Bernhard Hollunder. Hybrid inferences in KL-ONE-based knowledge representation systems. In Proceedings of the 14th German Workshop on Artificial Intelligence, pages 38--47, Eringerfeld, FRG, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....complexity. The first such algorithm was proposed by Schmidt Schau and Smolka (1991) for a DL that they called ALC (for attributive concept description language with complements ) 2 It quickly turned out that this approach for deciding subsumption can be extended to various other DLs (Hollunder et al. 1990; Hollunder and Baader, 1991; Baader and Hanschke, 1991; Baader, 1991; Hanschke, 1992) and also to other inference problems such as the instance problem (Hollunder, 1990) Early on, DL researchers started to call the algorithms obtained this way tableau based algorithms since they observed that ....

.... complements ) 2 It quickly turned out that this approach for deciding subsumption can be extended to various other DLs (Hollunder et al. 1990; Hollunder and Baader, 1991; Baader and Hanschke, 1991; Baader, 1991; Hanschke, 1992) and also to other inference problems such as the instance problem (Hollunder, 1990). Early on, DL researchers started to call the algorithms obtained this way tableau based algorithms since they observed that the original algorithm by Schmidt Schau and Smolka for ALC, as well as subsequent algorithms for more expressive DLs, could be seen as specialisations of the tableau ....

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Hollunder, B.: 1990, `Hybrid Inferences in KL-ONE-based Knowledge Representation Systems'. In: Proc. of GWAI'90, Vol. 251 of Informatik-Fachberichte. pp. 38--47, Springer-Verlag.

....the EXT (nondeterministic) algorithm that computes (when it exists) an extension of a T DL theory. 4.1 Correctness and completeness issues The EXT algorithm is heavily dependent on the decision of the monotonic fragment of T DL , i.e. of the ## and = relations. It is well known (see [9]) that in most TLs (and the monotonic fragment of T DL is no exception) deciding ## can be reduced to the decision of = and that the decision of = can in turn be reduced to deciding if # is unsatisfiable. There exists a well known technique, based on constraint propagation (see [9] ....

....[9] that in most TLs (and the monotonic fragment of T DL is no exception) deciding ## can be reduced to the decision of = and that the decision of = can in turn be reduced to deciding if # is unsatisfiable. There exists a well known technique, based on constraint propagation (see [9]) for deciding unsatisfiability in TLs. By using this technique, it may be shown that it is decidable whether a finite and acyclic T set (i.e. a T set that contains no namings in which the definiendum is defined, either directly or indirectly, in terms of itself) is unsatisfiable. By ....

Bernhard Hollunder. Hybrid inferences in KL-ONE-based knowledge representation systems. In Proceedings of the 14th German Workshop on Artificial Intelligence, pages 38--47, Eringerfeld, FRG, 1990.

.... individual a in O is said to be an instance of a concept C if Sigma j= C(a) The instance recognition problem, i.e. checking whether Sigma j= C(a) can be reduced to satisfiability since a is an instance of C with respect to a knowledge base Sigma if and only if Sigma [f:C(a)g is unsatisfiable (Hollunder, 1990). Coming back to our example regarding the Beatles, let us see how the concept representing any pop group can be defined using the ALCS language: POP GROUP : 83.PERSON u 8LED BY .PERSONu 8 DeltaBORN IN .CITY u 8 ThetaSI NG.POP SONG: The definition states that a pop group is composed by ....

....dialogue given in section 6 there is only one missed inference, which has a minor impact in the flux of the conversation. In the following we will refer to the language ALCS Gamma . The rule based calculus to decide the satisfiability of ALCS Gamma and ALCS concepts operates on constraints (Hollunder et al. 1990). A constraint can be of the type x : C or xRy, where C is a concept, R is a role, and x; y are variables belonging to a predefined alphabet of variable symbols. The interpretation of constraints is defined as follows. Let I be an interpretation of the concept language. An I assignment ff is a ....

Hollunder, B. 1990. Hybrid inferences in KL-ONE-based knowledge representation systems. In Proc. of the 14 th German Workshop on Artificial Intelligence. Springer-Verlag.

.... [50] for a DL that they called ALC (for attributive concept description language with complements ) 1 It quickly turned out that this approach for deciding subsumption could be extended to various other DLs [28, 26, 4, 1, 23] and also to other inference problems such as the instance problem [24]. Early on, DL researchers started to call the algorithms obtained this way tableau based algorithms since they observed that the original algorithm by Schmidt Schau and Smolka for ALC, as well as subsequent algorithms for more expressive DL, could be seen as specialisations of the tab 1 ....

