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Temporal and modal logic
 HANDBOOK OF THEORETICAL COMPUTER SCIENCE
, 1995
"... We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic. ..."
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Cited by 1300 (17 self)
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We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic.
Reasoning about Infinite Computations
 Information and Computation
, 1994
"... We investigate extensions of temporal logic by connectives defined by finite automata on infinite words. We consider three different logics, corresponding to three different types of acceptance conditions (finite, looping and repeating) for the automata. It turns out, however, that these logics all ..."
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Cited by 316 (59 self)
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We investigate extensions of temporal logic by connectives defined by finite automata on infinite words. We consider three different logics, corresponding to three different types of acceptance conditions (finite, looping and repeating) for the automata. It turns out, however, that these logics all have the same expressive power and that their decision problems are all PSPACEcomplete. We also investigate connectives defined by alternating automata and show that they do not increase the expressive power of the logic or the complexity of the decision problem. 1 Introduction For many years, logics of programs have been tools for reasoning about the input/output behavior of programs. When dealing with concurrent or nonterminating processes (like operating systems) there is, however, a need to reason about infinite computations. Thus, instead of considering the first and last states of finite computations, we need to consider the infinite sequences of states that the program goes through...
A Correspondence Theory for Terminological Logics: Preliminary Report
 In Proc. of IJCAI91
, 1991
"... We show that the terminological logic ALC comprising Boolean operations on concepts and value restrictions is a notational variant of the propositional modal logic K (m) . To demonstrate the utility of the correspondence, we give two of its immediate byproducts. Namely, we axiomatize ALC and give a ..."
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Cited by 312 (0 self)
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We show that the terminological logic ALC comprising Boolean operations on concepts and value restrictions is a notational variant of the propositional modal logic K (m) . To demonstrate the utility of the correspondence, we give two of its immediate byproducts. Namely, we axiomatize ALC and give a simple proof that subsumption in ALC is PSPACEcomplete, replacing the original sixpage one. Furthermore, we consider an extension of ALC additionally containing both the identity role and the composition, union, transitivereflexive closure, range restriction, and inverse of roles. It turns out that this language, called T SL, is a notational variant of the propositional dynamic logic converse PDL. Using this correspondence, we prove that it suffices to consider finite T SLmodels, show that T SLsubsumption is decidable, and obtain an axiomatization of T SL. By discovering that features correspond to deterministic programs in dynamic logic, we show that adding them to T SL preserves...
Tableau Algorithms for Description Logics
 STUDIA LOGICA
, 2000
"... Description logics are a family of knowledge representation formalisms that are descended from semantic networks and frames via the system Klone. During the last decade, it has been shown that the important reasoning problems (like subsumption and satisfiability) in a great variety of descriptio ..."
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Cited by 265 (27 self)
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Description logics are a family of knowledge representation formalisms that are descended from semantic networks and frames via the system Klone. During the last decade, it has been shown that the important reasoning problems (like subsumption and satisfiability) in a great variety of description logics can be decided using tableaulike algorithms. This is not very surprising since description logics have turned out to be closely related to propositional modal logics and logics of programs (such as propositional dynamic logic), for which tableau procedures have been quite successful. Nevertheless, due to different underlying intuitions and applications, most description logics differ significantly from runofthemill modal and program logics. Consequently, the research on tableau algorithms in description logics led to new techniques and results, which are, however, also of interest for modal logicians. In this article, we will focus on three features that play an important role in description logics (number restrictions, terminological axioms, and role constructors), and show how they can be taken into account by tableau algorithms.
Practical reasoning for very expressive description logics
 Journal of the Interest Group in Pure and Applied Logics 8
, 2000
"... Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We present an algorithm t ..."
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Cited by 188 (23 self)
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Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We present an algorithm that decides satisfiability of the DL ALC extended with transitive and inverse roles and functional restrictions with respect to general concept inclusion axioms and role hierarchies; early experiments indicate that this algorithm is wellsuited for implementation. Additionally, we show that ALC extended with just transitive and inverse roles is still in PSpace. We investigate the limits of decidability for this family of DLs, showing that relaxing the constraints placed on the kinds of roles used in number restrictions leads to the undecidability of all inference problems. Finally, we describe a number of optimisation techniques that are crucial in obtaining implementations of the decision procedures, which, despite the hight worstcase complexity of the problem, exhibit good performance with reallife problems. 1
Did I Damage my Ontology? A Case for Conservative Extensions in Description Logics
 IN PROC. OF KR2006
, 2006
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The Complexity of Reasoning with Cardinality Restrictions and Nominals in Expressive Description Logics
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 2000
"... We study the complexity of the combination of the Description Logics ALCQ and ALCQI with a terminological formalism based on cardinality restrictions on concepts. These combinations can naturally be embedded into C², the two variable fragment of predicate logic with counting quantifiers, which yi ..."
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We study the complexity of the combination of the Description Logics ALCQ and ALCQI with a terminological formalism based on cardinality restrictions on concepts. These combinations can naturally be embedded into C², the two variable fragment of predicate logic with counting quantifiers, which yields decidability in NExpTime. We show that this approach leads to an optimal solution for ALCQI, as ALCQI with cardinality restrictions has the same complexity as C² (NExpTimecomplete). In contrast, we show that for ALCQ, the problem can be solved in ExpTime. This result is obtained by a reduction of reasoning with cardinality restrictions to reasoning with the (in general weaker) terminological formalism of general axioms for ALCQ extended with nominals . Using the same reduction, we show that, for the extension of ALCQI with nominals, reasoning with general axioms is a NExpTimecomplete problem. Finally, we sharpen this result and show that pure concept satisfiability for A...
XPath with conditional axis relations
 In EDBT
, 2004
"... This paper is about the W3C standard nodeaddressing language for XML documents, called XPath. XPath is still under development. Version 2.0 appeared in 2001 while the theoretical foundations of Version 1.0 (dating from 1998) are still being widely studied. The paper aims at bringing XPath to a & ..."
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Cited by 71 (7 self)
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This paper is about the W3C standard nodeaddressing language for XML documents, called XPath. XPath is still under development. Version 2.0 appeared in 2001 while the theoretical foundations of Version 1.0 (dating from 1998) are still being widely studied. The paper aims at bringing XPath to a "stable fixed point" in its development: a version which is expressively complete, still manageable computationally, with a userfriendly syntax and a natural semantics.