Results 1  10
of
184
Econnections of abstract description systems
"... Combining knowledge representation and reasoning formalisms is an important and challenging task. It is important because nontrivial AI applications often comprise different aspects of the world, thus requiring suitable combinations of available formalisms modeling each of these aspects. It is chal ..."
Abstract

Cited by 126 (34 self)
 Add to MetaCart
(Show Context)
Combining knowledge representation and reasoning formalisms is an important and challenging task. It is important because nontrivial AI applications often comprise different aspects of the world, thus requiring suitable combinations of available formalisms modeling each of these aspects. It is challenging because the computational behavior of the resulting hybrids is often much worse than the behavior of their components. In this paper, we propose a new combination method which is computationally robust in the sense that the combination of decidable formalisms is again decidable, and which, nonetheless, allows nontrivial interactions between the combined components. The new method, called Econnection, is defined in terms of abstract description systems (ADSs), a common generalization of description logics, many logics of time and space, as well as modal and epistemic logics. The basic idea of Econnections is that the interpretation domains of n combined systems are disjoint, and that these domains are connected by means of nary ‘link relations. ’ We define several natural variants of Econnections and study indepth the transfer of decidability from the component systems to their Econnections. Key words: description logics, temporal logics, spatial logics, combining logics, decidability.
Temporal Description Logics: A Survey
, 2008
"... We survey temporal description logics that are based on standard temporal logics such as LTL and CTL. In particular, we concentrate on the computational complexity of the satisfiability problem and algorithms for deciding it. ..."
Abstract

Cited by 56 (11 self)
 Add to MetaCart
We survey temporal description logics that are based on standard temporal logics such as LTL and CTL. In particular, we concentrate on the computational complexity of the satisfiability problem and algorithms for deciding it.
LTL over description logic axioms
 In Proceedings of DL08, CEUR Workshop Proceedings. CEURWS.org
, 2008
"... In many applications of Description Logics (DLs) [7], such as the use of DLs as ontology languages or conceptual modeling languages, being able to represent dynamic aspects of the application domain would be quite useful. This is, for instance, the case if one wants to use DLs as conceptual modeling ..."
Abstract

Cited by 43 (13 self)
 Add to MetaCart
(Show Context)
In many applications of Description Logics (DLs) [7], such as the use of DLs as ontology languages or conceptual modeling languages, being able to represent dynamic aspects of the application domain would be quite useful. This is, for instance, the case if one wants to use DLs as conceptual modeling languages
An AutomataTheoretic Approach to Constraint LTL
, 2003
"... We consider an extension of lineartime temporal logic (LTL) with constraints interpreted over a concrete domain. We use a new automatatheoretic technique to show pspace decidability of the logic for the constraint systems (Z, <, =) and (N, <, =). Along the way, we give an automatatheoretic ..."
Abstract

Cited by 32 (7 self)
 Add to MetaCart
We consider an extension of lineartime temporal logic (LTL) with constraints interpreted over a concrete domain. We use a new automatatheoretic technique to show pspace decidability of the logic for the constraint systems (Z, <, =) and (N, <, =). Along the way, we give an automatatheoretic proof of a result of [BC02] when the constraint system D satisfies the completion property. Our decision procedures extend easily to handle extensions of the logic with past operators and constants, as well as an extension of the temporal language itself to monadic second order logic. Finally, we show that the logic...
Rules and Queries with Ontologies: Unified Logical Framework
 In Workshop on Principles and Practice of Semantic Web Reasoning (PPSWR04
, 2004
"... In this paper we present a common framework for investigating the problem of combining ontology and rule languages. The focus of this paper is in the context of Semantic Web (SW), but the approach can be applied in any Description Logics (DL) based system. In the last part, we will show how rule ..."
Abstract

Cited by 29 (1 self)
 Add to MetaCart
In this paper we present a common framework for investigating the problem of combining ontology and rule languages. The focus of this paper is in the context of Semantic Web (SW), but the approach can be applied in any Description Logics (DL) based system. In the last part, we will show how rules are strictly related to queries.
Temporalising Tractable Description Logics
"... It is known that for temporal languages, such as firstorder LTL, reasoning about constant (timeindependent) relations is almost always undecidable. This applies to temporal description logics as well: constant binary relations together with general concept subsumptions in combinations of LTL and t ..."
Abstract

Cited by 28 (8 self)
 Add to MetaCart
(Show Context)
It is known that for temporal languages, such as firstorder LTL, reasoning about constant (timeindependent) relations is almost always undecidable. This applies to temporal description logics as well: constant binary relations together with general concept subsumptions in combinations of LTL and the basic description logic ALC cause undecidability. In this paper, we explore temporal extensions of two recently introduced families of ‘weak’ description logics known as DLLite and EL. Our results are twofold: temporalisations of even rather expressive variants of DLLite turn out to be decidable, while the temporalisation of EL with general concept subsumptions and constant relations is undecidable.
On the Products of Linear Modal Logics
 JOURNAL OF LOGIC AND COMPUTATION
, 2001
"... We study twodimensional Cartesian products of modal logics determined by infinite or arbitrarily long finite linear orders and prove a general theorem showing that in many cases these products are undecidable, in particular, such are the squares of standard linear logics like K4:3, S4:3, GL:3, Grz: ..."
Abstract

Cited by 27 (10 self)
 Add to MetaCart
We study twodimensional Cartesian products of modal logics determined by infinite or arbitrarily long finite linear orders and prove a general theorem showing that in many cases these products are undecidable, in particular, such are the squares of standard linear logics like K4:3, S4:3, GL:3, Grz:3, or the logic determined by the Cartesian square of any infinite linear order. This theorem solves a number of open problems of Gabbay and Shehtman [7]. We also prove a sufficient condition for such products to be not recursively enumerable and give a simple axiomatisation for the square K4:3 K4:3 of the minimal liner logic using nonstructural Gabbaytype inference rules.
MODAL LOGICS OF TOPOLOGICAL RELATIONS
 ACCEPTED FOR PUBLICATION IN LOGICAL METHODS IN COMPUTER SCIENCE
, 2006
"... Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham’s modal logic of time intervals based on the Allen relations, we int ..."
Abstract

Cited by 26 (6 self)
 Add to MetaCart
(Show Context)
Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham’s modal logic of time intervals based on the Allen relations, we introduce a family of modal logics equipped with eight modal operators that are interpreted by the EgenhoferFranzosa (or RCC8) relations between regions in topological spaces such as the real plane. We investigate the expressive power and computational complexity of logics obtained in this way. It turns out that our modal logics have the same expressive power as the twovariable fragment of firstorder logic, but are exponentially less succinct. The complexity ranges from (undecidable and) recursively enumerable to Π 1 1hard, where the recursively enumerable logics are obtained by considering substructures of structures induced by topological spaces. As our undecidability results also capture logics based on the real line, they improve upon undecidability results for interval temporal logics by Halpern and Shoham. We also analyze modal logics based on the five RCC5 relations, with similar results regarding the expressive power, but weaker results regarding the complexity.