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273
Bayesian Description Logics. In:
- Proc. of DL’14. CEUR Workshop Proceedings,
, 2014
"... Abstract This chapter considers, on the one hand, extensions of Description Logics by features not available in the basic framework, but considered important for using Description Logics as a modeling language. In particular, it addresses the extensions concerning: concrete domain constraints; moda ..."
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Cited by 394 (49 self)
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Abstract This chapter considers, on the one hand, extensions of Description Logics by features not available in the basic framework, but considered important for using Description Logics as a modeling language. In particular, it addresses the extensions concerning: concrete domain constraints; modal, epistemic, and temporal operators; probabilities and fuzzy logic; and defaults. On the other hand, it considers non-standard inference problems for Description Logics, i.e., inference problems that-unlike subsumption or instance checking-are not available in all systems, but have turned out to be useful in applications. In particular, it addresses the non-standard inference problems: least common subsumer and most specific concept; unification and matching of concepts; and rewriting.
A general Datalog-based framework for tractable query answering over ontologies
- In Proc. PODS-2009. ACM
, 2009
"... Ontologies play a key role in the Semantic Web [4], data modeling, and information integration [16]. Recent trends in ontological reasoning have shifted from decidability issues to tractability ones, as e.g. reflected by the work on the DL-Lite family of tractable description logics (DLs) [11, 19]. ..."
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Cited by 135 (24 self)
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Ontologies play a key role in the Semantic Web [4], data modeling, and information integration [16]. Recent trends in ontological reasoning have shifted from decidability issues to tractability ones, as e.g. reflected by the work on the DL-Lite family of tractable description logics (DLs) [11, 19]. An important result of these works is that the main
E-connections of abstract description systems
, 2003
"... Combining knowledge representation and reasoning formalisms is an important and challenging task. It is important because non-trivial 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 125 (34 self)
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Combining knowledge representation and reasoning formalisms is an important and challenging task. It is important because non-trivial 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 non-trivial interactions between the combined components. The new method, called E-connection, 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 E-connections is that the interpretation domains of n combined systems are disjoint, and that these domains are connected by means of n-ary ‘link relations. ’ We define several natural variants of E-connections and study in-depth the transfer of decidability from the component systems to their E-connections.
Hybrid Logics: Characterization, Interpolation and Complexity
- Journal of Symbolic Logic
, 1999
"... Hybrid languages are expansions of propositional modal languages which can refer to (or even quantify over) worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work (for example [BS98, BT98a, BT99]) has focussed on a more constrained system called H(#; @). We sho ..."
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Cited by 109 (36 self)
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Hybrid languages are expansions of propositional modal languages which can refer to (or even quantify over) worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work (for example [BS98, BT98a, BT99]) has focussed on a more constrained system called H(#; @). We show in detail that H(#; @) is modally natural. We begin by studying its expressivity, and provide model theoretic characterizations (via a restricted notion of Ehrenfeucht-Frasse game, and an enriched notion of bisimulation) and a syntactic characterization (in terms of bounded formulas). The key result to emerge is that H(#; @) corresponds to the fragment of rst-order logic which is invariant for generated submodels. We then show that H(#; @) enjoys (strong) interpolation, provide counterexamples for its nite variable fragments, and show that weak interpolation holds for the sublanguage H(@). Finally, we provide complexity results for H(@) and other fragments and variants, and sh...
Guarded Fixed Point Logic
, 1999
"... Guarded fixed point logics are obtained by adding least and greatest fixed points to the guarded fragments of firstorder logic that were recently introduced by Andr eka, van Benthem and N emeti. Guarded fixed point logics can also be viewed as the natural common extensions of the modal µ-calculus an ..."
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Cited by 81 (6 self)
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Guarded fixed point logics are obtained by adding least and greatest fixed points to the guarded fragments of firstorder logic that were recently introduced by Andr eka, van Benthem and N emeti. Guarded fixed point logics can also be viewed as the natural common extensions of the modal µ-calculus and the guarded fragments. We prove that the satisfiability problems for guarded fixed point logics are decidable and complete for deterministic double exponential time. For guarded fixed point sentences of bounded width, the most important case for applications, the satisfiability problem is EXPTIME-complete.
