## Decidable reasoning in terminological knowledge representation systems (1993)

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Venue: | Journal of Artificial Intelligence Research |

Citations: | 185 - 12 self |

### BibTeX

@ARTICLE{Buchheit93decidablereasoning,

author = {Martin Buchheit},

title = {Decidable reasoning in terminological knowledge representation systems},

journal = {Journal of Artificial Intelligence Research},

year = {1993},

volume = {1},

pages = {109--138}

}

### Years of Citing Articles

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### Abstract

Terminological Knowledge Representation Systems (TKRSs) are tools for designing and using knowledge bases that make use of terminological languages (or concept languages). The TKRS we consider in this paper is of practical interest since it goes beyond the capabilities of presently available TKRSs. First, our TKRS is equipped with a highly expressive concept, language, called ALCNR, including general complements of concepts, number restrictions and role conjunction. Second, it allows one to express inclusion statements between general concepts, in particular to express terminological cycles. We provide a sound, complete and terminating calculus for reasoning in ALCNR-knowledge bases based on the general technique of constraint systems.

### Citations

3836 | J.D.: Introduction to automata theory, languages, and computation - Hopcroft, Motwani, et al. |

821 | Dynamic logic
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- 1984
(Show Context)
Citation Context ...that ALCNR-knowledge bases have the finite model property, i.e. any satisfiable knowledge base has a finite model. This property has been extensively studied in modal logics [HC84] and dynamic logics =-=[Har84]-=-. In particular a technique, called filtration, has been developed both to prove the finite model property and to build a finite model for a satisfiable formula. This technique allows one to build a f... |

710 |
An Introduction to Modal Logic
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(Show Context)
Citation Context ...ve also implicitly proved that ALCNR-knowledge bases have the finite model property, i.e. any satisfiable knowledge base has a finite model. This property has been extensively studied in modal logics =-=[HC84]-=- and dynamic logics [Har84]. In particular a technique, called filtration, has been developed both to prove the finite model property and to build a finite model for a satisfiable formula. This techni... |

582 | An overview of the KL-ONE knowledge representation system
- Brachman, Schmolze
- 1985
(Show Context)
Citation Context ...ion of this schema, containing assertions relating either individuals to classes, or individuals to each other. This characteristic, which the mentioned proposals inherit from the seminal TKRS kl-one =-=[BS85]-=-, is shared also by several proposals of Database models such as Abrial's [Abr74], candide [BGN89], and taxis [MBW80]. Retrieving information in actual Knowledge Bases (KBs) built up using one of thes... |

409 |
First-Order Logic and Automated Theorem Proving
- Fitting
- 2012
(Show Context)
Citation Context ...relationships between the four problems. 3.1 The calculus and its correctness Our method makes use of the notion of constraint system [DLNN91a, SSS91, DLNS91], and is based on a tableau-like calculus =-=[Fit90]-=- that tries to build a model for the logical formula corresponding to a KB. Consider an alphabet of variable symbols V (disjoint from the other alphabets defined so far). The elements of V are denoted... |

347 | Resnick: CLASSIC: A Structural Data Model for Objects
- Borgida, Brachman, et al.
- 1989
(Show Context)
Citation Context ...Discussion 29 1 Introduction A general characteristic of many proposed Terminological Knowledge Representation Systems (TKRSs) such as kripton [BPL85], nikl [KBR86], back [QK90], loom [MB87], classic =-=[BBMAR89]-=-, KRIS [BH91], and others (see [Ric91, WS92]), is that they are made up of two different components. Informally speaking, the first is a general schema concerning the classes of individuals to be repr... |

276 | Elements of the Theory of Computation - Lewis, Papadimitriou - 1981 |

275 | Basic description logics
- Baader, Nu�
- 2003
(Show Context)
Citation Context ... problem w.r.t. descriptive semantics is given with the help of deterministic automata (whereas Buchi automata are nondeterministic). This also yields a PSPACE-algorithm for deciding subsumption. In (=-=Baader et al., 1990-=-) the attention is restricted to the language ALC . In particular, that paper considers the problem of checking the satisfiability of a single equation of the form C = ?, where C is an ALC-concept. Th... |

