M. Schmidt-Schauss. Subsumption in KL-ONE is undecidable. In Proc. of KR-89, pages 421-431, Boston (USA), 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in a knowledge base into a taxonomy, and satis ability of single concepts, which was used to check the consistency of the knowledge base. Unfortunately, when the underlying representational formalism was studied in detail, it turned out that the above mentioned inference problems were undecidable [ Sch89 ] It might be argued that semi decidability is ne for other applications, and thus could be tolerated, but since subsumption can be reduced to unsatis ability and satis ability to non subsumption, one of both problems would always be truly undecidable. Following this observation, the ....

M. Schmidt-Schauss. Subsumption in KL-ONE is undecidable. In Proc. of KR-89, pages 421-431, Boston (USA), 1989.

....data updates, are not considered in such approaches. Knowledge representation systems are more concerned with inference capabilities allowing the classification of concepts (or points of view) in a global taxonomy, as well as the inference of the membership of objects to such concepts [BS85, SS89, Neb90] Theoretical results related to complexity and computability of the classification activity have been obtained from knowledge representation investigations, but, again, persistence and updates are not a main issue. Usually, updates can be performed on a very restricted basis: new ....

M. Schmidt-Schau. Subsumption in KL-ONE is undecidable. In Proceedings of the !st Int'l Conf. on Principles of Knowledge Representation and Reasoning, pages 421--431, Toronto, 1989.

.... have the same rst name by the expression (equal (compose father first name) compose father father first name) Interestingly, agreements between attribute chains do not make reasoning in the language undecidable [HN90] whereas agreements between arbitrary role chains cause undecidability [Sch89] The basic reasoning facilities concerning the TBox are the determination whether a concept denotes nothing, i.e. whether a concept denotes the empty set in every interpretation, and the computation of the subsumption hierarchy. A concept C subsumes (is more general than) a concept D i in ....

M. Schmidt-Schau. \Subsumption in KL-ONE is undecidable." In R. J. Brachmann, H. J. Levesque, R. Reiter (editors), Proceedings of the 1st International Conference on Principles of Knowledge Representation and Reasoning, pp. 421-431, Toronto, Ont., 1989.

....They are independent data pools with speci c data organization 4 descriptors are useful to both objectives. With respect to complexity of reasoning, the pioneering work [8] showed the computational cli encountered when apparently minor changes are made to the representation language. In [16, 18, 14, 24] languages with reasoning problems from polynomial to undecidable are reported. With this in mind, we have included in the languages just the necessary to satisfy the goal. Summarizing, we use concept constructors that focus primarily on structural properties. Structure is described specifying ....

....satisfy the goal. Summarizing, we use concept constructors that focus primarily on structural properties. Structure is described specifying several kinds of constraints on roles. Di erent groupings of various constraints provide di erent expressiveness and complexity of reasoning, in particular [24] shows the undecidability caused by the role value map 2 operator discussed in [6] Our interest in not discarding tractability have guided us to select a collection of constructors, used in a di erent context of query optimization [9] that were proved polynomial. However, those constructors ....

M. Schmidt-Schauss. Subsumption in KL-ONE is Undecidable. In Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning. (KR-89). Toronto, Ont., pages 421-431, 1989.

....w.r.t. general TBoxes in ALC. We also show that the further augmentation of ALCRASG with unqualified number restrictions, yielding the language ALCNRASG , is again undecidable. 1 1 Introduction and Motivation Since the famous Subsumption in KL ONE is undecidable result by SchmidtSchau ([14]) who identified the so called role value maps as a primary source of undecidability in the seminal description logic system KL ONE, role inclusion expressions containing the composition operator have not regained much attention in the DL community again (please refer to [2] for a more gentle and ....

M. Schmidt-Schau. Subsumption in KL-ONE is Undecidable. In Principle of Knowledge Representation and Reasoning -- Proceedings of the First International Conference KR '89, 1989.

.... Logics (DLs) Buchheit et al. 1993; Donini et al. 1991; Donini et al. 1992a; Donini et al. 1992b; SchmidtSchau and Smolka, 1991; Sebastiani and Straccia, 1991 ] Unfortunately, also negative results have appeared, e.g. showing that some DLs (e.g. NIKL [ Patel Schneider, 1989 ] and KL ONE [ Schmidt Schau, 1989 ] are undecidable. This work contributes to this latter literature by showing a negative result for another DL (called Mirtl) which had not been previously studied from the standpoint of computational complexity, and which is not directly related to the ones already shown undecidable; in more ....

