning (OL) is the computational task of generating a knowledge base in the form of an ontology given an unstructured corpus whose content is in natural language (NL). Several works can be found in this area most of which are limited to statistical and lexico-syntactic pattern matching based techniques Light-Weight OL. These techniques do not lead to very accurate learning mostly because of several linguistic nuances in NL. Formal OL is an alternative (less explored) methodology were deep linguistics analysis is made using theory and tools found in computational linguistics to generate formal axioms and definitions instead simply inducing a taxonomy. In this paper we propose "Description Logic (DL)" based formal OL framework for learning factual IS-A type sentences in English. We claim that semantic construction of IS-A sentences is non trivial. Hence, we also claim that such sentences requires special studies in the context of OL before any truly formal OL can be proposed. We introduce a learner tool, called DLOL_IS-A, that generated such ontologies in the owl format. We have adopted "Gold Standard" based OL evaluation on IS-A rich WCL v.1.1 dataset and our own Community representative IS-A dataset. We observed significant improvement of DLOL_IS-A when compared to the light-weight OL tool Text2Onto and formal OL tool FRED.

We consider existential rules (aka Datalog +/-) as a formalism for specifying ontologies. In recent years, many classes of existential rules have been exhibited for which conjunctive query (CQ) entailment is decidable. However, most of these classes cannot express transitivity of binary relations, a frequently used modelling construct. In this paper, we address the issue of whether transitivity can be safely combined with decidable classes of existential rules. First, we prove that transitivity is incompatible with one of the simplest decidable classes, namely aGRD (acyclic graph of rule dependencies), which clarifies the landscape of ‘finite expansion sets’ of rules. Second, we show that transitivity can be safely added to linear rules (a subclass of guarded rules, which generalizes the description logic DL-LiteR) in the case of atomic CQs, and also for general CQs if we place a minor syntactic restriction on the rule set. This is shown by means of a novel query rewriting algorithm that is specially tailored to handle transitivity rules. Third, for the identified decidable cases, we pinpoint the combined and data complexities of query entailment.

Artifact-centric models for business processes recently raised a lot of attention, as they manage to combine structural (i.e. data related) with dynamical (i.e. process related) aspects in a seamless way. Many frameworks developed under this approach, although, are not built explicitly for planning, one of the most prominent operations related to business processes. In this paper, we try to overcome this by proposing a framework named Dynamic Knowledge Bases, aimed at describing rich business domains through Description Logic-based ontologies, and where a set of actions allows the system to evolve by modifying such ontologies. This framework, by offering action rewriting and knowledge partialization, represents a viable and formal environment to develop decision making and planning techniques for DL-based artifact-centric business domains.

Formal ontology provides axiomatizations of domain independent principles which, among other applications, can be used to identify modeling errors within a knowledge base. The Ontoclean methodology is probably the best-known illustration of this strategy, but its cost in terms of manual work is often considered dissuasive. This article investigates the applicability of such debugging strategies to Description Logics knowledge bases, showing that even a partial and shallow analysis rapidly performed with a top-level ontology can reveal the presence of violations of common sense, and that the bottleneck, if there is one, may instead reside in the resolution of the resulting inconsistency or incoherence.

We design a tractable Horn fragment of the Halpern-Shoham temporal logic and extend it to interval-based temporal description logics, instance checking in which is P-complete for both combined and data complexity.

Knowledge and Action Bases (KABs) have been recently proposed as a formal framework to capture the dynamics of systems which manipulate Description Logic (DL) Knowledge Bases (KBs) through action execution. In this work, we enrich the KAB setting with contextual information, making use of different context dimensions. On the one hand, context is determined by the environment using context-changing actions that make use of the current state of the KB and the current context. On the other hand, it affects the set of TBox assertions that are relevant at each time point, and that have to be considered when processing queries posed over the KAB. Here we extend to our enriched setting the results on verification of rich temporal properties expressed in mu-calculus, which had been established for standard KABs. Specifically, we show that under a run-boundedness condition, verification stays decidable.