Bernhard Hollunder. Hybrid inferences in KL-ONE-based knowledge representation systems. In Proc. of GWAI'90, volume 251 of Informatik-Fachberichte, pages 38--47. Springer-Verlag, 1990.

....knowledge representation system. The satisfiability algorithm presented in this chapter is based on the idea of reducing hybrid reasoning to terminological reasoning. In the literature different hybrid techniques for knowledge base satisfiability have been presented (see [Neb90] Sch94] and [Hol90] On the other hand, a great effort to develop efficient algorithms for terminological reasoning has resulted in several good optimisation techniques [HPS98] The aim of the work presented here is to extend these good results to the assertional part, as well as to avoid developing a completely ....

Bernhard Hollunder. Hybrid inferences in kl-one-based knowledge representation system. Technical report, DFKI, 1990.

....algorithm that computes (when it exists) an extension of a T DL Gamma theory. 4.1 Correctness and completeness issues The EXT algorithm is heavily dependent on the decision of the monotonic fragment of T DL Gamma , i.e. of the Omega and j= relations. It is well known (see [9]) that in most TLs (and the monotonic fragment of T DL Gamma is no exception) deciding Omega can be reduced to the decision of j= and that the decision of j= can in turn be reduced to deciding if Omega is unsatisfiable. There exists a well known technique, based on constraint propagation ....

....in most TLs (and the monotonic fragment of T DL Gamma is no exception) deciding Omega can be reduced to the decision of j= and that the decision of j= can in turn be reduced to deciding if Omega is unsatisfiable. There exists a well known technique, based on constraint propagation (see [9]) for deciding unsatisfiability in TLs. By using this technique, it may be shown that it is decidable whether a finite and acyclic T set (i.e. a T set that contains no namings in which the definiendum is defined, either directly or indirectly, in terms of itself) is unsatisfiable. By ....

Bernhard Hollunder. Hybrid inferences in KL-ONE-based knowledge representation systems. In Proceedings of the 14th German Workshop on Artificial Intelligence, pages 38--47, Eringerfeld, FRG, 1990.

....automata problems, concept trees and reduction to PDL, deal only with TBoxes and they don t seem to be suitable to deal also with ABoxes. On the other hand, the constraint system technique, even though it was conceived for TBox reasoning, can be easily extended to ABox reasoning, as also shown in [Hol90] BH91] and [DLNS92] 5.2 Inclusions versus Concept Definitions Now we compare the expressive power of TBoxes defined as a set of inclusions (as done in this paper) and TBoxes defined as a set of (possibly cyclic) concept definitions of the form A D and A : D. Unlike [Baa90a] and [Sch91] ....

Bernhard Hollunder. Hybrid inferences in KL-ONE-based knowledge representation systems. In German Workshop on Artificial Intelligence. Springer Verlag, 1990.

....so it seems natural to implement them as logic programs. Moreover, the limited expressiveness of terminological formalisms allows for decision procedures for a number of interesting reasoning problems. These problems include consistency of assertions and classification of concepts. The key idea of [Hol90, ScSm91, BDS93]) for constructing such inference algorithms is to reduce all reasoning services to consistency checking. This essential algorithm can be considered as constraint solving, where concepts and roles are the constraints. We therefore aim at implementing reasoning with terminologies as constraint ....

.... C I 2 . Figure 1.1 shows the subsumption graph of the terminology developed in sections 1.4 and 1.5. The consistency test is the central reasoning service for terminological knowledge representation systems with complete inference algorithms. Various other services can be reduced to this test [Hol90]. In particular, the subsumption (and similarly membership) services can be implemented on the basis of the consistency test of A boxes: 6 This declaration introduces a concept name that is not defined any further. 12 Chapter 1 Gamma Gamma Gamma Psi R i i i i i i i) B B BN H H H H Hj A ....

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B. Hollunder. Hybrid inferences in KL-ONE-based knowledge representation systems. In 14th German Workshop on Artificial Intelligence (GWAI-90), volume 251, pages 38--47. Springer, 1990.

....24] both for the design of algorithms for concept satisfiability and subsumption, and for studying their computational properties. In this work, since we are interested in knowledge base satisfiability and instance checking, we extend the calculus to the treatment of individuals (as proposed in [9]) The calculus operates on constraints consisting of individuals, variables, concepts and roles. Concepts are assumed to be in a particular form, called simple, which is the analogous of the negation normal form for formulae. A concept is called simple if it contains only complements of the form ....