261 | A schema for integrating concrete domains into concept languages
- Baader, Hanschke
- 1991
(Show Context)
Citation Context ...esearch is still needed to address problems issuing from practical systems. For example, to completely express role restrictions inside number restrictions, qualified number restrictions (Hollunder & =-=Baader, 1991-=-) should be taken into account. Also, the language resulting from the addition of enumerated sets (called one-of in classic), and role fillers to ALCNR is still to be studied, although it does not see... |

255 | A correspondence theory for terminological logics: Preliminary report
- Schild
- 1991
(Show Context)
Citation Context ...gation is still needed. Previous theoretical work on cycles was done in (Baader, 1990a, 1990b; Baader, Burkert, Hollunder, Nutt, & Siekmann, 1990; Dionne, Mays, & Oles, 1992, 1993; Nebel, 1990, 1991; =-=Schild, 1991-=-), but considering KBs formed by the TBox alone. Moreover, these approaches do not deal with number restrictions (except for Nebel, 1990, Section 5.3.5) ---a basic feature already provided by TKRSs---... |

228 | The complexity of concept languages
- Donini, Lenzerini, et al.
- 1991
(Show Context)
Citation Context ...sumed to be simple, i.e. the only complements they contain are of the form :A, where A is a primitive concept. Arbitrary ALCNR-concepts can be rewritten into equivalent simple concepts in linear time =-=[DLNN91a]-=-. A constraint system is a finite nonempty set of constraints. Given an interpretation I, we define an I-assignment ff as a function that maps every variable of V to an element of \Delta I , and every... |

205 | Automata-Theoretic Techniques for Modal Logics of Programs - VARDI, WOLPER - 1986 |

201 | Reasoning and Revision in Hybrid Representation Systems
- Nebel
- 1990
(Show Context)
Citation Context ... a theoretical analysis of the general problems 1--4 is to be done. Previous theoretical results do not deal with the problems 1--4 in their full generality. For example, the problems are studied in (=-=Nebel, 1990-=-, Chapter 4), but only incomplete Buchheit, Donini, & Schaerf procedures are given, and cycles are not considered. In (Donini, Lenzerini, Nardi, & Schaerf, 1993; Schaerf, 1993a) the complexity of inst... |

180 |
The tractability of subsumption in framebased description languages
- Brachman, Levesque
- 1984
(Show Context)
Citation Context ...e corresponding problems is not known. Recent research on the computational complexity of subsumption had an influence in many TKRSs on the choice for incomplete procedures. The research started with =-=[BL84]-=-, which analyzed complexity of subsumption between pure concept expressions, abstracting from KBs (we call this problem in the sequel as pure subsumption). The motivation for focusing on such a small ... |

159 | The KL-ONE family - Woods, Schmolze - 1992 |

151 |
Foundations of a functional approach to knowledge representation
- Levesque
- 1984
(Show Context)
Citation Context ...g subroles with domain and range restrictions it is also possible to partially express the constructor for role restriction, which is present in various proposals (e.g., the language FL in Brachman & =-=Levesque, 1984-=-). Role restriction, written as R : C, is defined by (R : C) I = f(d 1 ; d 2 ) 2 \Delta I \Theta \Delta I j (d 1 ; d 2 ) 2 R Isd 2 2 C I g. For example the role DAUGHTER, which can be formulated as CH... |

147 | Attributive concept descriptions with complements - Schmidt-Schau��, Smolka - 1991 |

139 | Representing and Using Interschema Knowledge in Cooperative - Catarci, Lenzerini - 1993 |

