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Practical reasoning for very expressive description logics
 Journal of the Interest Group in Pure and Applied Logics 8
, 2000
"... 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 t ..."
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Cited by 188 (23 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 satisfiability of the DL ALC extended with transitive and inverse roles and functional restrictions with respect to general concept inclusion axioms and role hierarchies; 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. We investigate the limits of decidability for this family of DLs, showing that relaxing the constraints placed on the kinds of roles used in number restrictions leads to the undecidability of all inference problems. Finally, we describe a number of optimisation techniques that are crucial in obtaining implementations of the decision procedures, which, despite the hight worstcase complexity of the problem, exhibit good performance with reallife problems. 1
Description Logics For Conceptual Data Modeling
, 1998
"... The article aims at establishing a logical approach to classbased data modeling. After a discussion on classbased formalisms for data modeling, we introduce a family of logics, called Description Logics, which stem from research on Knowledge Representation in Arti cial Intelligence. The logics ..."
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Cited by 144 (22 self)
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The article aims at establishing a logical approach to classbased data modeling. After a discussion on classbased formalisms for data modeling, we introduce a family of logics, called Description Logics, which stem from research on Knowledge Representation in Arti cial Intelligence. The logics of this family are particularly well suited for specifying data classes and relationships among classes, and are equipped with both formal semantics and inference mechanisms. We demonstrate that several popular data modeling formalisms, including the EntityRelationship Model, and the most common variants of objectoriented data models, can be expressed in terms of speci c logics of the family. For this purpose we use a unifying Description Logic, which incorporates all the features needed for the logical reformulation of the data models used in the various contexts. We also discuss the problem of devising reasoning procedures for the unifying formalism, and show that they provide valuable supports for several important data modeling activities.
Unifying classbased representation formalisms
 J. of Artificial Intelligence Research
, 1999
"... The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues underlying such representation formalisms and single out both their c ..."
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Cited by 100 (33 self)
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The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues underlying such representation formalisms and single out both their common characteristics and their distinguishing features. Such investigation leads us to propose a unifying framework in which we are able to capture the fundamental aspects of several representation languages used in different contexts. The proposed formalism is expressed in the style of description logics, which have been introduced in knowledge representation as a means to provide a semantically wellfounded basis for the structural aspects of knowledge representation systems. The description logic considered in this paper is a subset of first order logic with nice computational characteristics. It is quite expressive and features a novel combination of constructs that has not been studied before. The distinguishing constructs are number restrictions, which generalize existence and functional dependencies, inverse roles, which allow one to refer to the inverse of a relationship, and possibly cyclic assertions, which are necessary for capturing real world
Information integration: Conceptual modeling and reasoning support
 In Proceedings of the International Conference on Cooperative Information Systems
, 1998
"... Information Integration is one of the core problems in cooperative information systems. We argue that two critical factors for the design and maintenance of applications requiring Information Integration are conceptual modeling of the domain, and reasoning support over the conceptual representation. ..."
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Cited by 76 (9 self)
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Information Integration is one of the core problems in cooperative information systems. We argue that two critical factors for the design and maintenance of applications requiring Information Integration are conceptual modeling of the domain, and reasoning support over the conceptual representation. In particular, we present a general architecture for Information Integration that explicitly includes a conceptual representation of the application. We illustrate how the architecture can express several integration settings and existing systems. We provide various arguments in favor of the conceptual level in the architecture and of automated reasoning over the conceptual representation. Finally, we present a specific proposal of an integration system which realizes the general architecture and is equipped with decidable reasoning procedures. 1.
DATA INTEGRATION IN DATA WAREHOUSING
, 2001
"... Information integration is one of the most important aspects of a Data Warehouse. When data passes from the sources of the applicationoriented operational environment to the Data Warehouse, possible inconsistencies and redundancies should be resolved, so that the warehouse is able to provide an int ..."
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Cited by 68 (16 self)
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Information integration is one of the most important aspects of a Data Warehouse. When data passes from the sources of the applicationoriented operational environment to the Data Warehouse, possible inconsistencies and redundancies should be resolved, so that the warehouse is able to provide an integrated and reconciled view of data of the organization. We describe a novel approach to data integration in Data Warehousing. Our approach is based on a conceptual representation of the Data Warehouse application domain, and follows the socalled localasview paradigm: both source and Data Warehouse relations are defined as views over the conceptual model. We propose a technique for declaratively specifying suitable reconciliation correspondences to be used in order to solve conflicts among data in different sources. The main goal of the method is to support the design of mediators that materialize the data in the Data Warehouse relations. Starting from the specification of one such relation as a query over the conceptual model, a rewriting algorithm reformulates the query in terms of both the source relations and the reconciliation correspondences, thus obtaining a correct specification of how to load the data in the materialized view.
