We propose a new Description Logic, called DL-Lite, specifically tailored to capture basic ontology languages, while keeping low complexity of reasoning. Reasoning here means not only computing subsumption between concepts, and checking satisfiability of the whole knowledge base, but also answering complex queries (in particular, conjunctive queries) over the set of instances maintained in secondary storage. We show that in DL-Lite the usual DL reasoning tasks are polynomial in the size of the TBox, and query answering is polynomial in the size of the ABox (i.e., in data complexity). To the best of our knowledge, this is the first result of polynomial data complexity for query answering over DL knowledge bases. A notable feature of our logic is to allow for a separation between TBox and ABox reasoning during query evaluation: the part of the process requiring TBox reasoning is independent of the ABox, and the part of the process requiring access to the ABox can be carried out by an SQL engine, thus taking advantage of the query optimization strategies provided by current DBMSs.

In peer-to-peer data integration, each peer exports data in terms of its own schema, and data interoperation is achieved by means of mappings among the peer schemas. Peers are autonomous systems and mappings are dynamically created and changed. One of the challenges in these systems is answering queries posed to one peer taking into account the mappings. Obviously, query answering strongly depends on the semantics of the overall system. In this paper, we compare the commonly adopted approach of interpreting peerto-peer systems using a first-order semantics, with an alternative approach based on epistemic logic. We consider several central properties of peer-to-peer systems: modularity, generality, and decidability. We argue that the approach based on epistemic logic is superior with respect to all the above properties. In particular, we show that, in systems in which peers have decidable schemas and conjunctive mappings, but are arbitrarily interconnected, the first-order approach may lead to undecidability of query answering, while the epistemic approach always preserves decidability. This is a fundamental property, since the actual interconnections among peers are not under the control of any actor in the system. 1.

We consider a class of knowledge-based programs with sense actions. These programs refer explicitly to an agent's knowledge, and are designed to...

Abstract. In this paper, we study the problem of data integration in P2P systems. Differently from the traditional setting, data integration in these systems is not based on the existence of a global view. Instead, each peer exports data in terms of its own schema, and information integration is achieved by establishing mappings among the various peer schemas. We present a framework that captures this general architecture, and then we discuss the problem of characterizing the semantics of such framework. We show that the usual approach of resorting to a first-order logic intepretation of P2P mappings, leads both to a poor modeling of the whole system, and to undecidability of query answering, even for mappings of a restricted form. This motivates the need of a new semantics for P2P system. We then present a novel proposal, based on epistemic logic, and show that not only it adequately models the interactions among peers, but it also supports decidable query answering. In particular, for the restricted form of mapping mentioned above, query answering is polynomial with respect to the size of data stored in the peers. 1

in this paper, we develop an account of the kind of deliberation that an agent that is doing planning or executing high-level programs under incomplete information must be able to perform.

We study the notion of update of an ontology expressed as a Description Logic knowledge base. Such a knowledge base is constituted by two components, called TBox and ABox. The former expresses general knowledge about the concepts and their relationships, whereas the latter describes the state of affairs regarding the instances of concepts. We investigate the case where the update affects only the instance level of the ontology, i.e., the ABox. Building on classical approaches on knowledge base update, our first contribution is to provide a general semantics for instance level update in Description Logics. We then focus on DL-Lite, a specific Description Logic where the basic reasoning tasks are computationally tractable. We show that DL-Lite is closed with respect to instance level update, in the sense that the result of an update is always expressible as a new DL-Lite ABox. Finally we provide an algorithm that computes the result of an update in DL-Lite, and we show that it runs in polynomial time with respect to the size of both the original knowledge base and the update formula.

Querying Description Logic knowledge bases has received great attention in the last years. In such a problem, the need of coping with incomplete information is the distinguishing feature with respect to querying databases. Due to this feature, we have to deal with two conflicting needs: on the one hand, we would like to query the knowledge base with sophisticated mechanisms provided by full first-order logic (FOL); on the other hand, the presence of incomplete information makes query answering a much more difficult task than in databases. In this paper we advocate the use of a nonmonotonic epistemic FOL query language as a means for expressing sophisticated queries over Description Logic knowledge bases. We show that through a controlled use of the epistemic operator, resulting in the language called EQL-Lite, we are able to formulate full FOL queries over Description Logic knowledge bases, while keeping computational complexity of query answering under control. In particular, we show that EQL-Lite queries over DL-Lite knowledge bases are FOL reducible (i.e., compilable into SQL) and hence can be answered in LOGSPACE through standard database technologies. 1

Abstract. We study peer-to-peer data integration, where each peer models an autonomous system that exports data in terms of its own schema, and data interoperation is achieved by means of mappings among the peer schemas, rather than through a global schema. We propose a multi-modal epistemic semantics based on the idea that each peer is conceived as a rational agent that exchanges knowledge/belief with other peers, thus nicely modeling the modular structure of the system. We then address the issue of dealing with possible inconsistencies, and distinguish between two types of inconsistencies, called local and P2P, respectively. We define a nonmonotonic extension of our logic that is able to reason on the beliefs of peers under inconsistency tolerance. Tolerance to local inconsistency essentially means that the presence of inconsistency within one peer does not affect the consistency of the whole system. Tolerance to P2P inconsistency means being able to resolve inconsistencies arising from the interaction between peers. We study query answering and its data complexity in this setting, and we present an algorithm that is sound and complete with respect to the proposed semantics, and optimal with respect to worst-case complexity. 1

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Fuzzy Description Logics (fuzzy DLs) allow to describe structured knowledge with vague concepts. Unlike classical DLs, in fuzzy DLs an answer is a set of tuples ranked according to the degree they satisfy the query. In this paper, we consider fuzzy DL-Lite. We show how to compute e#ciently the top-k answers of a complex query (i.e. conjunctive queries) over a huge set of instances.