125 |
A fundamental tradeoff in knowledge representation and reasoning
- Levesque, Brachman
- 1985
(Show Context)
Citation Context ...herefore the result of this research could be summarized as: The more a TKRS language is expressive, the higher is the computational complexity of reasoning in that language---as Levesque first noted =-=[Lev84]-=-. This result has been interpreted in two different ways, leading to two different TKRSs design philosophies: 1. `General-purpose languages for TKRSs are intractable, or even undecidable, and tractabl... |

125 | Embedding defaults into terminological knowledge representation formalisms - Baader, Hollunder - 1992 |

123 | Augmenting concept languages by transitive closure of roles: An alternative to terminological cycles
- Baader
- 1991
(Show Context)
Citation Context ..., where C is an ALC-concept. This problem, called the universal satisfiability problem, is shown to be equivalent to checking the satisfiability of an ALC-TBox (see Proposition 5.1 in the sequel). In =-=[Baa90a]-=-, an extension of ALC, called ALC reg , is introduced, which supports a constructor to express the transitive closure of roles. By means of transitive closure of roles it is possible to replace cyclic... |

109 |
The Loom Knowledge Representation Language
- MacGregor, Bates
- 1987
(Show Context)
Citation Context ... : : : : : 26 6 Discussion 29 1 Introduction A general characteristic of many proposed Terminological Knowledge Representation Systems (TKRSs) such as kripton [BPL85], nikl [KBR86], back [QK90], loom =-=[MB87]-=-, classic [BBMAR89], KRIS [BH91], and others (see [Ric91, WS92]), is that they are made up of two different components. Informally speaking, the first is a general schema concerning the classes of ind... |

102 |
Terminological cycles: Semantics and computational properties
- Nebel
- 1991
(Show Context)
Citation Context ...on problems for finite automata. In particular, he shows that subsumption w.r.t. descriptive semantics can be decided in polynomial space using Buchi automata. Using results from (Baader, 1990b), in (=-=Nebel, 1991-=-) a characterization of the above subsumption problem w.r.t. descriptive semantics is given with the help of deterministic automata (whereas Buchi automata are nondeterministic). This also yields a PS... |

95 | A terminological knowledge representation system with complete inference algorithms
- Baader, Hollunder
- 1991
(Show Context)
Citation Context ...Introduction A general characteristic of many proposed Terminological Knowledge Representation Systems (TKRSs) such as kripton [BPL85], nikl [KBR86], back [QK90], loom [MB87], classic [BBMAR89], KRIS =-=[BH91]-=-, and others (see [Ric91, WS92]), is that they are made up of two different components. Informally speaking, the first is a general schema concerning the classes of individuals to be represented, thei... |

84 |
alifying number restrictions in concept languages
- Hollunder, Baader
- 1991
(Show Context)
Citation Context ...que, 1985), nikl (Kaczmarek, Bates, & Robins, 1986), back (Quantz & Kindermann, 1990), loom (MacGregor & Bates, 1987), classic (Borgida, Brachman, McGuinness, & Alperin Resnick, 1989), kris (Baader & =-=Hollunder, 1991-=-), k-rep (Mays, Dionne, & Weida, 1991), and others (see Rich, editor, 1991; Woods & Schmolze, 1992), is that they are made up of two different components. Informally speaking, the first is a general s... |

83 | Subsumption algorithms for concept description languages - Hollunder, Nu�, et al. - 1990 |

79 | Deduction in concept languages: From subsumption to instance checking
- Donini, Lenzerini, et al.
- 1994
(Show Context)
Citation Context ...he 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 (Hollunder, 1990; Baader & Hollunder, 1991; =-=Donini et al., 1993-=-). 4.2 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) conce... |

78 |
Inside the LOOM description classifier
- MacGregor
- 1991
(Show Context)
Citation Context ...em, completeness of overall reasoning procedures is not an issue anymore; but other issues arise, such as how to compare incomplete procedures [HKNP92], and how to judge a procedure "complete eno=-=ugh" [Mac91]-=-. As a practical tool, inference rules can be used in such systems to achieve the expected behavior of the KB w.r.t. the information contained in it. 2. `A TKRS is (by definition) general-purpose, hen... |

