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Updating description logic aboxes
 In International Conference of Principles of Knowledge Representation and Reasoning(KR
, 2006
"... Description logic (DL) ABoxes are a tool for describing the state of affairs in an application domain. In this paper, we consider the problem of updating ABoxes when the state changes. We assume that changes are described at an atomic level, i.e., in terms of possibly negated ABox assertions that in ..."
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Cited by 76 (5 self)
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Description logic (DL) ABoxes are a tool for describing the state of affairs in an application domain. In this paper, we consider the problem of updating ABoxes when the state changes. We assume that changes are described at an atomic level, i.e., in terms of possibly negated ABox assertions that involve only atomic concepts and roles. We analyze such basic ABox updates in several standard DLs by investigating whether the updated ABox can be expressed in these DLs and, if so, whether it is computable and what is its size. It turns out that DLs have to include nominals and the “@” constructor of hybrid logic (or, equivalently, admit Boolean ABoxes) for updated ABoxes to be expressible. We devise algorithms to compute updated ABoxes in several expressive DLs and show that an exponential blowup in the size of the whole input (original ABox + update information) cannot be avoided unless every PTIME problem is LOGTIMEparallelizable. We also exhibit ways to avoid an exponential blowup in the size of the original ABox, which is usually large compared to the update information.
Wellfounded semantics for description logic programs in the Semantic Web
, 2009
"... The realization of the Semantic Web vision, in which computational logic has a prominent role, has stimulated a lot of research on combining rules and ontologies, which are formulated in different formalisms, into a framework that is more useful for describing semantic content. In particular, combin ..."
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Cited by 71 (19 self)
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The realization of the Semantic Web vision, in which computational logic has a prominent role, has stimulated a lot of research on combining rules and ontologies, which are formulated in different formalisms, into a framework that is more useful for describing semantic content. In particular, combining logic programming with the Web Ontology Language (OWL), which is a standard based on description logics, emerged as an important issue for linking the Rules and Ontology Layers of the Semantic Web. Nonmonotonic description logic programs (or dlprograms) were introduced for such a combination, in which a pair (L,P) of a description logic knowledge base L and a set of rules P with negation as failure is given a modelbased semantics that generalizes the answer set semantics of logic programs. In this paper, we reconsider dlprograms and present a wellfounded semantics for them as an analog for the other main semantics of logic programs. It generalizes the canonical definition of the wellfounded semantics based on unfounded sets, and, as we show, lifts many of the wellknown properties from ordinary logic programs to dlprograms. Among these properties: our semantics amounts to a partial model approximating the answer set semantics, which yields for positive and stratified dlprograms a total model coinciding with the answer set semantics; it has polynomial data complexity provided the access to the description logic
RIQ and SROIQ are harder than SHOIQ
 In Proc. KR’08
, 2008
"... Abstract. We identify the complexity of (finite model) reasoning in the DL SROIQ to be N2ExpTimecomplete. We also prove that (finite model) reasoning in the DL SR—a fragment of SROIQ without nominals, number restrictions, and inverse roles—is 2ExpTimehard. 1 From SHIQ to SROIQ In this paper we stu ..."
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Cited by 60 (6 self)
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Abstract. We identify the complexity of (finite model) reasoning in the DL SROIQ to be N2ExpTimecomplete. We also prove that (finite model) reasoning in the DL SR—a fragment of SROIQ without nominals, number restrictions, and inverse roles—is 2ExpTimehard. 1 From SHIQ to SROIQ In this paper we study the complexity of reasoning in the DL SROIQ—the logic chosen as a candidate for OWL 2. 1 SROIQ has been introduced in [1] as an extension of SRIQ, which itself was introduced previously in [2] as an extension of RIQ [3]. These papers present tableaubased procedures for the respective DLs and prove their soundness, completeness and termination. In contrast to sublanguages of SHOIQ whose computational complexities are currently well understood [4], almost nothing was known, up until now, about the complexity of SROIQ, SRIQ and RIQ except for the hardness results inherited from their sublanbuages: SROIQ is NExpTimehard as an extension of SHOIQ, SRIQ and RIQ are ExpTimehard as extensions of SHIQ. The
On the Properties of Metamodeling in OWL
 In 4th Int. Semantic Web Conf. (ISWC 2005
, 2005
"... Abstract. A common practice in conceptual modeling is to separate the intensional from the extensional model. Although very intuitive, this approach is inadequate for many complex domains, where the borderline between the two models is not clearcut. Therefore, OWLFull, the most expressive of the S ..."