Reasoning in expressive description logics with fixpoints based on automata on infinite trees
 In Proc. of the 16th Int. Joint Conf. on Artificial Intelligence (IJCAI’99
, 1999
"... In the last years, the investigation on Description Logics (DLs) has been driven by the goal of applying them in several areas, such as, software engineering, information systems, databases, information integration, and intelligent access to the web. The modeling requirements arising in the above ar ..."
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Cited by 59 (12 self)
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In the last years, the investigation on Description Logics (DLs) has been driven by the goal of applying them in several areas, such as, software engineering, information systems, databases, information integration, and intelligent access to the web. The modeling requirements arising in the above areas have stimulated the need for very rich languages, including fixpoint constructs to represent recursive structures. We study a DL comprising the most general form of fixpoint constructs on concepts, all classical concept forming constructs, plus inverse roles, nary relations, qualified number restrictions, and inclusion assertions. We establish the EXPTIME decidability of such logic by presenting a decision procedure based on a reduction to nonemptiness of alternating automata on infinite trees. We observe that this is the first decidability result for a logic combining inverse roles, number restrictions, and general fixpoints. 1
What's in an aggregate: Foundations for description logics with tuples and sets
 In Proc. of IJCAI95
, 1995
"... Based on the research done in the last decade, attempts have been made to propose description logics as unifying formalisms for the various classbased representation languages used in different areas. These attempts have made apparent that sound, complete, and decidable description logics still suf ..."
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Cited by 50 (19 self)
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Based on the research done in the last decade, attempts have been made to propose description logics as unifying formalisms for the various classbased representation languages used in different areas. These attempts have made apparent that sound, complete, and decidable description logics still suffer from several limitations, regarding modeling classes of aggregate objects, expressing general inclusion axioms, and the ability of navigating links between classes. In this paper we make description logics accomplish the necessary leap in order to become suitable for the new challenging applications they are faced with. In particular, we propose a powerful description logic overcoming the above limitations and we show that its reasoning tasks are decidable in worst case exponential time. 1
Reasoning with inclusion axioms in description logics: Algorithms and complexity
 In Wahlster, W. (Ed.), Proc. of the 12th European Conf. on Artificial Intelligence (ECAI96
, 1996
"... Abstract. The computational complexity of reasoning on pure concept expressions has been characterized completely for all relevant description logics. On the contrary, reasoning in the presence of schema axioms is not so well understood and far from being settled completely. An important class of sc ..."
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Cited by 38 (10 self)
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Abstract. The computational complexity of reasoning on pure concept expressions has been characterized completely for all relevant description logics. On the contrary, reasoning in the presence of schema axioms is not so well understood and far from being settled completely. An important class of schemata is that of primitive schemata (in which the schema axioms express only necessary conditions) possibly containing cycles. In this paper we provide, for a relevant class of description logics, a complete characterization of computational complexity of reasoning in these types of schemata, both in the presence and in the absence of cycles. The results are obtained by devising reasoning procedures, establishing direct reductions to show lower bounds, and introducing a general technique by which the constructor for existential quantification can be removed without influencing the result of reasoning. 1
PSpace Reasoning for Graded Modal Logics
, 1999
"... We present a PSpace algorithm that decides satisfiability of the graded modal logic Gr(KR)  a natural extension of propositional modal logic KR by counting expressions  which plays an important role in the area of knowledge representation. The algorithm employs a tableaux approach and is the rst k ..."
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Cited by 36 (1 self)
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We present a PSpace algorithm that decides satisfiability of the graded modal logic Gr(KR)  a natural extension of propositional modal logic KR by counting expressions  which plays an important role in the area of knowledge representation. The algorithm employs a tableaux approach and is the rst known algorithm which meets the lower bound for the complexity of the problem. Thus, we exactly fix the complexity of the problem and refute an ExpTimehardness conjecture. We extend the results to the logic Gr(K R 1 \ ), which augments Gr(KR) with inverse modalities and intersection of accessibility relations. This establishes a kind of "theoretical benchmark" that all algorithmic approaches can be measured with.