Franz Baader
Tu Dresden Germany, Computer Science, Faculty Member
Simple counting quantifiers that can be used to compare the number of role successors of an individual or the cardinality of a concept with a fixed natural number have been employed in Description Logics (DLs) for more than two decades... more
Simple counting quantifiers that can be used to compare the number of role successors of an individual or the cardinality of a concept with a fixed natural number have been employed in Description Logics (DLs) for more than two decades under the respective names of number restrictions and cardinality restrictions on concepts. Recently, we have considerably extended the expressivity of such quantifiers by allowing to impose set and cardinality constraints formulated in the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA) on sets of role successors and concepts, respectively. We were able to prove that this extension does not increase the complexity of reasoning. In the present paper, we investigate the expressive power of the DLs obtained in this way, using appropriate bisimulation characterizations and 0–1 laws as tools to differentiate between the expressiveness of different logics. In particular, we show that, in contrast to most classical DLs, these...
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Simple counting quantifiers that can be used to compare the number of role successors of an individual or the cardinality of a concept with a fixed natural number have been employed in Description Logics (DLs) for more than two decades... more
Simple counting quantifiers that can be used to compare the number of role successors of an individual or the cardinality of a concept with a fixed natural number have been employed in Description Logics (DLs) for more than two decades under the respective names of number restrictions and cardinality restriction on concepts. Recently, we have considerably extended the expressivity of such quantifiers by allowing to impose set and cardinality constraints formulated in the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA) on sets of role successors and concepts, respectively. We were able to prove that this extension does not increase the complexity of reasoning.In the present paper, we investigate the expressive power of the DLs obtained this way, using appropriate bisimulation characterizations and 0--1 laws as tools for distinguishing the expressiveness of different logics. In particular, we show that, in contrast to most classical DLs, these logics ar...
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In two previous publications we have, on the one hand, extended the description logic (DL) ALCQ by more expressive number restrictions using numerical and set constraints expressed in the quantifier-free fragment of Boolean Algebra with... more
In two previous publications we have, on the one hand, extended the description logic (DL) ALCQ by more expressive number restrictions using numerical and set constraints expressed in the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA). The resulting DL was called ALCSCC . On the other hand, we have extended the terminological formalism of the well-known description logic ALC from concept inclusions (CIs) to more general cardinality constraints expressed in QFBAPA, which we called extended cardinality constraints. Here, we combine the two extensions, i.e., we consider extended cardinality constraints on ALCSCC concepts. We show that this does not increase the complexity of reasoning, which is NExpTime-complete both for extended cardinality constraints in the DL ALC and in its extension ALCSCC . The same is true for a restricted version of such cardinality constraints, where the complexity of reasoning decreases to ExpTime, not just for ALC , but also ...
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Unification in description logics (DLs) has been proposed as a means to detect redundancies in ontologies. The DL EL, even though quite inexpressive, can be used to formulate large medical ontologies like SNOMED CT. Previously, several... more
Unification in description logics (DLs) has been proposed as a means to detect redundancies in ontologies. The DL EL, even though quite inexpressive, can be used to formulate large medical ontologies like SNOMED CT. Previously, several unification algorithms for EL were developed that can only deal with acyclic terminologies. In this paper, we give an overview over our recent efforts to generalize these algorithms to allow for general concept inclusions, transitive roles, and role hierarchies. For our new algorithms to be complete, the ontology needs to satisfy a certain cycle restriction.
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Fusions are a simple way of combining logics. For normal modal logics, fusions have been investigated in detail. In particular, it is known that, under certain conditions, decidability transfers from the component logics to their fusion.... more
Fusions are a simple way of combining logics. For normal modal logics, fusions have been investigated in detail. In particular, it is known that, under certain conditions, decidability transfers from the component logics to their fusion. Though description logics are closely related to modal logics, they are not necessarily normal. In addition, ABox reasoning in description logics is not covered by the results from modal logics. In this paper, we extend the decidability transfer results from normal modal logics to a large class of description logics. To cover different description logics in a uniform way, we introduce abstract description systems, which can be seen as a common generalization of description and modal logics, and show the transfer results in this general setting.
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Temporal query entailment in the Description Logic <mml:math altimg="si5.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/...more
ABSTRACT Ontology-based data access (OBDA) generalizes query answering in databases towards deductive entailment since (i) the fact base is not assumed to contain complete knowledge (i.e., there is no closed world assumption), and (ii)... more
ABSTRACT Ontology-based data access (OBDA) generalizes query answering in databases towards deductive entailment since (i) the fact base is not assumed to contain complete knowledge (i.e., there is no closed world assumption), and (ii) the interpretation of the predicates occurring in the queries is constrained by axioms of an ontology. OBDA has been investigated in detail for the case where the ontology is expressed by an appropriate Description Logic (DL) and the queries are conjunctive queries. Motivated by situation awareness applications, we investigate an extension of OBDA to the temporal case. As the query language we consider an extension of the well-known propositional temporal logic LTL where conjunctive queries can occur in place of propositional variables, and as the ontology language we use the expressive DL SHQ. For the resulting instance of temporalized OBDA, we investigate both data complexity and combined complexity of the query entailment problem. In the course of this investigation, we also establish the complexity of consistency of Boolean knowledge bases in SHQ.