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Cited by 52 (0 self)
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Abstract. A common practice in conceptual modeling is to separate the intensional from the extensional model. Although very intuitive, this approach is inadequate for many complex domains, where the borderline between the two models is not clearcut. Therefore, OWLFull, the most expressive of the Semantic Web ontology languages, allows combining the intensional and the extensional model by a feature we refer to as metamodeling. In this paper, we show that the semantics of metamodeling adopted in OWLFull leads to undecidability of basic inference problems, due to free mixing of logical and metalogical symbols. Based on this result, we propose two alternative semantics for metamodeling: the contextual and the HiLog semantics. We show that SHOIQ — a description logic underlying OWLDL — extended with metamodeling under either semantics is decidable. Finally, we show how the latter semantics can be used in practice to axiomatize the logical interaction between concepts and metaconcepts. 1
Answering regular path queries in expressive description logics: An automatatheoretic approach
 In Proc. of the 22nd Nat. Conf. on Artificial Intelligence (AAAI 2007
, 2007
"... Expressive Description Logics (DLs) have been advocated as formalisms for modeling the domain of interest in various application areas. An important requirement is the ability to answer complex queries beyond instance retrieval, taking into account constraints expressed in a knowledge base. We consi ..."
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Cited by 52 (22 self)
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Expressive Description Logics (DLs) have been advocated as formalisms for modeling the domain of interest in various application areas. An important requirement is the ability to answer complex queries beyond instance retrieval, taking into account constraints expressed in a knowledge base. We consider this task for positive existential path queries (which generalize conjunctive queries and unions thereof), whose atoms are regular expressions over the roles (and concepts) of a knowledge base in the expressive DL ALCQIbreg. Using techniques based on twoway treeautomata, we first provide an elegant characterization of TBox and ABox reasoning, which gives us also a tight EXPTIME bound. We then prove decidability (more precisely, a 2EXPTIME upper bound) of query answering, thus significantly pushing the decidability frontier, both with respect to the query language and the considered DL. We also show that query answering is EXPSPACEhard already in rather restricted settings.
A Better Uncle For OWL  Nominal Schemas for Integrating Rules and Ontologies
, 2011
"... We propose a descriptionlogic style extension of OWL 2 with nominal schemas which can be used like “variable nominal classes”within axioms. This feature allows ontology languages to express arbitrary DLsafe rules (as expressible in SWRL or RIF) in their native syntax. We show that adding nominal s ..."
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Cited by 38 (17 self)
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We propose a descriptionlogic style extension of OWL 2 with nominal schemas which can be used like “variable nominal classes”within axioms. This feature allows ontology languages to express arbitrary DLsafe rules (as expressible in SWRL or RIF) in their native syntax. We show that adding nominal schemas to OWL 2 does not increase the worstcase reasoning complexity, and we identify a novel tractable language SROELV 3(⊓, ×) that is versatile enough to capture the lightweight languages OWL EL and OWL RL.
Querying the guarded fragment
 PROCEEDINGS OF THE 25TH ANNUAL IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE, LICS 2010
, 2010
"... Evaluating a Boolean conjunctive query q against a guarded firstorder theory ϕ is equivalent to checking whether ϕ ∧ ¬q is unsatisfiable. This problem is relevant to the areas of database theory and description logic. Since q may not be guarded, well known results about the decidability, complexity ..."