Bernhard Hollunder. Hybrid inferences in KL-ONE-based knowledge representation systems. In Proc. of the German Workshop on Artificial Intelligence, pages 38--47. Springer-Verlag, 1990.

....of S. If there is no such solution, then S is said to be Sigma unsolvable. Given an ALC knowledge base Sigma, we define S Sigma to be the constraint system that includes one constraint a: C for each assertion C(a) of Sigma, and one constraint aRb for each assertion R(a; b) of Sigma (see [8]) The next proposition shows that answering a query posed to a knowledge base Sigma can be reduced to checking a particular constraint system for Sigma solvability. Proposition 3.1 Let Sigma be an ALC knowledge base, C be an ALCK concept, and a an individual. Then Sigma j C(a) iff S ....

Hollunder, B. Hybrid inferences in KL-ONEbased knowledge representation systems. In Proc. of the German Workshop on Artificial Intelligence (1990), Springer-Verlag.

....than subsumption. As a matter of fact, in a standard open world database, subsumption can be reduced to realization. On the other hand, realization is usually not much harder than subsumption since from a theoretical point of view a slight modification of the subsumption algorithm can be used [19]. For closed world databases the picture is sometimes different, however [32, Chap. 4] 19 As a matter of fact, co reference constraints over single valued roles are computationally very well behaved, which leads to a polynomial subsumption algorithm in classic an insight gained from the ....

B. Hollunder. Hybrid inferences in KL-ONE-based knowledge representation systems. In H. Marburger, editor, GWAI-90. 14th German Workshop on Artificial Intelligence. Springer-Verlag, Berlin, Germany, 1990.

....language, as opposed to both standard LP and first order logic. As current description logics are all subsets of OLP, the latter may also indicate directions for enhancing the expressivity of the former. 1 Introduction At the base of research on Description Logics (or Concept Languages) [14], 15] 13] 4] 5] 8] 1] lies the idea in [3] and [2] that an expert system and a knowledge representation language in general needs to deal with two different kinds of information: on the one hand so called assertional information about the world, and on the other hand ....

....knowledge base consists of a terminological part (the T Box) which uses a frame based language, and an assertional part (the A Box) which uses FOL as a representation language. This idea of a distinction between A Box and T Box is further explored in current description logics (see for example [14], 8] The T Box consists of a set of concept definitions in a limited concept definition language. The ABox contains assertions about concept membership of individual constants. Current research (for example [15] 13] 1] is mostly concerned with determining definition languages that combine ....

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B. Hollunder. Hybrid inferences in kl-one-based knowledge representation systems. In German National Conference on Artificial Intelligence, 1990.

....of tableau based inference methods in DL) The first tableau based subsumption algorithm was developed in [104] for the language ALC, which allows for the first five constructors of Figure 2. Since then, this approach for designing subsumption algorithms was extended to the instance problem [56, 8] and to various description languages extending ALC (see, e.g. 58, 57, 11, 12] for languages with number restrictions; 3] for transitive closure of roles and [98] for transitive roles; 6] for constructs that allow to refer to concrete domains such as numbers; and [25] for the treatment of ....

B. Hollunder. Hybrid inferences in KL-ONE-based knowledge representation systems. In 14th German Workshop on Artificial Intelligence, volume 251 of Informatik-Fachberichte, pages 38--47, Ebingerfeld, Germany, 1990. Springer--Verlag.

....they are called Host Individuals. However, they miss the expressive power of the full use of O. 5 A technique for complete reasoning The technique we present here is a refinement of the tableaux calculus for first order logic [BM77] and is employed in [DHL 92, DLNN91, DLNS92, HNSS90, SSS91, Hol90] both for the design of algorithms for the various reasoning tasks, and for studying their computational properties. The calculus in this paper is a straightforward extension, to deal with O and B, of the calculus in the cited papers. For the sake of simplicity, we restrict our attention to the ....

....rule, then S is satisfiable if S 0 is satisfiable. Furthermore, if the nondeterministic rule applies to S, then it can be applied in a way that it yields a constraint system S 0 such that S 0 is satisfiable if S is satisfiable. Proof. The correctness of rules 1 4 is stated in [Hol90] the extension to rules 5 and 6 is straightforward. A clash is a set of constraints of one of the following forms 1. fs: g, 2. fs: A; s: Ag, 3. fa: fa 1 ; a n gg with a 6= a i for all i = 1; n, 4. fa: fa 1 ; a n gg with a = a i for some i = 1; n. The ....

