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16
The power of commuting with finite sets of words
 In Proc. STACS’05, Springer LNCS 3404
, 2005
"... We construct a finite language L such that the largest language commuting with L is not recursively enumerable. This gives a negative answer to the question raised by Conway in 1971 and also strongly disproves Conway’s conjecture on contextfreeness of maximal solutions of systems of semilinear ine ..."
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We construct a finite language L such that the largest language commuting with L is not recursively enumerable. This gives a negative answer to the question raised by Conway in 1971 and also strongly disproves Conway’s conjecture on contextfreeness of maximal solutions of systems of semilinear inequalities. 1
Unification in the Description Logic EL
"... Abstract. The Description Logic EL has recently drawn considerable attention since, on the one hand, important inference problems such as the subsumption problem are polynomial. On the other hand, EL is used to define large biomedical ontologies. Unification in Description Logics has been proposed a ..."
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Abstract. The Description Logic EL has recently drawn considerable attention since, on the one hand, important inference problems such as the subsumption problem are polynomial. On the other hand, EL is used to define large biomedical ontologies. Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. The main result of this paper is that unification in EL is decidable. More precisely, we show that ELunification is NPcomplete, and thus has the same complexity as ELmatching. 1
Strict language inequalities and their decision problems
 Mathematical Foundations of Computer Science (MFCS 2005
, 2005
"... Abstract. Systems of language equations of the form {ϕ(X1,..., Xn) = ∅, ψ(X1,..., Xn) � = ∅} are studied, where ϕ, ψ may contain settheoretic operations and concatenation; they can be equivalently represented as strict inequalities ξ(X1,..., Xn) ⊂ L0. It is proved that the problem whether such an ..."
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Abstract. Systems of language equations of the form {ϕ(X1,..., Xn) = ∅, ψ(X1,..., Xn) � = ∅} are studied, where ϕ, ψ may contain settheoretic operations and concatenation; they can be equivalently represented as strict inequalities ξ(X1,..., Xn) ⊂ L0. It is proved that the problem whether such an inequality has a solution is Σ2complete, the problem whether it has a unique solution is in (Σ3 ∩Π3)\(Σ2 ∪Π2), the existence of a regular solution is a Σ1complete problem, while testing whether there are finitely many solutions is Σ3complete. The class of languages representable by their unique solutions is exactly the class of recursive sets, though a decision procedure cannot be algorithmically constructed out of an inequality, even if a proof of solution uniqueness is attached. 1
Simplifying Schema Mappings
"... A schema mapping is a formal specification of the relationship holding between the databases conforming to two given schemas, called source and target, respectively. While in the general case a schema mapping is specified in terms of assertions relating two queries in some given language, various si ..."
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A schema mapping is a formal specification of the relationship holding between the databases conforming to two given schemas, called source and target, respectively. While in the general case a schema mapping is specified in terms of assertions relating two queries in some given language, various simplified forms of mappings, in particular LAV and GAV, have been considered, based on desirable properties that these forms enjoy. Recent works propose methods for transforming schema mappings to logically equivalent ones of a simplified form. In many cases, this transformation is impossible, and one might be interested in finding simplifications based on a weaker notion, namely logical implication, rather than equivalence. More precisely, given a schema mapping M, find a simplified (LAV, or GAV) schema mapping M ′ such that M ′ logically implies M. In this paper we formally introduce this problem, and study it in a variety of cases, providing techniques and complexity bounds. The various cases we consider depend on three parameters: the simplified form to achieve (LAV, or GAV), the type of schema mapping considered (sound, or exact), and the query language used in the schema mapping specification (conjunctive queries and variants over relational databases, or regular path queries and variants over graph databases). Notably, this is the first work on comparing schema mappings for graph databases. Categories and Subject Descriptors D.2.12 [Software Engineering]: Interoperability—data mapping; H.2.3 [Database Management]: Languages—
Description Logics: Foundations for Classbased Knowledge Representation
 IN LICS'02
, 2002
"... Classbased languages express knowledge in terms of objects and classes, and have inspired a huge number of formalisms in computer science. Description logics form a family of both classbased and logicbased knowledge representation languages which allow for modeling an application domain in terms ..."
