We study the computational complexity of conjunctive query answering w.r.t. ontologies formulated in fragments of the description logic SHIQ. Our main result is the identification of two new sources of complexity: the combination of transitive roles and role hierarchies which results in 2ExpTime-hardness, and transitive roles alone which result in coNExpTime-hardness. These bounds complement the existing result that inverse roles make query answering in SHIQ 2ExpTime-hard.  We also show that conjunctive query answering with transitive roles, but without inverse roles and role hierarchies, remains in ExpTime if the ABox is tree-shaped.

Least Common Subsumers (LCS) have been proposed in Description Logics (DL) to capture the commonalities between two or more concepts. Since its introduction in 1992,  LCS have been successfully employed  as a logical tool for a variety of applications, spanning from inductive learning, to bottom-up construction of knowledge bases, information retrieval,  to name a few. The best known algorithm for computing LCS uses structural comparison on normal forms, and the most expressive DL it is applied to is ALEN. We provide a general tableau-based calculus for computing LCS, via substitutions on concept terms containing concept variables. We show the applicability of our method to an expressive DL (but without disjunction and full negation), discuss complexity issues, and show the generality of our proposal.

We analyze the complexity of reasoning with circumscribed low-complexity DLs such as DL-lite and the EL family, under suitable restrictions on the use of abnormality predicates. We prove that in circumscribed DL-lite R complexity drops from NExp NP to the second level of the polynomial hierarchy. In EL, reasoning remains ExpTime-hard, in general. However, by restricting the possible occurrences of existential restrictions, we obtain membership in Sigma p 2 and Pi p 2 for an extension of EL.

Knowledge compilation is a common technique for propositional logic knowledge bases. A given knowledge base is transformed into a normal form, for which queries can be answered efficiently. This precompilation step is expensive, but it only has to be performed once.  We apply this technique to knowledge bases defined  in the Description Logic ALC. We discuss an efficient satisfiability test as well as a subsumption test for precompiled concepts and Tboxes. Further we use the precompiled Tboxes for efficient Tbox reasoning. Finally we present first experimental results of our approach.

Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, conjunctive query answering over DL knowledge bases is only poorly understood if transitive roles are admitted in the query. In this paper, we consider unions of conjunctive queries over knowledge bases formulated in the prominent DL SHIQ and allow transitive roles in both the query and the knowledge base. We show decidability of query answering in this setting and establish two tight complexity bounds: regarding combined complexity, we prove that there is a deterministic algorithm for query answering that needs time single exponential in the size of the KB and double exponential in the size of the query, which is optimal. Regarding data complexity, we prove containment in co-NP.

It is widely recognized today that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. Description Logics (DLs) are a family of knowledge representation languages that have gained considerable attention the last decade, mainly due to their decidability and the existence of empirically high performance of reasoning algorithms. In this paper, we extend the well known fuzzy ALC DL to the fuzzy SHIN DL, which extends the fuzzy ALC DL with transitive role axioms (S), inverse roles (I), role hierarchies (H) and number restrictions (N). We illustrate why transitive role axioms are difficult to handle in the presence of fuzzy interpretations and how to handle them properly. Then we extend these results by adding role hierarchies and finally number restrictions. The main contributions of the paper are the decidability proof of the fuzzy DL languages fuzzy-SI and fuzzy-SHIN, as well as decision procedures for the knowledge base satisfiability problem of the fuzzy-SI and fuzzy-SHIN.

Matchmaking arises when supply and demand meet in an electronic marketplace, or when agents search for a web service to perform some task, or even when recruiting agencies match curricula and job profiles. In such open environments, the objective of a matchmaking process is to discover best available offers to a given request. We address the problem of matchmaking from a knowledge representation perspective, with a formalization based on Description Logics. We devise Concept Abduction and Concept Contraction as non-monotonic inferences in Description Logics suitable for modeling matchmaking in a logical framework, and prove some related complexity results. We also present reasonable algorithms for semantic matchmaking based on the devised inferences, and prove that they obey to some commonsense properties. Finally, we report on the implementation of the proposed matchmaking framework, which has been used both as a mediator in e-marketplaces and for semantic web services discovery.

This article surveys previous work on combining planning techniques with expressive representations of knowledge in description logics to reason about tasks, plans, and goals. Description logics can reason about the logical definition of a class and automatically infer class-subclass subsumption relations as well as classify instances into classes based on their definitions. Descriptions of actions, plans, and goals can be exploited during plan generation, plan recognition, or plan evaluation. Another emerging use of these techniques is the semantic web, where current ontology languages based on description logics need to be extended to reason about goals and capabilities for web services and agents.

This article surveys previous work on combining planning techniques with expressive representations of knowledge in description logics to reason about tasks, plans, and goals. Description logics can reason about the logical definition of a class and automatically infer class-subclass subsumption relations as well as classify instances into classes based on their definitions. Descriptions of actions, plans, and goals can be exploited during plan generation, plan recognition, or plan evaluation. These techniques should be of interest to planning practitioners working on knowledge-rich application domains. Another emerging use of these techniques is the semantic web, where current ontology languages based on description logics need to be extended to reason about goals and capabilities for web services and agents.

Data integration is the problem of combining data residing at different autonomous, heterogeneous sources and providing the client with a unified, reconciled global view of the data. We discuss dataintegration systems, taking the abstract viewpoint that the global view is an ontology expressed in a class-based formalism. We resort to an expressive description logic, ALCQI, that fully captures classbased representation formalisms, and we show that query answering in data integration, as well as all other relevant reasoning tasks, is decidable. However, when we have to deal with large amounts of data, the high computational complexity in the size of the data makes the use of a fullfledged expressive description logic infeasible in practice. This leads us to consider DL-Lite, a specifically tailored restriction of ALCQI that ensures tractability of query answering in data integration while keeping enough expressive power to capture the most relevant features of class-based formalisms.