Manfred Schmidt-Schau. Subsumption in KL-ONE is undecidable. In Proceedings of KR-89, 1st International Conference on Principles of Knowledge Representation and Reasoning, pages 421-- 431, Toronto, Ontario, 1989.

.... of DL constructors: in #######, coreferences between attribute chains (as in the above examples) can be reasoned with eciently (Borgida Patel Schneider, 1994) while if wechanged to roles, e.g. allowed #same as ######### ######## ################, the subsumption problem becomes undecidable (Schmidt Schau , 1989). Whereas the distinction between roles and attributes in DLs is both theoretically and practically well understood, wehave discovered that another distinction, namely the one between attributes being interpreted as total functions (total attributes) and those interpreted as partial functions ....

Schmidt-Schau, M. (1989). Subsumption in KL-ONE is undecidable. In Brachman, R. J.

....constructors. The first result in this area (Levesque 278 Subsumption in CLASSIC Brachman, 1987) showed that even a seemingly simple addition to a very small language can lead to subsumption determination becoming NP hard. A more recent, striking pair of results (Patel Schneider, 1989b; Schmidt Schauss, 1989) shows that adding the ability to represent equalities of role compositions makes the complexity of the subsumption problem leap from quadratic to undecidable. There are three possible responses to these intractability results: ffl Provide an incomplete implementation of the DL reasoner, in the ....

Schmidt-Schauss, M. (1989). Subsumption in KL-ONE is undecidable. In Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning, pp. 421--431. Morgan Kaufmann.

....wellprincipled, space and time efficient, and embeddable as sub systems in a wide variety of applications. Since complexity analyses show inference in knowledge representation systems with normally expected representational capabilities is intractable (Brachman and Levesque, 1984; Nebel, 1988; Schmidt Schau, 1989), it has been suggested that the representational and deductive capabilities of knowledge representation services should be limited for the sake of tractability (Levesque and Brachman, 1987) The reasons for and against this have been surveyed by Doyle 16 and Patil (1991) who conclude that, while ....

Schmidt-Schau, M. (1989). Subsumption in KL-ONE is undecidable. Proceedings of KR'89: First International Conference on Principles of Knowledge Representation and Reasoning. pp.421-431. San Mateo, California, Morgan Kauffman.

.... krypton [6] kris [3] loom [29] meson [13] nikl [41] sb one [23] and yak [10] Moreover, formal aspects of ter1 minological representation languages have been thoroughly investigated, with the highest emphasis having been placed on the decidability and complexity of the subsumption problem [24, 31, 39, 35, 33, 40, 11, 12]. As a result of these investigations, it is known that subsumption determination is at least NP hard or even undecidable for most languages that appear to be useful in applications. The developers of terminological representation systems usually have reacted to this problem in one of the ....

M. Schmidt-Schau. Subsumption in KL-ONE is undecidable. In R. Brachman, H. J. Levesque, and R. Reiter, editors, Principles of Knowledge Representation and Reasoning: Proceedings of the 1st International Conference, pages 421-431, Toronto, ON, May 1989. Morgan Kaufmann.

....of the difference operation by the structural difference directly depends on an implementation of the semantic equivalence relation j . In general, the semantic equivalence in description logics can be intractable or it can even be undecidable [Donini et al. 1991b; Donini et al. 1991a; Schmidt Schau, 1989] If, on the other hand, the subsumption in a description logic is tractable or decidable, the same holds true for the structural difference, respectively. Here, however, we do not investigate the complexity of the difference operation any further. 3.2.3 Structural Subsumption Next we will ....

Schmidt-Schau, M.: Subsumption in KL-ONE is Undecidable. In: Brachman, R. J., Levesque, H. J., Reiter, R. (eds.): Proceedings of the 1st International Conference on Principles of Knowledge Representation and Reasoning KR'89, San Mateo, Calif.: MorganKaufmann, 1989, pp. 421--431

....formal investigations of the subsumption problem in DLs were carried out. It turned out that (under the assumption P 6= NP) already quite inexpressive DLs cannot have polynomial subsumption algorithms [10, 39] and that the DL used by the Kl one system even has an undecidable subsumption problem [49]. In particular, these results showed the incompleteness of the (polynomial) structural subsumption algorithms. One reaction to these results (e.g. by the designers of Back and Loom) was to call the incompleteness of the subsumption algorithm a feature rather than a bug of the DL system. The ....

Manfred Schmidt-Schau. Subsumption in KL-ONE is undecidable. In R. J. Brachman, H. J. Levesque, and R. Reiter, editors, Proc. of KR-89, pages 421--431. Morgan Kaufmann, 1989.

