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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 251 (54 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 156 (21 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 136 (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
The Model Evolution Calculus
, 2003
"... The DPLL procedure is the basis of some of the most successful propositional satisfiability solvers to date. Although originally devised as a proofprocedure for firstorder logic, it has been used almost exclusively for propositional logic so far because of its highly inefficient treatment of quanti ..."
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Cited by 87 (14 self)
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The DPLL procedure is the basis of some of the most successful propositional satisfiability solvers to date. Although originally devised as a proofprocedure for firstorder logic, it has been used almost exclusively for propositional logic so far because of its highly inefficient treatment of quantifiers, based on instantiation into ground formulas. The recent FDPLL calculus by Baumgartner was the first successful attempt to lift the procedure to the firstorder level without resorting to ground instantiations. FDPLL lifts to the firstorder case the core of the DPLL procedure, the splitting rule, but ignores other aspects of the procedure that, although not necessary for completeness, are crucial for its effectiveness in practice. In this paper, we present a new calculus loosely based on FDPLL that lifts these aspects as well. In addition to being a more faithful litfing of the DPLL procedure, the new calculus contains a more systematic treatment of universal literals, one of FDPLL's optimizations, and so has the potential of leading to much faster implementations.
leanTAP: Lean Tableaubased Deduction
 Journal of Automated Reasoning
, 1995
"... . "prove((E,F),A,B,C,D) : !, prove(E,[FA],B,C,D). prove((E;F),A,B,C,D) : !, prove(E,A,B,C,D), prove(F,A,B,C,D). prove(all(H,I),A,B,C,D) : !, "+length(C,D), copyterm((H,I,C),(G,F,C)), append(A,[all(H,I)],E), prove(F,E,B,[GC],D). prove(A,,[CD],,) : ((A= (B); (A)=B)) ? (unify(B,C); pro ..."
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Cited by 78 (11 self)
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. "prove((E,F),A,B,C,D) : !, prove(E,[FA],B,C,D). prove((E;F),A,B,C,D) : !, prove(E,A,B,C,D), prove(F,A,B,C,D). prove(all(H,I),A,B,C,D) : !, "+length(C,D), copyterm((H,I,C),(G,F,C)), append(A,[all(H,I)],E), prove(F,E,B,[GC],D). prove(A,,[CD],,) : ((A= (B); (A)=B)) ? (unify(B,C); prove(A,[],D,,)). prove(A,[EF],B,C,D) : prove(E,F,[AB],C,D)." implements a firstorder theorem prover based on freevariable semantic tableaux. It is complete, sound, and efficient. 1 Introduction The Prolog program listed in the abstract implements a complete and sound theorem prover for firstorder logic; it is based on freevariable semantic tableaux (Fitting, 1990). We call this lean deduction: the idea is to achieve maximal efficiency from minimal means. We will see that the above program is indeed very efficientnot although but because it is extremely short and compact. Our approach surely does not lead to a deduction system which is superior to highly sophisticated systems li...
Hyper Tableaux
, 1996
"... This paper introduces a variant of clausal normal form tableaux that we call "hyper tableaux". Hyper tableaux keep many desirable features of analytic tableaux while taking advantage of the central idea from (positive) hyper resolution, namely to resolve away all negative literals of a clause in a s ..."
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Cited by 73 (17 self)
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This paper introduces a variant of clausal normal form tableaux that we call "hyper tableaux". Hyper tableaux keep many desirable features of analytic tableaux while taking advantage of the central idea from (positive) hyper resolution, namely to resolve away all negative literals of a clause in a single inference step. Another feature of the proposed calculus is the extensive use of universally quantified variables. This enables new efficient forwardchaining proof procedures for full first order theories as variants of tableaux calculi.
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 55 (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.
Explaining ALC subsumption
 In Proc. of DL’99
, 1999
"... Abstract. Knowledge representation systems, including ones based on Description Logics (DLs), use explanation facilities to, among others, debug knowledge bases. Until now, such facilities were not available for expressive DLs, whose reasoning is an unnatural refutationbased tableau. We offer a so ..."
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Cited by 54 (15 self)
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Abstract. Knowledge representation systems, including ones based on Description Logics (DLs), use explanation facilities to, among others, debug knowledge bases. Until now, such facilities were not available for expressive DLs, whose reasoning is an unnatural refutationbased tableau. We offer a solution based on a sequent calculus that is closely related to the tableau implementation, exploiting its optimisations. The resulting proofs are pruned and then presented as simply as possible using templates. 1
EXPTIME tableaux for ALC
 ARTIFICIAL INTELLIGENCE
, 2000
"... The last years have seen two major advances in Knowledge Representation and Reasoning. First, many interesting problems (ranging from Semistructured Data to Linguistics) were shown to be expressible in logics whose main deductive problems are EXPTIMEcomplete. Second, experiments in automated reaso ..."
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Cited by 51 (3 self)
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The last years have seen two major advances in Knowledge Representation and Reasoning. First, many interesting problems (ranging from Semistructured Data to Linguistics) were shown to be expressible in logics whose main deductive problems are EXPTIMEcomplete. Second, experiments in automated reasoning have substantially broadened the meaning of “practical tractability”. Instances of realistic size for PSPACEcomplete problems are now within reach for implemented systems. Still, there is a gap between the reasoning services needed by the expressive logics mentioned above and those provided by the current systems. Indeed, the algorithms based on treeautomata, which are used to prove EXPTIMEcompleteness, require exponential time and space even in simple cases. On the other hand, current algorithms based on tableau methods can take advantage of such cases, but require double exponential time in the worst case. We propose a tableau calculus for the description logic ALC for checking the satisfiability of a concept with respect to a TBox with general axioms, and transform it into the first simple tableaubased decision procedure working in single exponential time. To guarantee the ease of implementation, we also discuss the effects that optimizations (propositional backjumping, simplification, semantic branching, etc.) might have on our complexity result, and introduce a few optimizations ourselves.