In this chapter, we summarize the research on querying inconsistent databases we have been conducting over the last five years. The formal framework we have used is based on two concepts: repair and consistent query answer. We describe different approaches to the issue of computing consistent query answers: query transformation, logic programming, inference in annotated logics, and specialized algorithms. We also characterize the computational complexity of this problem. Finally, we discuss related research in artificial intelligence, databases, and logic programming.

In the situation calculus, it is sometimes necessary to prove that certain properties are true in all world states accessible from the initial state. This is the case for some forms of reasoning about the physical world, for certain planning applications, and for verifying integrity constraints in databases. Not surprisingly, this requires a suitable form of mathematical induction. This paper motivates the need for proving properties of states in the situation calculus, proposes appropriate induction principles for this task, and gives examples of their use in databases and for reasoning about the physical world. Abbreviated title: Proving Properties of States 1 Introduction The situation calculus [8] is enjoying new popularity these days. One reason is that its expressiveness is considerably richer than has been commonly believed (Gelfond, Lifschitz and Rabinov [2], Pinto and Reiter [10], Schubert [16]). Another is the possibility of precisely characterizing the strengths and limi...

Fangzhen Lin and Yoav Shoham defined a propositional nonmonotonic logic which uses two independent modal operators. One of them represents minimal knowledge, the other is related to the ideas of justification (as understood in default logic) and of negation as failure. We describe a simplified version of that system, show how quantifiers can be included in it, and study its relation to circumscription and default logic, to logic programming, and to the theory of epistemic queries developed by Hector Levesque and Ray Reiter. 1 Introduction Lin and Shoham [16] defined a propositional nonmonotonic logic which uses two independent modal operators. One of them represents minimal knowledge, 1 the other is related to the ideas of justification (as understood in default logic) and of negation as failure. In this paper, we consider a special case of that system, in which Kripke structures of a particularly simple kind are used, and show how quantifiers can be included in it. This extension i...

Integrating description logics (DL) and logic programming (LP) would produce a very powerful and useful formalism. However, DLs and LP are based on quite different principles, so achieving a seamless integration is not trivial. In this paper, we introduce hybrid MKNF knowledge bases that faithfully integrate DLs with LP using the logic of Minimal Knowledge and Negation as Failure (MKNF) [Lifschitz, 1991]. We also give reasoning algorithms and tight data complexity bounds for several interesting fragments of our logic. 1

In this paper we give a robust logical and computational characterisation of peer-to-peer database systems. We rst de ne a precise model-theoretic semantics of a peer-to-peer system, which allows for local inconsistency handling. We then characterise the general computational properties for the problem of answering queries to such a peer-topeer system. Finally, we devise tight complexity bounds and distributed procedures for the problem of answering queries in few relevant special cases.

Abstract. Logic programming (LP) is often seen as a way to overcome several shortcomings of the Web Ontology Language (OWL), such as the inability to model integrity constraints or perform closed-world querying. However, the open-world semantics of OWL seems to be fundamentally incompatible with the closed-world semantics of LP. This has sparked a heated debate in the Semantic Web community, resulting in proposals for alternative ontology languages based entirely on logic programming. To help resolving this debate, we investigate the practical use cases which seem to be addressed by logic programming. In fact, many of these requirements have already been addressed outside the Semantic Web. By drawing inspiration from these existing formalisms, we present a novel logic of hybrid MKNF knowledge bases, which seamlessly integrates OWL with LP. We are thus capable of addressing the identified use cases without a radical change in the architecture of the Semantic Web. 1

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We address the problem of formalizing the evolution of a database under the effect of an arbitrary sequence of update transactions. We do so by appealing to a first order representation language called the situation calculus, which is a standard approach in artificial intelligence to the formalization of planning problems. We formalize database transactions in exactly the same way as actions in the artificial intelligence planning domain. This leads to a database version of the frame problem in artificial intelligence. We provide a solution to the frame problem for a special, but substantial, class of update transactions. We next briefly describe some of the results obtained within this axiomatization. Specifically, we provide procedures for determining whether a given sequence of update transactions is legal, and for query evaluation in an updated database. These procedures have the nice property that they appeal to theorem-proving only with respect to the initial database state. We a...

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

We present Autoepistemic Description Logics (ADLs), in which the language of Description Logics is augmented with modal operators interpreted according to the nonmonotonic logic MKNF . We provide decision procedures for query answering in two very expressive ADLs. We show their representational features by addressing defaults, integrity constraints, role and concept closure. Hence, ADLs provide a formal characterization of a wide variety of nonmonotonic features commonly available in frame-based systems and needed in the development of practical applications. 1 Introduction Description Logics (DL) have been studied in the past years to provide a formal characterization of frame-based systems. However, while the fragment of first-order logic which characterizes the most popular constructs of these languages has been clearly identified (see for example [Woods & Schmolze, 1992]), there is not yet consensus on the features of framebased systems that cannot be formalized in a classical fi...