74 | An essential hybrid reasoning system: knowledge and symbol level accounts of KRYPTON
- Brachman, Pigman, et al.
- 1985
(Show Context)
Citation Context ...sus Concept Definitions : : : : : : : : : : : : : : 26 6 Discussion 29 1 Introduction A general characteristic of many proposed Terminological Knowledge Representation Systems (TKRSs) such as kripton =-=[BPL85]-=-, nikl [KBR86], back [QK90], loom [MB87], classic [BBMAR89], KRIS [BH91], and others (see [Ric91, WS92]), is that they are made up of two different components. Informally speaking, the first is a gene... |

71 | Reasoning with individuals in concept languages
- Schaerf
- 1994
(Show Context)
Citation Context ...For example, the problems are studied in (Nebel, 1990, Chapter 4), but only incomplete Buchheit, Donini, & Schaerf procedures are given, and cycles are not considered. In (Donini, Lenzerini, Nardi, & =-=Schaerf, 1993-=-; Schaerf, 1993a) the complexity of instance checking has been analyzed, but only KBs without a TBox are treated. Instance checking has also been analyzed in (Vilain, 1991), but addressing only that p... |

66 | Subsumption algorithms for concept languages - Hollunder, Nutt - 1990 |

64 | Tractable concept languages - Donini, Lenzerini, et al. - 1991 |

61 | Computational complexity of terminological reasoning in BACK
- Nebel
- 1988
(Show Context)
Citation Context ...t pure subsumption is tractable (i.e., worst-case polynomial-time solvable) for simple languages, and intractable for slight extensions of such languages, as subsequent research definitely confirmed (=-=Nebel, 1988; Do-=-nini, Lenzerini, Nardi, & Nutt, 1991a, 1991b; Schmidt-Schau�� & Smolka, 1991; Donini, Hollunder, Lenzerini, Marchetti Spaccamela, Nardi, & Nutt, 1992). Also, beyond computational complexity, pure ... |

55 |
Wong: “A Language Facility for Designing Database-Intensive
- Mylopoulos, Bernstein, et al.
- 1980
(Show Context)
Citation Context ... characteristic, which the mentioned proposals inherit from the seminal TKRS kl-one [BS85], is shared also by several proposals of Database models such as Abrial's [Abr74], candide [BGN89], and taxis =-=[MBW80]-=-. Retrieving information in actual Knowledge Bases (KBs) built up using one of these systems is a deductive process involving both the schema (TBox) and its instantiation (ABox). In fact, the TBox is ... |

53 |
Data Semantics
- Abrial
- 1974
(Show Context)
Citation Context ..., or individuals to each other. This characteristic, which the mentioned proposals inherit from the seminal TKRS kl-one [BS85], is shared also by several proposals of Database models such as Abrial's =-=[Abr74]-=-, candide [BGN89], and taxis [MBW80]. Retrieving information in actual Knowledge Bases (KBs) built up using one of these systems is a deductive process involving both the schema (TBox) and its instant... |

49 | The complexity of existential quantification in concept languages - Donini, Hollunder, et al. - 1992 |

49 |
can be beautiful in knowledge representation
- Small
- 1984
(Show Context)
Citation Context ... reasoning to a user'. Following this line, other TKRSs (such as krypton and classic) provide limited tractable languages for expressing concepts, following the "small-can-be-beautiful" appr=-=oach (see Patel-Schneider, 1984-=-). The gap between what is expressible in the TKRS language and what is needed to be expressed for the application is then filled by the user, by a (sort of) programming with inference rules. Of cours... |

