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Practical Reasoning for Expressive Description Logics
, 1999
"... . Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We present an algorithm ..."
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Cited by 310 (68 self)
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. Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We present an algorithm that decides satis ability of the DL ALC extended with transitive and inverse roles, role hierarchies, and qualifying number restrictions. Early experiments indicate that this algorithm is wellsuited for implementation. Additionally, we show that ALC extended with just transitive and inverse roles is still in PSpace. Finally, we investigate the limits of decidability for this family of DLs.
Reasoning with Axioms: Theory and Practice
 IN PROC. OF THE 7TH INT. CONF. ON PRINCIPLES OF KNOWLEDGE REPRESENTATION AND REASONING (KR 2000
, 2000
"... When reasoning in description, modal or temporal logics it is often useful to consider axioms representing universal truths in the domain of discourse. Reasoning with respect to an arbitrary set of axioms is hard, even for relatively inexpressive logics, and it is essential to deal with such a ..."
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Cited by 45 (17 self)
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When reasoning in description, modal or temporal logics it is often useful to consider axioms representing universal truths in the domain of discourse. Reasoning with respect to an arbitrary set of axioms is hard, even for relatively inexpressive logics, and it is essential to deal with such axioms in an ecient manner if implemented systems are to be effective in real applications. This is particularly relevant to Description Logics, where subsumption reasoning with respect to a terminology is a fundamental problem. Two optimisation techniques that have proved to be particularly eective in dealing with terminologies are lazy unfolding and absorption. In this paper we seek to improve our theoretical understanding of these important techniques. We define a formal framework that allows the techniques to be precisely described, establish conditions under which they can be safely applied, and prove that, provided these conditions are respected, subsumption testing algo...
Answering regular path queries in expressive description logics: An automatatheoretic approach
 In Proc. of the 22nd Nat. Conf. on Artificial Intelligence (AAAI 2007
, 2007
"... Expressive Description Logics (DLs) have been advocated as formalisms for modeling the domain of interest in various application areas. An important requirement is the ability to answer complex queries beyond instance retrieval, taking into account constraints expressed in a knowledge base. We consi ..."
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Cited by 35 (17 self)
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Expressive Description Logics (DLs) have been advocated as formalisms for modeling the domain of interest in various application areas. An important requirement is the ability to answer complex queries beyond instance retrieval, taking into account constraints expressed in a knowledge base. We consider this task for positive existential path queries (which generalize conjunctive queries and unions thereof), whose atoms are regular expressions over the roles (and concepts) of a knowledge base in the expressive DL ALCQIbreg. Using techniques based on twoway treeautomata, we first provide an elegant characterization of TBox and ABox reasoning, which gives us also a tight EXPTIME bound. We then prove decidability (more precisely, a 2EXPTIME upper bound) of query answering, thus significantly pushing the decidability frontier, both with respect to the query language and the considered DL. We also show that query answering is EXPSPACEhard already in rather restricted settings.
Hybrid Logics
"... This chapter provides a modern overview of the field of hybrid logic. Hybrid logics are extensions of standard modal logics, involving symbols that name individual states in models. The first results that are nowadays considered as part of the field date back to the early work of Arthur ..."
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Cited by 34 (10 self)
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This chapter provides a modern overview of the field of hybrid logic. Hybrid logics are extensions of standard modal logics, involving symbols that name individual states in models. The first results that are nowadays considered as part of the field date back to the early work of Arthur
Ontology of Integration and Integration of Ontologies
 Procs. of the 2001 Description Logic Workshop (DL 2001
"... One of the basic problems in the development of techniques for the semantic web is the integration of ontologies. In this paper we deal with a situation where we have various local ontologies, developed independently from each other, and we are required to build an integrated, global ontology as a m ..."