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Cited by 38 (12 self)
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Evaluating a Boolean conjunctive query q against a guarded firstorder theory ϕ is equivalent to checking whether ϕ ∧ ¬q is unsatisfiable. This problem is relevant to the areas of database theory and description logic. Since q may not be guarded, well known results about the decidability, complexity, and finitemodel property of the guarded fragment do not obviously carry over to conjunctive query answering over guarded theories, and had been left open in general. By investigating finite guarded bisimilar covers of hypergraphs and relational structures, and by substantially generalising Rosati’s finite chase, we prove for guarded theories ϕ and (unions of) conjunctive queries q that (i) ϕ  = q iff ϕ =fin q, that is, iff q is true in each finite model of ϕ and (ii) determining whether ϕ  = q is 2EXPTIMEcomplete. We further show the following results: (iii) the existence of polynomialsize conformal covers of arbitrary hypergraphs; (iv) a new proof of the finite model property of the cliqueguarded fragment; (v) the small model property of the guarded fragment with optimal bounds; (vi) a polynomialtime solution to the canonisation problem modulo guarded bisimulation, which yields (vii) a capturing result for guarded bisimulation invariant PTIME.
Description logics with circumscription
 In Proc. of KR
, 2006
"... We show that circumscription can be used to extend description logics (DLs) with nonmonotonic features in a straightforward and transparent way. In particular, we consider extensions with circumscription of the expressive DLsALCIO and ALCQO and prove that reasoning in these logics is decidable ..."
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Cited by 37 (3 self)
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We show that circumscription can be used to extend description logics (DLs) with nonmonotonic features in a straightforward and transparent way. In particular, we consider extensions with circumscription of the expressive DLsALCIO and ALCQO and prove that reasoning in these logics is decidable under a simple restriction: only concept names can be circumscribed, and role names vary freely during circumscription. We pinpoint the exact computational complexity of reasoning as complete for NPNEXP and NEXPNP, depending on whether or not the number of minimized and fixed predicates is assumed to be bounded by a constant. We also show that we cannot allow role names to be fixed during minimization rather than having them vary: this modification renders reasoning undecidable already in the basic DL ALC. Finally, we argue that nonmonotonic DLs based on circumscription are an appropriate tool for modelling defeasible inheritance. In particular, we can avoid the restriction of nonmonotonic reasoning to domain elements that are named by an individual constant, as adopted by other nonmonotonic DLs.
A resolutionbased decision procedure for SHOIQ
 Proc. of the 3rd Int. Joint Conf. on Automated Reasoning (IJCAR 2006), volume 4130 of LNAI
, 2006
"... Abstract. We present a resolutionbased decision procedure for the description logic SHOIQ—the logic underlying the Semantic Web ontology language OWLDL. Our procedure is goaloriented, and it naturally extends a similar procedure for SHIQ, which has proven itself in practice. Applying existing tec ..."
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Cited by 30 (6 self)
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Abstract. We present a resolutionbased decision procedure for the description logic SHOIQ—the logic underlying the Semantic Web ontology language OWLDL. Our procedure is goaloriented, and it naturally extends a similar procedure for SHIQ, which has proven itself in practice. Applying existing techniques for deriving saturationbased decision procedures to SHOIQ is not straightforward due to nominals, number restrictions, and inverse roles—a combination known to cause termination problems. We overcome this difficulty by using the basic superposition calculus, extended with custom simplification rules. 1
Cheap Boolean Role Constructors for Description Logics
"... Abstract. We investigate the possibility of incorporating Boolean role constructors on simple roles into some of today’s most popular description logics, focussing on cases where those extensions do not increase complexity of reasoning. We show that the expressive DLsSHOIQ andSROIQ, serving as the l ..."
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Cited by 28 (10 self)
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Abstract. We investigate the possibility of incorporating Boolean role constructors on simple roles into some of today’s most popular description logics, focussing on cases where those extensions do not increase complexity of reasoning. We show that the expressive DLsSHOIQ andSROIQ, serving as the logical underpinning of OWL and the forthcoming OWL 2, can accommodate arbitrary Boolean expressions. The prominent OWLfragmentSHIQ can be safely extended by safe role expressions, and the tractable fragmentsEL ++ and DLP retain tractability if extended by conjunction on roles, where in the case of DLP the restriction on role simplicity can even be discarded. 1