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Abstract. Description logics are a family of knowledge representation formalisms that are descended from semantic networks and frames via the system Kl-one. During the last decade, it has been shown that the important reasoning problems... more
Abstract. Description logics are a family of knowledge representation formalisms that are descended from semantic networks and frames via the system Kl-one. During the last decade, it has been shown that the important reasoning problems (like subsumption and satisfiability) in a ...
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The Nelson-Oppen combination method can be used to combinedecision procedures for the validity of quantifier-free formulae in firstordertheories with disjoint signatures, provided that the theories tobe combined are stably infinite. We... more
The Nelson-Oppen combination method can be used to combinedecision procedures for the validity of quantifier-free formulae in firstordertheories with disjoint signatures, provided that the theories tobe combined are stably infinite. We show that, even though equationaltheories need not satisfy this property, Nelson and Oppen&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s method canbe applied, after some minor modifications, to combine decision proceduresfor the validity of quantifier-free formulae
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The knowledge representation system KL-ONE first appeared in 1977. Subsequently many systems based on the idea of KL-ONE have been built. The formal model-theoretic semantics which has been introduced for KL-ONE languages [9] provides... more
The knowledge representation system KL-ONE first appeared in 1977. Subsequently many systems based on the idea of KL-ONE have been built. The formal model-theoretic semantics which has been introduced for KL-ONE languages [9] provides means for investigating soundness ...
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Abstract. Description logics are a family of knowledge representation formalisms that are descended from semantic networks and frames via the system Kl-one. During the last decade, it has been shown that the important reasoning problems... more
Abstract. Description logics are a family of knowledge representation formalisms that are descended from semantic networks and frames via the system Kl-one. During the last decade, it has been shown that the important reasoning problems (like subsumption and satisfiability) in a ...
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Unification in acommunitativc theory Emaybereduced tosolving linear equations in the corresponding semiring S(E) (37). The unification type of E can thus be characterized by algebraic properties of S(E). The theory of Abelian groups with... more
Unification in acommunitativc theory Emaybereduced tosolving linear equations in the corresponding semiring S(E) (37). The unification type of E can thus be characterized by algebraic properties of S(E). The theory of Abelian groups with n commuting homomorphisms corresponds to the semiring ZIXI, ..., x,,). Thus, Hilbert&#x27;s Basis Theorem can bc used to show that this theory is unitary. But this
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Extensions of the description logic EL have recently been proposed as lightweight ontology languages. The most important feature of these extensions is that, despite including powerful expressive means such as general concept inclusion... more
Extensions of the description logic EL have recently been proposed as lightweight ontology languages. The most important feature of these extensions is that, despite including powerful expressive means such as general concept inclusion axioms, reasoning can be carried out in polynomial time. In this paper, we consider one of these extensions,EL + , and introduce a renement of the known
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... Our thanks in this respect go to the following companies: Microsoft, Siemens, Springer-Verlag, and Sysis, and the following institutions and organizations: the European Commis-sion, the Austrian Computer Society ... September 2001... more
... Our thanks in this respect go to the following companies: Microsoft, Siemens, Springer-Verlag, and Sysis, and the following institutions and organizations: the European Commis-sion, the Austrian Computer Society ... September 2001 Franz Baader Gerhard Brewka Thomas Eiter ...
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... 2 Description Logics ... Description Logics4 are logic-based formalisms that are based on the same ideas as Semantic Networks and Frames, but avoid the formal deficiencies that made the use of these precursor formalisms as KR... more
... 2 Description Logics ... Description Logics4 are logic-based formalisms that are based on the same ideas as Semantic Networks and Frames, but avoid the formal deficiencies that made the use of these precursor formalisms as KR formalisms problematic. Precursors. ...
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... Machine Learning, 17(2/3), 1994. 9. WW Cohen and H. Hirsh. Learning the classic descriptionlogic: Theoretical and experimental results. ... Morgan Kaufmann. 10. J.-U. Kietz and K. Morik. A polynomial approach to the constructive... more
... Machine Learning, 17(2/3), 1994. 9. WW Cohen and H. Hirsh. Learning the classic descriptionlogic: Theoretical and experimental results. ... Morgan Kaufmann. 10. J.-U. Kietz and K. Morik. A polynomial approach to the constructive induction of structural knowledge. ...