45 |
Terminological Cycles in KL-ONE-based Knowledge Representation Languages
- Baader
- 1990
(Show Context)
Citation Context ...ility w.r.t. a TBox is trivially harder than checking the satisfiability of a TBox, that paper extends the result given in (Baader et al., 1990). The technique exploited in (Baader et al., 1990) and (=-=Baader, 1990-=-a) is based on the notion of concept tree. A concept tree is generated starting from a concept C in order to check its satisfiability (or universal satisfiability). The way a concept tree is generated... |

45 | On the complexity of the instance checking problem in concept languages with existential quantification - Schaerf - 1993 |

44 | An empirical analysis of terminological representation systems - Heinsohn, Kudenko, et al. - 1994 |

44 |
Undecidability of subsumption in NIKL
- Patel-Schneider
- 1989
(Show Context)
Citation Context ...ini, Marchetti Spaccamela, Nardi, & Nutt, 1992). Also, beyond computational complexity, pure subsumption was proved undecidable in the TKRSs U (Schild, 1988), kl-one (Schmidt-Schau��, 1989) and ni=-=kl (Patel-Schneider, 1989-=-). Note that extending the language results in enhancing its expressiveness, therefore the result of that research could be summarized as: The more a TKRS language is expressive, the higher is the com... |

42 | Subsumption in KL-ONE is undecidable - Schmidt-Schau - 1989 |

37 |
Computational complexity of terminological reasoning
- Nebel
- 1988
(Show Context)
Citation Context ...hat pure subsumption is tractable (i.e., worst-case polynomial-time solvable) for simple languages, and intractable for slight extensions of such languages, as subsequent research de nitely con rmed (=-=Nebel, 1988-=-; Donini, Lenzerini, Nardi, & Nutt, 1991a, 1991b; Schmidt-Schau & Smolka, 1991; Donini, Hollunder, Lenzerini, Marchetti Spaccamela, Nardi, & Nutt, 1992). Also, beyond computational complexity, pure su... |

34 |
A practical decision method for propositional dynamic logic: Preliminary report
- Pratt
- 1978
(Show Context)
Citation Context ...ent constraint systems. This could be avoided if we allow a variable to be blocked by a witness that is in a previously analyzed constraint system. This technique would be similar to the one used in (=-=Pratt, 1978-=-), and to the tree-automata technique used in (Vardi & Wolper, 1986), improving on simple tableaux methods for variants of propositional dynamic logics. Since our calculus considers only one constrain... |

32 |
Classification as a query processing technique in the CANDIDE semantic data model
- Beck, Gala, et al.
- 1989
(Show Context)
Citation Context ...to each other. This characteristic, which the mentioned proposals inherit from the seminal TKRS kl-one [BS85], is shared also by several proposals of Database models such as Abrial's [Abr74], candide =-=[BGN89]-=-, and taxis [MBW80]. Retrieving information in actual Knowledge Bases (KBs) built up using one of these systems is a deductive process involving both the schema (TBox) and its instantiation (ABox). In... |

30 |
Hybrid Inferences in KL-ONE-based Knowledge Representation Systems”, DFKI Research Report RR-90-06
- Hollunder
- 1990
(Show Context)
Citation Context ...o 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 (po... |

30 | Recent Developments in NIKL
- Kaczmarek, Bates, et al.
- 1986
(Show Context)
Citation Context ...finitions : : : : : : : : : : : : : : 26 6 Discussion 29 1 Introduction A general characteristic of many proposed Terminological Knowledge Representation Systems (TKRSs) such as kripton [BPL85], nikl =-=[KBR86]-=-, back [QK90], loom [MB87], classic [BBMAR89], KRIS [BH91], and others (see [Ric91, WS92]), is that they are made up of two different components. Informally speaking, the first is a general schema con... |

22 | Computers and Intractability—A Guide to NPCompleteness - Garey, Johnson - 1979 |

22 | Concept languages as query languages - Lenzerini, Schaerf - 1991 |

20 | K-Rep system overview - Mays, Dionne, et al. - 1991 |