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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 ..."
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Cited by 95 (25 self)
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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.
Logics of Metric Spaces
, 2001
"... This paper investigates the expressive power and computational properties of languages designed for speaking about distances. `Distances' can be induced by difAuthors Addresses: Oliver Kutz, Frank Wolter, Institut fur Informatik, Abteilung intelligente Systeme, Universitat Leipzig, AugustusPlatz 10 ..."
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Cited by 27 (21 self)
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This paper investigates the expressive power and computational properties of languages designed for speaking about distances. `Distances' can be induced by difAuthors Addresses: Oliver Kutz, Frank Wolter, Institut fur Informatik, Abteilung intelligente Systeme, Universitat Leipzig, AugustusPlatz 1011, 04109 Leipzig, Germany; Holger Sturm, Fachbereich Philosophie, Universitat Konstanz, 78457 Konstanz, Germany; NobuYuki Suzuki, Department of Mathematics, Faculty of Science, Shizuoka University, Ohya 836, Shizuoka 422 8529, Japan; Michael Zakharyaschev, Department of Computer Science, King's College, Strand, London WC2R 2LS, U.K. Emails: {kutz, wolter}@informatik.unileipzig.de, holger.sturm@unikonstanz.de, smnsuzu@ipz.shizuoka.ac.jp, and mz@dcs.kcl.ac.uk Permission to make digital/hard copy of all or part of this material without fee for personal or classroom use provided that the copies are not made or distributed for profit or commercial advantage, the ACM copyright/server notice, the title of the publication, and its date appear, and notice is given that copying is by permission of the ACM, Inc. To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior specific permission and/or a fee
A Note on Concepts and Distances
, 2001
"... We combine the description logic ALC with the metric logics defined in [15]. Entities that are conceived of as abstract points in the realm of ALC are given a spatial extension via an `extension relation,' connecting abstract points in the domain of an ALCmodel to points in a metric space. Conv ..."
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Cited by 8 (2 self)
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We combine the description logic ALC with the metric logics defined in [15]. Entities that are conceived of as abstract points in the realm of ALC are given a spatial extension via an `extension relation,' connecting abstract points in the domain of an ALCmodel to points in a metric space. Conversely, regions in the metric space are connected via the converse `extension relation' to certain points in the ALCmodel. We prove the decidability of the satisfiability problem for the resulting hybrid formalism, give a few examples, and discuss further extensions of the ideas introduced.
Modal logics for metric spaces: Open problems
 We Will Show Them! Essays in Honour of Dov Gabbay, Volume Two
, 2005
"... The aim of this note is to attract attention to the most important open problems and new directions of research in this exciting and promising area. 1 Distance spaces Recall that a metric space is a pair (\Delta; d), where \Delta is a nonempty set (of points) and d is a function from \Delta \Theta \ ..."
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Cited by 5 (1 self)
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The aim of this note is to attract attention to the most important open problems and new directions of research in this exciting and promising area. 1 Distance spaces Recall that a metric space is a pair (\Delta; d), where \Delta is a nonempty set (of points) and d is a function from \Delta \Theta \Delta into the set R *0 (of nonnegative real numbers) satisfying the following
Axiomatizing Distance Logics
"... In [8, 6] we introduced a family of `modal' languages intended for talking about distances. These languages are interpreted in `distance spaces' which satisfy some (or all) of the standard axioms of metric spaces. Among other things, we singled out decidable logics of distance spaces and proved expr ..."
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Cited by 2 (1 self)
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In [8, 6] we introduced a family of `modal' languages intended for talking about distances. These languages are interpreted in `distance spaces' which satisfy some (or all) of the standard axioms of metric spaces. Among other things, we singled out decidable logics of distance spaces and proved expressive completeness results relating classical and modal languages. The aim of this paper is to axiomatize the modal fragments of the semantically defined distance logics of [6] and give a new proof of their decidability.
Connecting Description Systems
, 2002
"... Combining knowledge representation and reasoning formalisms like description logics (DLs), temporal logics, and logics of space, is worthwhile but difficult. It is worthwhile because usually application domains comprise various aspects of the world, thus requiring suitable combinations of formalisms ..."
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Combining knowledge representation and reasoning formalisms like description logics (DLs), temporal logics, and logics of space, is worthwhile but difficult. It is worthwhile because usually application domains comprise various aspects of the world, thus requiring suitable combinations of formalisms modeling each of the aspects. It is difficult because the computational behavior of the resulting hybrids is often much worth than the behavior of it components. In this paper we propose a combination method which is robust in the computational sense and still allows for interactions between the combined systems. The combination methodcalled Econnectionwill be defined and investigated for socalled abstract description systems (ADS) which subsume all standard description logics, various logics of time and space, modal logics, and epistemic logics. The main theoretical result is that the Econnection of any finite set of decidable ADSs is decidable as well. Four instances of Econnections of ADSs will be discussed: (1) The Econnection of DLs with the logic MS for quantitative reasoning about space, (2) the Econnection of DLs with the logic S4 u (containing RCC8) for qualitative reasoning about space, (3) the Econnection of two DLs (ALCO and SHIQ), and (4) the Econnection of DLs with propositional temporal logic PTL and S4 u . 1 1
Axiomatizing Distance Logics
"... In [8, 6] we introduced a family of `modal' languages intended for talking about distances. These languages are interpreted in `distance spaces' which satisfy some (or all) of the standard axioms of metric spaces. Among other things, we singled out decidable logics of distance spaces and proved ..."
Abstract
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In [8, 6] we introduced a family of `modal' languages intended for talking about distances. These languages are interpreted in `distance spaces' which satisfy some (or all) of the standard axioms of metric spaces. Among other things, we singled out decidable logics of distance spaces and proved expressive completeness results relating classical and modal languages. The aim of this paper is to axiomatize the modal fragments of the semantically de ned distance logics of [6] and give a new proof of their decidability.
A Multimodal Logic Approach to Order of
"... In this work we develop a logic for formalizing qualitative reasoning. ..."