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Using an Expressive Description Logic: FaCT or Fiction?
 In Proc. of KR98
, 1998
"... Description Logics form a family of formalisms closely related to semantic networks but with the distinguishing characteristic that the semantics of the concept description language is formally defined, so that the subsumption relationship between two concept descriptions can be computed by a suitab ..."
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Cited by 274 (53 self)
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Description Logics form a family of formalisms closely related to semantic networks but with the distinguishing characteristic that the semantics of the concept description language is formally defined, so that the subsumption relationship between two concept descriptions can be computed by a suitable algorithm. Description Logics have proved useful in a range of applications but their wider acceptance has been hindered by their limited expressiveness and the intractability of their subsumption algorithms. This paper addresses both these issues by describing a sound and complete tableaux subsumption testing algorithm for a relatively expressive Description Logic which, in spite of the logic's worst case complexity, has been shown to perform well in realistic applications. 1 INTRODUCTION Description Logics (DLs) form a family of formalisms which have grown out of knowledge representation techniques using frames and semantic networks
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
The FaCT system
 In Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX’98), volume 1397 in Lecture Notes in Artificial Intelligence
, 1998
"... Abstract. FaCT is a Description Logic classifier which has been implemented as a testbed for a highly optimised tableaux satisfiability (subsumption) testing algorithm. The correspondence between modal and description logics also allows FaCT to be used as a theorem prover for the propositional moda ..."
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Cited by 145 (15 self)
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Abstract. FaCT is a Description Logic classifier which has been implemented as a testbed for a highly optimised tableaux satisfiability (subsumption) testing algorithm. The correspondence between modal and description logics also allows FaCT to be used as a theorem prover for the propositional modal logics K, KT, K4 and S4. Empirical tests have demonstrated the effectiveness of the optimised implementation and, in particular, of the dependency directed backtracking optimisation. 1
Hypertableau Reasoning for Description Logics
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 2007
"... We present a novel reasoning calculus for the description logic SHOIQ + —a knowledge representation formalism with applications in areas such as the Semantic Web. Unnecessary nondeterminism and the construction of large models are two primary sources of inefficiency in the tableaubased reasoning ca ..."
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Cited by 119 (25 self)
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We present a novel reasoning calculus for the description logic SHOIQ + —a knowledge representation formalism with applications in areas such as the Semantic Web. Unnecessary nondeterminism and the construction of large models are two primary sources of inefficiency in the tableaubased reasoning calculi used in stateoftheart reasoners. In order to reduce nondeterminism, we base our calculus on hypertableau and hyperresolution calculi, which we extend with a blocking condition to ensure termination. In order to reduce the size of the constructed models, we introduce anywhere pairwise blocking. We also present an improved nominal introduction rule that ensures termination in the presence of nominals, inverse roles, and number restrictions—a combination of DL constructs that has proven notoriously difficult to handle. Our implementation shows significant performance improvements over stateoftheart reasoners on several wellknown ontologies.
Optimising Description Logic Subsumption
 Journal of Logic and Computation
, 1999
"... Effective optimisation techniques can make a dramatic difference in the performance of knowledge representation systems based on expressive description logics. With currentlyavailable desktop computers, systems that incorporate these techniques can effectively reason in description logics with intr ..."
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Cited by 56 (17 self)
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Effective optimisation techniques can make a dramatic difference in the performance of knowledge representation systems based on expressive description logics. With currentlyavailable desktop computers, systems that incorporate these techniques can effectively reason in description logics with intractable inference. Because of the correspondence between description logics and propositional modal logic, difficult problems in propositional modal logic can be effectively solved using the same techniques.
DLP System Description
 Collected Papers from the International Description Logics Workshop (DL'98
, 1998
"... DLP (Description Logic Prover) is an experimental description logic knowledge representation system. DLP currently implements a superset of propositional dynamic logic as well as K (m) and KT (m) . Although DLP is an experimental system, it nonetheless provides a fast satisfiability checker for ..."
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Cited by 47 (9 self)
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DLP (Description Logic Prover) is an experimental description logic knowledge representation system. DLP currently implements a superset of propositional dynamic logic as well as K (m) and KT (m) . Although DLP is an experimental system, it nonetheless provides a fast satisfiability checker for the above propositional modal logics as well as a fast reasonder for knowledge bases.