[Article contains additional citation context not shown here]

Bernhard Hollunder. Hybrid inferences in KL-ONE-based knowledge representation systems. In Proc. of the German Workshop on Artificial Intelligence. Springer-Verlag, 1990.

....Classic use structural subsumption algorithms. These algorithms are efficient and sound, but incomplete for expressive description languages. In contrast to that, Kris and Taxon provide sound and complete algorithms based on a model generating procedure [14] for testing the consistency of an ABox [6, 1]. All systems provide different description languages and inferences, preventing a comparison of the systems as well as the transfer of descriptions from one system to another. Within the Krss project, a concrete and an abstract syntax for a very expressive language description logic was developed ....

Hollunder, B. Hybrid inferences in kl-one-based knowledge representation systems. In Proc. GWAI-90 (Ehringerfeld, Germany, 1990), Informatik Fachberichte, Springer.

....ALC concepts is known to be decidable; more precisely, it is Pspace complete, as shown in [ Schmidt Schau and Smolka,1991 ] The algorithm described there is based on a tableau calculus. The underlying ideas can also be used to derive algorithms for various other concept languages (see, e.g. Hollunder et al. 1990; Hollunder,1990; Donini et al. 1991a; 1991b; 1992; Hollunder and Baader,1991 ] 3 Integrating concrete domains In this section we introduce a formalism that is able to refer to concrete objects (like numbers) and can use predefined relations on these objects in concept descriptions. For ....

....be decidable; more precisely, it is Pspace complete, as shown in [ Schmidt Schau and Smolka,1991 ] The algorithm described there is based on a tableau calculus. The underlying ideas can also be used to derive algorithms for various other concept languages (see, e.g. Hollunder et al. 1990; Hollunder,1990; Donini et al. 1991a; 1991b; 1992; Hollunder and Baader,1991 ] 3 Integrating concrete domains In this section we introduce a formalism that is able to refer to concrete objects (like numbers) and can use predefined relations on these objects in concept descriptions. For example, one might ....

B. Hollunder. Hybrid inferences in KL-ONE-based knowledge representation systems. In 14th German Workshop on Artificial Intelligence, volume 251 of InformatikFachberichte, pages 38--47, Ebingerfeld, Germany, 1990. Springer--Verlag.

....really exists; but if its answer is negative, then we do not know anything. A subsumption relationship may or may not exist. In [ Schmidt Schau and Smolka, 1991 ] a sound and complete subsumption algorithm for ALC is described. The underlying method of constraint propagation was used in [ Hollunder et al. 1990 ] to derive algorithms for various other concept languages. This method can with appropriate modifications also be applied to the languages of the form ALC(D) As a subtask, such an algorithm for ALC(D) will have to decide satisfiability of conjunctions of the form V k i=1 P i (x (i) in ....

....As a subtask, such an algorithm for ALC(D) will have to decide satisfiability of conjunctions of the form V k i=1 P i (x (i) in the concrete domain. Thus we shall have to require that D is admissible. In the literature (e.g. Levesque and Brachman, 1987; Schmidt Schau and Smolka, 1991; Hollunder et al. 1990 ] subsumption is often defined without reference to a T box as a relationship between concept terms. For two concept terms C, D we say that D subsumes C (written C v D) iff C I D I holds for all interpretations I. Two concept terms C, D are said to be equivalent iff C subsumes D and ....

[Article contains additional citation context not shown here]

B. Hollunder. Hybrid inferences in kl-one-based knowledge representation systems. In GWAI-90; 14th German Workshop on Artificial Intelligence, volume 251 of Informatik-Fachberichte, pages 38--47. Springer, 1990.

....is combined with a theorem prover for predicate logic. This system is based on the theory resolution calculus (Stickel, 1985) which will be discussed later on. Nowadays numerous works on defining concept languages with well understood semantics for the definition of taxonomical knowledge exist (Hollunder, 1990). 1 Introduction 3 Viewpoint of this paper The aim of this paper is twofold: Firstly, we want to classify the various kinds of treating theories within deduction systems, and secondly, we want to compare a special subclass of these methods. It is easier to compare the theory reasoning calculi ....

Hollunder, B. (1990). Hybrid Inferences in KL-ONE-based Knowledge Representation Systems.