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Classbased languages express knowledge in terms of objects and classes, and have inspired a huge number of formalisms in computer science. Description logics form a family of both classbased and logicbased knowledge representation languages which allow for modeling an application domain in terms of objects, classes and relationships between classes, and for reasoning about them. This paper presents an overview of the research carried out in the last years in description logics, with the main goal of illustrating how these logics provide the foundations for classbased knowledge representation formalisms.
Simple language equations
 Bull. Eur. Assoc. Theor. Comput. Sci. EATCS
, 2005
"... Abstract. We survey results, both positive and negative, on regularity of maximal solutions of systems of implicit language equations and inequalities. These results concern inequalities with constant righthand sides, onesided linear inequalities, inequalities with restrictions on constants, and c ..."
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Abstract. We survey results, both positive and negative, on regularity of maximal solutions of systems of implicit language equations and inequalities. These results concern inequalities with constant righthand sides, onesided linear inequalities, inequalities with restrictions on constants, and commutation equations and inequalities. In addition, we present some of these results in a generalized form in order to underline common principles. 1.
Unification in a Description Logic with Inconsistency and Transitive Closure of Roles
, 2002
"... Unification considers concept patterns, i.e., concept descriptions with variables, and tries to make these descriptions equivalent by replacing the variables by appropriate concept descriptions. Baader and Küsters have shown that unification in FL reg , a description logic that allows for the co ..."
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Unification considers concept patterns, i.e., concept descriptions with variables, and tries to make these descriptions equivalent by replacing the variables by appropriate concept descriptions. Baader and Küsters have shown that unification in FL reg , a description logic that allows for the concept constructors top concept, concept conjunction, and value restrictions as well as the role constructors union, composition, and transitive closure, is an ExpTimecomplete problem and that solvable FL reg  unification problems always have least unifiers. In the present paper, we generalize these results to a DL which extends FL reg by the bottom concept. The proof
Capability Management and Discovery in Description Logic, in "3rd International Workshop on Enterprise Modelling and Ontologies for Interoperability  EMOI’06, in connection with CAiSE’2006
 Proceedings of the EMOI’06 (3rd International Workshop on Enterprise Modelling and Ontologies for Interoperability), in connection with the 18th Conference on Advanced Information Systems Engineering, CAiSE’2006., Oui, Presses Universitaires de Namur
"... Abstract. In some application domains as composite software, ranging from search engines, to more general applications, like cooperative and distributed applications or ebusiness and ecommerce applications, more and more rely on capability description. In this paper we try to highlight some concep ..."
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Abstract. In some application domains as composite software, ranging from search engines, to more general applications, like cooperative and distributed applications or ebusiness and ecommerce applications, more and more rely on capability description. In this paper we try to highlight some concepts concerning capability description and discovery, and we discuss the relationship between capabilities. Specifically, we choose a capability description language, as and extension of ALN Description Logics languages. The mediation services are expected to play an important role in helping automated processes to access heterogeneous information. They are not Yes/No answers from the mediator, when no single object meets the search criteria, they may be cooperative answers to make a composite answer. 1.
On Language Equations with OneSided Concatenation
, 2006
"... Language equations are equations where both the constants occurring in the equations and the solutions are formal languages. They have first been introduced in formal language theory, but are now also considered in other areas of computer science. In the present paper, we restrict the attention to l ..."
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Language equations are equations where both the constants occurring in the equations and the solutions are formal languages. They have first been introduced in formal language theory, but are now also considered in other areas of computer science. In the present paper, we restrict the attention to language equations with onesided concatenation, but in contrast to previous work on these equations, we allow not just union but all Boolean operations to be used when formulating them. In addition, we are not just interested in deciding solvability of such equations, but also in deciding other properties of the set of solutions, like its cardinality (finite, infinite, uncountable) and whether it contains least/greatest solutions. We show that all these decision problems are ExpTimecomplete.
NonStandard Inferences in Description Logics: The Story So Far
"... Abstract Description logics (DLs) are a successful family of logicbased knowledge representation formalisms that can be used to represent the terminological knowledge of an ..."
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Abstract Description logics (DLs) are a successful family of logicbased knowledge representation formalisms that can be used to represent the terminological knowledge of an