Towards a benchmark for Semantic Web reasoners  an analysis of the DAML ontology library
, 2003
"... Introduction Bet hmarksare one important asp ex of pe rformance e aluation. This pap e conce trate on the de e86)1 t of a re1888) tative be1 hmark forSe71 tic We87 To thise te t we pe rform a statistical analysis of available Seab tic We b ontologie] in our case the DAML ontology library, andde7F ..."
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Cited by 41 (4 self)
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Introduction Bet hmarksare one important asp ex of pe rformance e aluation. This pap e conce trate on the de e86)1 t of a re1888) tative be1 hmark forSe71 tic We87 To thise te t we pe rform a statistical analysis of available Seab tic We b ontologie] in our case the DAML ontology library, andde7F e paramex]7 that can be use forthe ge1)F66x] of syntheK) ontologiex Theg syntheF1 ontologie can be use as workloads in be1 hmarks. Naturally, pe)661x]1j e aluation can also be pe1FjI#x using a re7 workload, viz. a workload that isobseK e on a re11)IF be ing use for normal ope x7K)#6 Howe ve r, such workloads can usually not be applie ree78I7I in a controlle manne) Thee)x] synthe)j workloads are typicallyuse in pe rformance e aluations. SyntheF7 workloads should be areII77x tation or mo de ofthe re7 workload. Heloa it isne8K#K6x tome67#8 and characte]16 the workload one isting reingx7K to produce me7#Kx]1 synthejI workloads. This should allow us to syste7x]1)787 e aluate di#ee t rej#j#x] an
Symbolic Decision Procedures for QBF
 Proceedings of 10th Int. Conf. on Principles and Practice of Constraint Programming (CP 2004
, 2004
"... Much recent work has gone into adapting techniques that were originally developed for SAT solving to QBF solving. In particular, QBF solvers are often based on SAT solvers. Most competitive QBF solvers are searchbased. In this work we explore an alternative approach to QBF solving, based on symb ..."
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Cited by 28 (1 self)
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Much recent work has gone into adapting techniques that were originally developed for SAT solving to QBF solving. In particular, QBF solvers are often based on SAT solvers. Most competitive QBF solvers are searchbased. In this work we explore an alternative approach to QBF solving, based on symbolic quantifier elimination. We extend some recent symbolic approaches for SAT solving to symbolic QBF solving, using various decisiondiagram formalisms such as OBDDs and ZDDs. In both approaches, QBF formulas are solved by eliminating all their quantifiers. Our first solver, QMRES, maintains a set of clauses represented by a ZDD and eliminates quantifiers via multiresolution. Our second solver, QBDD, maintains a set of OBDDs, and eliminate quantifier by applying them to the underlying OBDDs. We compare our symbolic solvers to several competitive searchbased solvers. We show that QBDD is not competitive, but QMRES compares favorably with searchbased solvers on various benchmarks consisting of nonrandom formulas.
BDDBased Decision Procedures for the Modal Logic K
 Journal of Applied Nonclassical Logics
, 2005
"... We describe BDDbased decision procedures for the modal logic K. Our approach is inspired by the automatatheoretic approach, but we avoid explicit automata construction. Instead, we compute certain fixpoints of a set of typeswhich can be viewed as an onthefly emptiness of the automaton. We use ..."
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Cited by 28 (1 self)
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We describe BDDbased decision procedures for the modal logic K. Our approach is inspired by the automatatheoretic approach, but we avoid explicit automata construction. Instead, we compute certain fixpoints of a set of typeswhich can be viewed as an onthefly emptiness of the automaton. We use BDDs to represent and manipulate such type sets, and investigate different kinds of representations as well as a "levelbased" representation scheme. The latter turns out to speed up construction and reduce memory consumption considerably. We also study the effect of formula simplification on our decision procedures. To proof the viability of our approach, we compare our approach with a representative selection of other approaches, including a translation of to QBF. Our results indicate that the BDDbased approach dominates for modally heavy formulae, while searchbased approaches dominate for propositionally heavy formulae.
DL systems comparison
 In Collected Papers from the Int. Description Logics Workshop (DL’98
, 1998
"... The tradeoff between expressiveness and tractability in Description Logics (DLs) has long been recognised [9]. For DL system designers and implementors there are several possible approaches to this problem [3]. These ..."
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Cited by 27 (5 self)
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The tradeoff between expressiveness and tractability in Description Logics (DLs) has long been recognised [9]. For DL system designers and implementors there are several possible approaches to this problem [3]. These