....complete algorithms have to be intractable, whereas incomplete algorithms may still be polynomial. However, one should keep in mind that these complexity results are worst case results. It is not at all clear how complete algorithms may behave for typical knowledge bases. In [SS88, HNS90, Hol90] it is shown how to devise sound and complete algorithms for the above mentioned inferences in various concept languages. Thus it has become possible to implement a kl one system (KRIS) which provides a very expressive concept language, powerful reasoning facilities, and sound and ....

....language contains only few constructs for building complex role or attribute terms. If is of the form (assert ind a C) the instantiation problem can be reduced to the consistency problem as follows: A; T j= assert ind a C) i A [ f(assert ind a (not C) g is not consistent w.r.t. T . In [Hol90] a sound and complete algorithm for the consistency and instantiation problem for a sublanguage of the language de ned in Section 2 is described. KRIS also provides the user with algorithms which nd out certain relationships between the de ned concepts, roles, attributes, and individuals. ....

B. Hollunder. \Hybrid Inferences in kl-one-based Knowledge Representation Systems." In Proceedings of the 14th German Workshop on Articial Intelligence, pp. 38-47, Eringerfeld, Germany, 1990.

....of 9. Retrieval. Given an concept C. Which objects occurring in the assertional axioms are instances of C With this formalization of our services we can develop procedures or algorithms for the services and prove their correctness, completeness, complexity, decidability; see for example [SS88, HN90, Hol90, Baa91, DLNN91a, DHLMNN91, HB91, BH91, DLNN91b]. ....

B. Hollunder. "Hybrid Inferences in kl-one-based Knowledge Representation Systems." In Proceedings of the 14th German Workshop on Artificial Intelligence, pp. 38--47, Eringerfeld, Germany, 1990.

....proofs for assertional facts which can be seen as an abduction problem for ABoxes and for Schwind and Risch s method one must find maximal consistent sets of assertional facts. In Section 6 we shall point out how the tableaux based methods for assertional reasoning developed in our group ([10, 2]) can be modified to solve these problems. 2 The Representation Formalisms First we shall briefly review the terminological language ALCF [11] and Reiter s default logic. Then terminological default logic is defined as the specialization of default logic to ALCF . Finally an example will ....

....of whether (the translation of) a given ABox fact C(a) is a (logical) consequence of (the translation of) a given ABox A. If the answer is yes we say that a is an instance of C with respect to A (A j= C(a) Algorithms which solve this inference problem have, for example, been described in [10, 2]. 2.2 Reiter s default logic Reiter [25] deals with the problem of how to formalize nonmonotonic reasoning by introducing nonstandard, nonmonotonic inference rules, which he calls default rules. A default rule is any expression of the form ff : fi 1 ; fi n fl ; where ff, fi 1 , ....

[Article contains additional citation context not shown here]

B. Hollunder. Hybrid inferences in KL-ONE-based knowledge representation systems. In 14th German Workshop on Artificial Intelligence, volume 251 of Informatik-Fachberichte, pages 38--47, Ebingerfeld, Germany, 1990. Springer.

....= where t is a ground term and C is a concept. For testing constraint unifiability we now need an algorithm which tests such constraints on RQ satisfiability. Algorithms for testing satisfiability of constraints of the form o : C are well known if o is a constant and C is a concept (cf. e.g. [2, 11]) However, we have to solve three additional problems. First, in ALC constraints objects may be arbitrary ground terms instead of constants. Second, there may be ALC constraints of the form C = which are equivalent to :C = where is a concept such that A = U A for each structure A) ....

B. Hollunder, `Hybrid inferences in KL-ONE-based knowledge representation systems', in 14th German Workshop on Artificial Intelligence, volume 251 of Informatik-Fachberichte, pp. 38--47, Ebingerfeld, Germany, (1990). Springer.

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Bernhard Hollunder. Hybrid inferences in KL-ONE-based knowledge representation systems. In Proceedings of the 14th German Workshop on Artificial Intelligence, pages 38--47, Eringerfeld, FRG, 1990.

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Bernhard Hollunder. Hybrid inferences in KL-ONE-based knowledge representation systems. In Proc. of the German Workshop on Arti cial Intelligence, pages 38-47. Springer, 1990.

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B. Hollunder. Hybrid inferences in KL-ONE-based knowledge representation systems. In Proceedings of GWAI--90, Fourteenth German Workshop on Artificial Intelligence, pages 38--47, 1990.

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