.... have this kind of expressive power) Using role value maps (i.e. concepts like has component ffi owner v owner) to model this inheritance is not a good idea: even for very weak description logics, the extension with role value maps leads to the undecidability of subsumption and satisfiability [23]. However, there are some restrictions on or variants of role value maps that should be investigated since they might yield decidability of these inference problems. Summing up from what we have said above, SHIQ is able to model the general pw relation as well as various integral pwrelations ....

M. Schmidt-Schauss, `Subsumption in KL-ONE is undecidable', in Proc. of KR-89, Boston (USA), (1989).

.... helps identify tractable subsets of DL constructors: in classic, coreferences between attribute chains (as in the above examples) can be reasoned with e#ciently [10] while if we changed to roles (e.g. allowed (repairs # ownedBy # repairsPaidFor) the subsumption problem becomes undecidable [30]. The distinction between roles and attributes in DLs is both theoretically and practically well understood. However, it turns out that there is a distinction to be made between attributes being interpreted as total (total attributes) or partial functions (partial attributes) This distinction is ....

M. Schmidt-Schau. Subsumption in KL-ONE is undecidable. In R. J. Brachman, editor, Proceedings of the 1st International Conference on Principles of Knowledge Representation and Reasoning, pages 421--431, Toronto, Ont., 1989. 42

.... languages require completely different realizations of such an implication (cf. Table 2) This time, F Logic (or predicate logics) allows for a rather concise description, while description logics languages do not support composition of relations in general, since it makes subsumption undecidable [ScSm 1989]. In Loom, e.g. one may ressort to capabilities outside of the logic kernel, viz. production rules that achieve the intended effects 3 . Both ways may be easily summarized by the object description Composition(worksInProject,projectForCompany,knowsCompany) The transformation rule works ....

M. Schmidt-Schau and Gerd Smolka. Subsumption in KL-ONE is undecidable. KR-89 - Proceedings of the Conference on Knowledge Representation and Reasoning, Morgan Kaufmann, 1989, pp. 421-43.

.... helps identify tractable subsets of DL constructors: in classic, coreferences between attribute chains (as in the above examples) can be reasoned with efficiently [10] while if we changed to roles (e.g. allowed (repairs # ownedBy ffi repairsPaidFor) the subsumption problem becomes undecidable [30]. The distinction between roles and attributes in DLs is both theoretically and practically well understood. However, it turns out that there is a distinction to be made between attributes being interpreted as total (total attributes) or partial functions (partial attributes) This distinction is ....

M. Schmidt-Schau. Subsumption in KL-ONE is undecidable. In R. J. Brachman, editor, Proceedings of the 1st International Conference on Principles of Knowledge Representation and Reasoning, pages 421--431, Toronto, Ont., 1989. 60

.... there is a concept constructor already discussed in the literature, called subset of, with which one could express such a constraint as subset of( writtenIn] authoredBy,speaks] Unfortunately, reasoning in a language that supports constructors and, all and subset of is known to be undecidable (Schmidt Schauss, 1989). This means that the selection of concept constructors in the language is a matter of very careful consideration for the system designer, who is faced with several choices: a) Select a particular subset of constructors for which a sound and complete reasoning algorithm is known; if the language ....

Schmidt-Schauss, M. (1989). Subsumption in KL-ONE is undecidable. In Proceedings of KR'89.

....describe relationships among IS A relation, IS NOT A relation, and their roles. As a result, it is inevitably difficult to analyze the whole system and develop associated algorithms. Moreover, many problems associated with the system usually become complex; the subsumption of KL ONE is undecidable[19], and the satisfiability of several frameworks, including first order logic, are undecidable. Furthermore, it is generally impossible to identify and express all possible answers to a query in these systems. For many practical applications, however, several important issues should be considered: ....

Schmidt-Schau, M., "Subsumption in KL-ONE is Undecidable", Proc. of the 1st Int'l Conf. on Principles of Knowledge Representation and Reasoning, pp.421431, 1989.

....in positioning a view in the class lattice There are two ways out: i) Permit only decidable predicates. Research on knowledge representation languages in the KL ONE family [BS85] shows that, even with quite strong restrictions on the form of allowed predicates, the problem remains undecidable [SS89, Neb90] In our case, in the presence of computed functions and subqueries, the situation is even worse. ii) Implement an incomplete decision procedure. This means to consider only those parts of the class predicates during the classification that are known to be decidable. The position ....

M. Schmidt-Schauß. Subsumption in KL-ONE is undecidable. In Proc. First Int'l Conf. on Principles of Knowledge Representation and Reasoning, pages 421--431, Toronto, Ont., 1989.