Specification and Verification of Dynamics in Cognitive Agent Models
- In: Proceedings of the Sixth International Conference on Intelligent Agent Technology, IAT'06. IEEE Computer
, 2006
"... Within many domains, among which biological and cognitive areas, multiple interacting processes occur among agents with dynamics that are hard to handle. Current approaches to analyse the dynamics of such processes, often based on differential equations, are not always successful. As an alternative ..."
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Cited by 66 (57 self)
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Within many domains, among which biological and cognitive areas, multiple interacting processes occur among agents with dynamics that are hard to handle. Current approaches to analyse the dynamics of such processes, often based on differential equations, are not always successful. As an alternative to differential equations, this paper presents the predicate logical Temporal Trace Language (TTL) for the formal specification and analysis of dynamic properties. This language supports the specification of both qualitative and quantitative aspects, and therefore subsumes specification languages based on differential equations. A software environment has been developed for TTL, that supports editing TTL properties and enables the formal verification of properties against a set of traces. The TTL environment proved its value in a number of projects within different domains. 1.
Specification and Verification of Dynamics in Agent Models
"... Within many domains, among which biological, cognitive, and social areas, multiple interacting processes occur among agents with dynamics that are hard to handle. This paper presents the predicate logical Temporal Trace Language (TTL) for the formal specification and analysis of dynamic properties o ..."
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Cited by 64 (50 self)
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Within many domains, among which biological, cognitive, and social areas, multiple interacting processes occur among agents with dynamics that are hard to handle. This paper presents the predicate logical Temporal Trace Language (TTL) for the formal specification and analysis of dynamic properties of agents and multi-agent systems. This language supports the specification of both qualitative and quantitative aspects, and therefore subsumes specification languages based on differential equations and qualitative, logical approaches. A software environment has been developed for TTL, which supports editing TTL properties and enables the formal verification of properties against a set of traces. The TTL environment proved its value in a number of projects within different biological, cognitive and social domains.
A Superposition Decision Procedure for the Guarded Fragment with Equality
- In Proc. LICS'99
, 1999
"... We give a new decision procedure for the guarded fragment with equality. The procedure is based on resolution with superposition. We argue that this method will be more useful in practice than methods based on the enumeration of certain finite structures. It is surprising to see that one does not ne ..."
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Cited by 62 (3 self)
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We give a new decision procedure for the guarded fragment with equality. The procedure is based on resolution with superposition. We argue that this method will be more useful in practice than methods based on the enumeration of certain finite structures. It is surprising to see that one does not need any sophisticated simplification and redundancy elimination method to make superposition terminate on the class of clauses that is obtained from the clausification of guarded formulas. Yet the decision procedure obtained is optimal with regard to time complexity. We also show that the method can be extended to the loosely guarded fragment with equality. 1 Introduction The loosely guarded fragment was introduced in (Andreka, van Benthem &Nemeti 1996) as 'the modal fragment of classical logic'. It is obtained essentially by restricting quantification to the following forms: #y[R(x, y) # A(x, y)] and #y[R(x, y) # A(x, y)]. These forms naturally arise when modal formulae are transl...
The Computational Complexity of Hybrid Temporal Logics
- Logic Journal of the IGPL
, 2000
"... In their simplest form, hybrid languages are propositional modal languages which can refer to states. They were introduced by Arthur Prior, the inventor of tense logic, and played an important role in his work: because they make reference to specic times possible, they remove the most serious obstac ..."
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Cited by 59 (12 self)
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In their simplest form, hybrid languages are propositional modal languages which can refer to states. They were introduced by Arthur Prior, the inventor of tense logic, and played an important role in his work: because they make reference to specic times possible, they remove the most serious obstacle to developing modal approaches to temporal representation and reasoning. However very little is known about the computational complexity of hybrid temporal logics. In this paper we analyze the complexity of the satisability problem of a number of hybrid temporal logics: the basic hybrid language over transitive frames; nominal tense logic over transitive frames, strict total orders, and transitive trees; nominal Until logic; and referential interval logic. We discuss the eects of including nominals, the @ operator, the somewhere modality E, and the dierence operator D. Adding nominals to tense logic leads for several frame{classes to an increase in complexity of the satisability pro...