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Cited by 31 (0 self)
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One of the basic problems in the development of techniques for the semantic web is the integration of ontologies. In this paper we deal with a situation where we have various local ontologies, developed independently from each other, and we are required to build an integrated, global ontology as a mean for extracting information from the local ones. In this context, the problem of how to specify the mapping between the global ontology and the local ontologies is a fundamental one, and its solution is essential for establishing an ontology of integration. Description Logics (DLs) are an ideal candidate to formalize ontologies, due to their ability to express complex relationships between concepts. We argue, however, that, for capturing the mapping between different ontologies, the direct use of a DL, even a very expressive one, is not sufficient, and it is necessary to resort to more flexible mechanisms based on the notion of query. Also, we elaborate on the observation that, in the semantic web, the case of mutually inconsistent local ontologies will be very common, and we present the basic ideas in order to extend the integration framework with suitable nonmonotonic features for dealing with this case. 1
Ontologies and databases: The DLLite approach
 In Reasoning Web, volume 5689 of LNCS
, 2009
"... Abstract. Ontologies provide a conceptualization of a domain of interest. Nowadays, they are typically represented in terms of Description Logics (DLs), and are seen as the key technology used to describe the semantics of information at various sites. The idea of using ontologies as a conceptual vie ..."
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Cited by 26 (17 self)
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Abstract. Ontologies provide a conceptualization of a domain of interest. Nowadays, they are typically represented in terms of Description Logics (DLs), and are seen as the key technology used to describe the semantics of information at various sites. The idea of using ontologies as a conceptual view over data repositories is becoming more and more popular, but for it to become widespread in standard applications, it is fundamental that the conceptual layer through which the underlying data layer is accessed does not introduce a significant overhead in dealing with the data. Based on these observations, in recent years a family of DLs, called DLLite, has been proposed, which is specifically tailored to capture basic ontology and conceptual data modeling languages, while keeping low complexity of reasoning and of answering complex queries, in particular when the complexity is measured w.r.t. the size of the data. In this article, we present a detailed account of the major results that have been achieved for the DLLite family. Specifically, we concentrate on DLLiteA,id, an expressive member of this family, present algorithms for reasoning and query answering over DLLiteA,id ontologies,
A Logic of Reachable Patterns in Linked DataStructures
, 2007
"... We define a new decidable logic for expressing and checking invariants of programs that manipulate dynamicallyallocated objects via pointers and destructive pointer updates. The main feature of this logic is the ability to limit the neighborhood of a node that is reachable via a regular expression ..."
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Cited by 25 (3 self)
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We define a new decidable logic for expressing and checking invariants of programs that manipulate dynamicallyallocated objects via pointers and destructive pointer updates. The main feature of this logic is the ability to limit the neighborhood of a node that is reachable via a regular expression from a designated node. The logic is closed under boolean operations (entailment, negation) and has a finite model property. The key technical result is the proof of decidability. We show how to express preconditions, postconditions, and loop invariants for some interesting programs. It is also possible to express properties such as disjointness of datastructures, and lowlevel heap mutations. Moreover, our logic can express properties of arbitrary datastructures and of an arbitrary number of pointer fields. The latter provides a way to naturally specify postconditions that relate the fields on the entry of a procedure to the field on the exit of a procedure. Therefore, it is possible to use the logic to automatically prove partial correctness of programs performing lowlevel heap mutations.
The Complexity of the Graded µCalculus
"... In classical logic, existential and universal quantifiers express that there exists at least one individual satisfying a formula, or that all individuals satisfy a formula. In many logics, these quantifiers have been generalized to express that, for a nonnegative integer n, at least n individual ..."
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Cited by 20 (2 self)
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In classical logic, existential and universal quantifiers express that there exists at least one individual satisfying a formula, or that all individuals satisfy a formula. In many logics, these quantifiers have been generalized to express that, for a nonnegative integer n, at least n individuals or all but n individuals satisfy a formula. In modal logics, graded modalities generalize standard existential and universal modalities in that they express, e.g., that there exist at least n accessible worlds satisfying a certain formula. Graded modalities are useful expressive means in knowledge representation; they are present in a variety of other knowledge representation formalisms closely related to modal logic.