....there is no need to check whether the predicate suffp(c 1 ) subsumes suffp(c 2 ) Therefore the predicate subsumption, which is in general undecidable, is not to be checked in any case. Because predicate subsumption is undecidable in general (and remains so even in quite restricted cases [Neb90, SS89] we use an incomplete decision procedure [Ngu91] for positioning a class in a class hierarchy (resp. testing the predicate subsumption) The predicate is decomposed into conjunctive normal form and only those conjuncts that are known to be decidable are used, the others are ignored. This ....

M. Schmidt-Schauß. Subsumption in KL-ONE is undecidable. In Proc. First Int'l Conf. on Principles of Knowledge Representation and Reasoning, pages 421--431, Toronto, Ont., 1989.

....for FL = fand, all, some, restrg, while it is O(n 2 ) for FL Gamma = FL n frestrg. Unfortunately, nearly all results appeared after the one by Brachman and Levesque are negative in nature, as they show that, in the logics they refer to, computing subsumption is either undecidable [12, 13, 14] or computationally intractable [7, 10, 11, 15] The only positive result in this respect is the one due to Donini et al. 5] who have recently given a tractability result for the logic fand, a not, r all, c someg. In this work we show that computing subsumption is O(n log n) in the logic ALN , ....

Manfred Schmidt-Schauß. Subsumption in KL-ONE is undecidable. In Proceedings of KR-89, 1st International Conference on Principles of Knowledge Representation and Reasoning, pages 421--431, Toronto, Ontario, 1989.

.... complexity of Description Logics (DLs) Buchheit et al. 1993; Donini et al. 1991; 1992a; 1992b; Schmidt Schau and Smolka,1991; Sebastiani and Straccia,1991 ] Unfortunately, also negative results have appeared, e.g. showing that some DLs (e.g. NIKL [ PatelSchneider, 1989 ] and KL ONE [ Schmidt Schau ,1989 ] are undecidable. This work contributes to this latter literature by showing a negative result for another DL (called Mirtl) which had not been previously studied from the standpoint of computational complexity, and which is not directly related to the ones already shown undecidable; in more ....

Manfred Schmidt-Schauß. Subsumption in KL-ONE is undecidable. In Proceedings of KR-89, 1st International Conference on Principles of Knowledge Representation and Reasoning, pages 421-- 431, Toronto, Ontario, 1989.

....languages. On the other hand, DL systems are equipped with subsumption algorithms necessary for providing the envisioned modeling support, as outlined above. In the last decade, a great variety of different description logics has been investigated [ Levesque Brachman, 1987; Nebel, 1988; Schmidt Schauss, 1989; PatelSchneider, 1989; Hollunder et al. 1990; Donini et al. 1991; Baader Hanschke, 1993; De Giacomo Lenzerini, 1994; Calvanese et al. 1995 ] However, the adequate representation of standard building blocks for models in process engineering requires additional expressive power. ....

M. Schmidt-Schauss. Subsumption in KL-ONE is undecidable. In Proc. of KR-89, pages 421--431, Boston (USA), 1989.

.... be represented in the DL unless the particular DL we are using allows the famous role value map constructor: equal(subset(teaches, knows) top) However, since role value maps (together with relation composition and concept conjunction) induce the undecidability of the DL inference services [9], they are usually not provided in implemented DL systems with complete algorithms. Therefore, we will have to encode this constraint at the higher levels of the model (inference and or task level) On the other hand, the constraints that each class should be taught by a lecturer and that a ....

Schmidt-Schau M. Subsumption in KL-ONE is undecidable. Proceedings KR-89, pp. 421-431.

....models using description logics (Report on operationalization of CommonKADS expertise models with description logics) Liviu Badea Doina Tilivea PEKADS WP4 TR 4.5.1 1.1 2 Contents 1 Introduction 7 1. 1 Brief description of E x Claim : 8 2 The domain level 10 2.1 The description logic : 10 2.1.1 Concept and role constructors. Declarative semantics : 12 2.1.2 Inference services in description logics : 14 2.1.3 Reduction of the inference services to KB consistency ....

....models with description logics) Liviu Badea Doina Tilivea PEKADS WP4 TR 4.5.1 1.1 2 Contents 1 Introduction 7 1.1 Brief description of E x Claim : 8 2 The domain level 10 2. 1 The description logic : : 10 2.1.1 Concept and role constructors. Declarative semantics : 12 2.1.2 Inference services in description logics : 14 2.1.3 Reduction of the inference services to KB consistency testing : 15 2.2 The domain level extension : ....

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Schmidt-Schauß M. Subsumption in KL-ONE is undecidable. Proceedings KR-89, pp. 421-431.

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