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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 169 (22 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
A backbonesearch heuristic for efficient solving of hard 3SAT formulae
, 2001
"... Of late, new insight into the study of random kSAT formulae has been gained from the introduction of a concept inspired by models of physics, the `backbone ' of a SAT formula which corresponds to the variables having a fixed truth value in all assignments satisfying the maximum number of ..."
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Cited by 68 (1 self)
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Of late, new insight into the study of random kSAT formulae has been gained from the introduction of a concept inspired by models of physics, the `backbone ' of a SAT formula which corresponds to the variables having a fixed truth value in all assignments satisfying the maximum number of clauses.
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.
Implementation and Optimisation Techniques
"... This chapter will discuss the implementation of the reasoning services which form the core of Description Logic based Knowledge Representation Systems. To be useful in realistic applications, such systems need both expressive logics and fast reasoners. As expressive logics inevitably have high worst ..."
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Cited by 24 (5 self)
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This chapter will discuss the implementation of the reasoning services which form the core of Description Logic based Knowledge Representation Systems. To be useful in realistic applications, such systems need both expressive logics and fast reasoners. As expressive logics inevitably have high worstcase complexities, this can only be achieved by employing highly optimised implementations of suitable reasoning algorithms. Systems based on such implementations have demonstrated that they can perform well with problems that occur in realistic applications, including problems where unoptimised reasoning is hopelessly intractable.
Comparing subsumption optimizations
 Collected Papers from the International Description Logics Workshop (DL'98
, 1998
"... Effective systems for expressive description logics require a heavilyoptimised subsumption checker incorporating a range of optimisation techniques. Because of the correspondence between description logics and propositional modal logic most of these techniques carry over into propositional modal lo ..."
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Cited by 21 (12 self)
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Effective systems for expressive description logics require a heavilyoptimised subsumption checker incorporating a range of optimisation techniques. Because of the correspondence between description logics and propositional modal logic most of these techniques carry over into propositional modal logic satisfiability checking. Some of the techniques are extremely effective on various test suites for propositional modal satisfiability and others are less effective. Further, the effectiveness of a technique depends on the test performed. Description logic systems spend much of their time computing subsumption relationships between descriptions. If the system is based on an expressive description logic then the
Breadth first search 3SAT algorithms for DNA computers
, 1996
"... This paper demonstrates that some practical 3SAT algorithms on conventional computers can be implemented on a DNA computer as a polynomial time breadth first search procedure based only on the fundamental chemical operations identified by Adleman and Lipton’s method. In particular, the MonienSpecke ..."
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Cited by 17 (5 self)
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This paper demonstrates that some practical 3SAT algorithms on conventional computers can be implemented on a DNA computer as a polynomial time breadth first search procedure based only on the fundamental chemical operations identified by Adleman and Lipton’s method. In particular, the MonienSpeckenmeyer algorithm, when implemented on DNA, becomes an ¢¡¤£¦¥¨§�©�����������£���� ���� � ���� � time, space algorithm, with significant increase in time and significant decrease in space. This paper also proposes a fast breadth first search method with fixed split points. The running time is at most twice as that of Lipton. Although theoretical analysis of the algorithm is yet to be done, simulations on a conventional computer suggest that the algorithm could significantly reduce the search space for 3SAT for most cases. If the observation is correct, the algorithm would allow DNA computers to handle 3SAT formulas of more than 120 variables, thereby doubling the limit given by Lipton. 1
Optimising propositional modal satisfiability for description logic subsumption
 In Artificial Intelligence and Symbolic Computation: Int. Conf. AISC’98, number 1476 in LNAI
, 1998
"... Abstract. Effective optimisation techniques can make a dramatic difference in the performance of knowledge representation systems based on expressive description logics. Because of the correspondence between description logics and propositional modal logic many of these techniques carry over into pr ..."
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Cited by 12 (2 self)
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Abstract. Effective optimisation techniques can make a dramatic difference in the performance of knowledge representation systems based on expressive description logics. Because of the correspondence between description logics and propositional modal logic many of these techniques carry over into propositional modal logic satisfiability checking. Currentlyimplemented representation systems that employ these techniques, such as FaCT and DLP, make effective satisfiable checkers for various propositional modal logics. 1
Optimisation Techniques for Expressive Description Logics
, 1997
"... This report describes and evaluates optimisation techniques for a tableaux based satisfiability testing algorithm used to compute subsumption in Grail, an expressive description logic. Five techniques are studied in detail: normalisation and encoding, indexing, semantic branching, dependency directe ..."
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Cited by 11 (1 self)
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This report describes and evaluates optimisation techniques for a tableaux based satisfiability testing algorithm used to compute subsumption in Grail, an expressive description logic. Five techniques are studied in detail: normalisation and encoding, indexing, semantic branching, dependency directed backtracking and caching. The effectiveness of these techniques is evaluated by empirical testing using a large knowledge base from the Galen project. The performance of the optimised classifier and subsumption test are also compared with that of the Kris classifier and KSAT satisfiability testing procedure using both the Galen knowledge base and randomly generated test data.
Using a Description Logic with Concept Inclusions
"... The Galen project is constructing a conceptual schema for medical terminology using a Description Logic (DL) which supports transitive roles and general concept inclusions. Tableaux calculus subsumption testing algorithms for such a DL are well understood but serious worst case intractability would ..."
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Cited by 4 (3 self)
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The Galen project is constructing a conceptual schema for medical terminology using a Description Logic (DL) which supports transitive roles and general concept inclusions. Tableaux calculus subsumption testing algorithms for such a DL are well understood but serious worst case intractability would appear to limit their practical applicability. However by using heuristic speedup techniques adapted from constraint satisfaction problem solving procedures it is possible to dramatically improve performance with a realistic knowledge base.