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24
Integrating description logics and action formalisms: First results
 In Proceedings of the Twentieth National Conference on Artificial Intelligence (AAAI05
, 2005
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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 54 (4 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.
Complexity of the twovariable fragment with counting quantifiers
 Journal of Logic, Language and Information
"... The datacomplexity of both satisfiability and finite satisfiability for the twovariable fragment with counting is NPcomplete; the datacomplexity of both queryanswering and finite queryanswering for the twovariable guarded fragment with counting is coNPcomplete. ..."
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Cited by 44 (3 self)
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The datacomplexity of both satisfiability and finite satisfiability for the twovariable fragment with counting is NPcomplete; the datacomplexity of both queryanswering and finite queryanswering for the twovariable guarded fragment with counting is coNPcomplete.
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 39 (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
Modular Data Structure Verification
 EECS DEPARTMENT, MASSACHUSETTS INSTITUTE OF TECHNOLOGY
, 2007
"... This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java ..."
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Cited by 36 (21 self)
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This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java programs with dynamically allocated data structures. Developers write Jahob specifications in classical higherorder logic (HOL); Jahob reduces the verification problem to deciding the validity of HOL formulas. I present a new method for proving HOL formulas by combining automated reasoning techniques. My method consists of 1) splitting formulas into individual HOL conjuncts, 2) soundly approximating each HOL conjunct with a formula in a more tractable fragment and 3) proving the resulting approximation using a decision procedure or a theorem prover. I present three concrete logics; for each logic I show how to use it to approximate HOL formulas, and how to decide the validity of formulas in this logic. First, I present an approximation of HOL based on a translation to firstorder logic, which enables the use of existing resolutionbased theorem provers. Second, I present an approximation of HOL based on field constraint analysis, a new technique that enables
Three Theses of Representation in the Semantic Web
, 2003
"... The Sematic Web is vitally dependant on a formal meaning for the constructs of its languages. For Semantic Web languages to work well together their formal meanings must employ a common view (or thesis) of representation, otherwise it will not be possible to reconcile documents written in different ..."
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Cited by 26 (1 self)
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The Sematic Web is vitally dependant on a formal meaning for the constructs of its languages. For Semantic Web languages to work well together their formal meanings must employ a common view (or thesis) of representation, otherwise it will not be possible to reconcile documents written in different languages. The thesis of representation underlying RDF and RDFS is particularly troublesome in this regard, as it has several unusual aspects, both semantic and syntactic. A morestandard thesis of representation would result in the ability to reuse existing results and tools in the Semantic Web.
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 24 (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
The Complexity of the Graded µCalculus
"... In classical logic, existential and universal quantifiers express that there exists at least one individual satisfying a formula, or that all individuals satisfy a formula. In many logics, these quantifiers have been generalized to express that, for a nonnegative integer n, at least n individual ..."
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Cited by 20 (2 self)
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In classical logic, existential and universal quantifiers express that there exists at least one individual satisfying a formula, or that all individuals satisfy a formula. In many logics, these quantifiers have been generalized to express that, for a nonnegative integer n, at least n individuals or all but n individuals satisfy a formula. In modal logics, graded modalities generalize standard existential and universal modalities in that they express, e.g., that there exist at least n accessible worlds satisfying a certain formula. Graded modalities are useful expressive means in knowledge representation; they are present in a variety of other knowledge representation formalisms closely related to modal logic.
On Decision Procedures for SetValued Fields
, 2004
"... An important feature of objectoriented programming languages is the ability to dynamically instantiate userdefined container data structures such as lists, trees, and hash tables. Programs implement such data structures using references to dynamically allocated objects, which allows data structure ..."
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Cited by 19 (13 self)
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An important feature of objectoriented programming languages is the ability to dynamically instantiate userdefined container data structures such as lists, trees, and hash tables. Programs implement such data structures using references to dynamically allocated objects, which allows data structures to store unbounded numbers of objects, but makes reasoning about programs more difficult. Reasoning about objectoriented programs with complex data structures is simplified if data structure operations are specified in terms of abstract sets of objects associated with each data structure. For example, an insertion into a data structure in this approach becomes simply an insertion into a dynamically changing setvalued field of an object, as opposed to a manipulation of a dynamically linked structure linked to the object. In this paper we explore...
On Role Logic
, 2003
"... We present role logic, a notation for describing properties of relational structures in shape analysis, databases, and knowledge bases. We construct role logic using the ideas of de Bruijn's notation for lambda calculus, an encoding of firstorder logic in lambda calculus, and a simple rule for impl ..."
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Cited by 13 (7 self)
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We present role logic, a notation for describing properties of relational structures in shape analysis, databases, and knowledge bases. We construct role logic using the ideas of de Bruijn's notation for lambda calculus, an encoding of firstorder logic in lambda calculus, and a simple rule for implicit arguments of unary and binary predicates.