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380
Practical Reasoning for Expressive Description Logics
, 1999
"... . 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 ..."
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Cited by 363 (69 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 satis ability of the DL ALC extended with transitive and inverse roles, role hierarchies, and qualifying number restrictions. 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. Finally, we investigate the limits of decidability for this family of DLs.
On the Decidability of Query Containment under Constraints
 IN PROC. OF THE 17TH ACM SIGACT SIGMOD SIGART SYMP. ON PRINCIPLES OF DATABASE SYSTEMS (PODS’98
, 1998
"... Query containment under constraints is the problem of checking whether for every database satisfying a given set of constraints, the result of one query is a subset of the result of another query. Recent research points out that this is a central problem in several database applications, and we addr ..."
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Cited by 260 (59 self)
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Query containment under constraints is the problem of checking whether for every database satisfying a given set of constraints, the result of one query is a subset of the result of another query. Recent research points out that this is a central problem in several database applications, and we address it within a setting where constraints are specified in the form of special inclusion dependencies over complex expressions, built by using intersection and difference of relations, special forms of quantification, regular expressions over binary relations, and cardinality constraints. These types of constraints capture a great variety of data models, including the relational, the entityrelational, and the objectoriented model. We study the problem of checking whether q is contained in q 0 with respect to the constraints specified in a schema S, where q and q 0 are nonrecursive Datalog programs whose atoms are complex expressions. We present the following results on query containme...
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 186 (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
The programsize complexity of selfassembled squares
 In Proceedings of the thirtysecond annual ACM symposium on Theory of computing
, 2000
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Wang Tiles for Image and Texture Generation
, 2003
"... We present a simple stochastic system for nonperiodically tiling the plane with a small set of Wang Tiles. The tiles may be filled with texture, patterns, or geometry that when assembled create a continuous representation. The primary advantage of using Wang Tiles is that once the tiles are filled, ..."
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Cited by 179 (4 self)
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We present a simple stochastic system for nonperiodically tiling the plane with a small set of Wang Tiles. The tiles may be filled with texture, patterns, or geometry that when assembled create a continuous representation. The primary advantage of using Wang Tiles is that once the tiles are filled, large expanses of nonperiodic texture (or patterns or geometry) can be created as needed very efficiently at runtime. Wang Tiles
A Proposal for an OWL Rules Language
 In Proc. of the Thirteenth International World Wide Web Conference (WWW 2004
, 2004
"... Although the OWLWeb Ontology Language adds considerable expressive power to the Semantic Web it does have expressive limitations, particularly with respect to what can be said about properties. We present ORL (OWL Rules Language), a Horn clause rules extension to OWL that overcomes many of these lim ..."
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Cited by 167 (12 self)
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Although the OWLWeb Ontology Language adds considerable expressive power to the Semantic Web it does have expressive limitations, particularly with respect to what can be said about properties. We present ORL (OWL Rules Language), a Horn clause rules extension to OWL that overcomes many of these limitations. ORL extends OWL in a syntactically and semantically coherent manner: the basic syntax for ORL rules is an extension of the abstract syntax for OWL DL and OWL Lite; ORL rules are given formal meaning via an extension of the OWL DL modeltheoretic semantics; ORL rules are given an XML syntax based on the OWL XML presentation syntax; and a mapping from ORL rules to RDF graphs is given based on the OWL RDF/XML exchange syntax. We discuss the expressive power of ORL, showing that the ontology consistency problem is undecidable, provide several examples of ORL usage, and discuss how reasoning support for ORL might be provided.
Algorithmic SelfAssembly of DNA
, 1998
"... How can molecules compute? In his early studies of reversible computation, Bennett imagined an enzymatic Turing Machine which modified a heteropolymer (such as DNA) to perform computation with asymptotically low energy expenditures. Adleman's recent experimental demonstration of a DNA computat ..."
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Cited by 160 (6 self)
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How can molecules compute? In his early studies of reversible computation, Bennett imagined an enzymatic Turing Machine which modified a heteropolymer (such as DNA) to perform computation with asymptotically low energy expenditures. Adleman's recent experimental demonstration of a DNA computation, using an entirely different approach, has led to a wealth of ideas for how to build DNAbased computers in the laboratory, whose energy efficiency, information density, and parallelism may have potential to surpass conventional electronic computers for some purposes. In this thesis, I examine one mechanism used in all designs for DNAbased computer  the selfassembly of DNA by hybridization and formation of the double helix  and show that this mechanism alone in theory can perform universal computation. To do so, I borrow an important result in the mathematical theory of tiling: Wang showed how jigsawshaped tiles can be designed to simulate the operation of any Turing Machine. I propose...
On the Restraining Power of Guards
 Journal of Symbolic Logic
, 1998
"... Guarded fragments of firstorder logic were recently introduced by Andr'eka, van Benthem and N'emeti; they consist of relational firstorder formulae whose quantifiers are appropriately relativized by atoms. These fragments are interesting because they extend in a natural way many proposit ..."
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Cited by 155 (3 self)
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Guarded fragments of firstorder logic were recently introduced by Andr'eka, van Benthem and N'emeti; they consist of relational firstorder formulae whose quantifiers are appropriately relativized by atoms. These fragments are interesting because they extend in a natural way many propositional modal logics, because they have useful modeltheoretic properties and especially because they are decidable classes that avoid the usual syntactic restrictions (on the arity of relation symbols, the quantifier pattern or the number of variables) of almost all other known decidable fragments of firstorder logic. Here, we investigate the computational complexity of these fragments. We prove that the satisfiability problems for the guarded fragment (GF) and the loosely guarded fragment (LGF) of firstorder logic are complete for deterministic double exponential time. For the subfragments that have only a bounded number of variables or only relation symbols of bounded arity, satisfiability is EXPTI...