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19
Modal characterisation theorems over special classes of frames
 ANNALS OF PURE AND APPLIED LOGIC 161 (2009) 1–42
, 2009
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Formal Properties of Modularisation
"... Summary. Modularity of ontologies is currently an active research field, and many different notions of a module have been proposed. In this paper, we review the fundamental principles of modularity and identify formal properties that a robust notion of modularity should satisfy. We explore these pro ..."
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Cited by 11 (4 self)
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Summary. Modularity of ontologies is currently an active research field, and many different notions of a module have been proposed. In this paper, we review the fundamental principles of modularity and identify formal properties that a robust notion of modularity should satisfy. We explore these properties in detail in the contexts of description logic and classical predicate logic and put them into the perspective of wellknown concepts from logic and modular software specification such as interpolation, forgetting and uniform interpolation. We also discuss reasoning problems related to modularity. 1
Foundations for Uniform Interpolation and Forgetting in Expressive Description Logics
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2011
"... We study uniform interpolation and forgetting in the description logic ALC. Our main results are modeltheoretic characterizations of uniform interpolants and their existence in terms of bisimulations, tight complexity bounds for deciding the existence of uniform interpolants, an approach to computi ..."
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Cited by 7 (1 self)
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We study uniform interpolation and forgetting in the description logic ALC. Our main results are modeltheoretic characterizations of uniform interpolants and their existence in terms of bisimulations, tight complexity bounds for deciding the existence of uniform interpolants, an approach to computing interpolants when they exist, and tight bounds on their size. We use a mix of modeltheoretic and automatatheoretic methods that, as a byproduct, also provides characterizations of and decision procedures for conservative extensions.
Description Logic TBoxes: ModelTheoretic Characterizations and Rewritability
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2011
"... We characterize the expressive power of description logic (DL) TBoxes, both for expressive DLs such as ALC and ALCQIO and lightweight DLs such as DLLite and EL. Our characterizations are relative to firstorder logic, based on a wide range of semantic notions such as bisimulation, equisimulation, d ..."
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Cited by 5 (1 self)
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We characterize the expressive power of description logic (DL) TBoxes, both for expressive DLs such as ALC and ALCQIO and lightweight DLs such as DLLite and EL. Our characterizations are relative to firstorder logic, based on a wide range of semantic notions such as bisimulation, equisimulation, disjoint union, and direct product. We exemplify the use of the characterizations by a first study of the following novel family of decision problems: given a TBox T formulated in a DL L, decide whether T can be equivalently rewritten as a TBox in the fragment L ′ of L.
Relative Expressive Power of Navigational Querying on Graphs
"... Motivated by both established and new applications, we study navigational query languages for graphs (binary relations). The simplest language has only the two operators union and composition, together with the identity relation. We make more powerful languages by adding any of the following operato ..."
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Cited by 4 (0 self)
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Motivated by both established and new applications, we study navigational query languages for graphs (binary relations). The simplest language has only the two operators union and composition, together with the identity relation. We make more powerful languages by adding any of the following operators: intersection; set difference; projection; coprojection; converse; transitive closure; and the diversity relation. All these operators map binary relations to binary relations. We compare the expressive power of all resulting languages. We do this not only for general path queries (queries where the result may be any binary relation) but also for boolean or yes/no queries (expressed by the nonemptiness of an expression). For both cases, we present the complete Hasse diagram of relative expressiveness. In particular, the Hasse diagram for boolean queries contains nontrivial separations and a few surprising collapses.
ELConcepts go SecondOrder: Greatest Fixpoints and Simulation Quantifiers
"... The wellknown description logic (DL) ALC is usually regarded as the basic DL that comprises all Boolean concept constructors from which all expressive DLs are derived by admitting additional concept constructors. The fundamental role of ALC is largely due to the fact that it is very wellbehaved re ..."
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Cited by 2 (1 self)
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The wellknown description logic (DL) ALC is usually regarded as the basic DL that comprises all Boolean concept constructors from which all expressive DLs are derived by admitting additional concept constructors. The fundamental role of ALC is largely due to the fact that it is very wellbehaved regarding its logical, modeltheoretic, and
Beth Definability in Expressive Description Logics
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2011
"... The Beth definability property, a wellknown property from classical logic, is investigated in the context of description logics (DLs): if a general LTBox implicitly defines an Lconcept in terms of a given signature, where L is a DL, then does there always exist over this signature an explicit def ..."
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Cited by 1 (1 self)
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The Beth definability property, a wellknown property from classical logic, is investigated in the context of description logics (DLs): if a general LTBox implicitly defines an Lconcept in terms of a given signature, where L is a DL, then does there always exist over this signature an explicit definition in L for the concept? This property has been studied before and used to optimize reasoning in DLs. In this paper a complete classification of Beth definability is provided for extensions of the basic DL ALC with transitive roles, inverse roles, role hierarchies, and/or functionality restrictions, both on arbitrary and on finite structures. Moreover, we present a tableaubased algorithm which computes explicit definitions of at most double exponential size. This algorithm is optimal because it is also shown that the smallest explicit definition of an implicitly defined concept may be double exponentially long in the size of the input TBox. Finally, if explicit definitions are allowed to be expressed in firstorder logic then we show how to compute them in EXPTIME.
Towards a Theory of Search Queries
"... The need to manage diverse information sources has triggered the rise of very loosely structured data models, known as “dataspace models. ” Such information management systems must allow querying in simple ways, mostly by a form of searching. Motivated by these developments, we propose a theory of s ..."
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Cited by 1 (0 self)
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The need to manage diverse information sources has triggered the rise of very loosely structured data models, known as “dataspace models. ” Such information management systems must allow querying in simple ways, mostly by a form of searching. Motivated by these developments, we propose a theory of search queries in a general model of dataspaces. In this model, a dataspace is a collection of data objects, where each data object is a collection of data items. Basic search queries are expressed using filters on data items, following the basic model of boolean search in information retrieval. We characterise semantically the class of queries that can be expressed by searching. We apply our theory to classical relational databases, where we connect search queries to the known class of fully generic queries, and to dataspaces where data items are formed by attribute–value pairs. We also extend our theory to a more powerful, associative form of searching where one can ask for objects that are similar to objects satisfying given search conditions. Such associative search queries are shown to correspond to a very limited kind of joins. Specifically, we show that the basic search language extended with associative search can define exactly the queries definable in a restricted fragment of the semijoin algebra working on an explicit relational representation of the dataspace. 1.
Doing Argumentation Theory in Modal Logic
, 2009
"... The present paper applies wellinvestigated modal logics to provide formal foundations to specific fragments of argumentation theory. This logicdriven analysis of argumentation allows: first, to systematize several results of argumentation theory reformulating them within suitable formal languages; ..."
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The present paper applies wellinvestigated modal logics to provide formal foundations to specific fragments of argumentation theory. This logicdriven analysis of argumentation allows: first, to systematize several results of argumentation theory reformulating them within suitable formal languages; second, to import several techniques (calculi, modelchecking, evaluation games, bisimulation games); third, to import results (eminently completeness of axiomatizations, and complexity of modelchecking) from modal logic to argumentation theory.