## Subsumption Algorithms for Concept Languages (1990)

Citations: | 66 - 6 self |

### BibTeX

@TECHREPORT{Hollunder90subsumptionalgorithms,

author = {Bernhard Hollunder and Werner Nutt},

title = {Subsumption Algorithms for Concept Languages},

institution = {},

year = {1990}

}

### Years of Citing Articles

### OpenURL

### Abstract

We investigate the subsumption problem in logic-based knowledge representation languages of the kl-one family and give decision procedures. All our languages contain as a kernel the logical connectives conjunction, disjunction, and negation for concepts, as well as role quantification. The algorithms are rule-based and can be understood as variants of tableaux calculus with a special control strategy. In the first part of the paper, we add number restrictions and conjunction of roles to the kernel language. We show that subsumption in this language is decidable, and we investigate sublanguages for which the problem of deciding subsumption is PSPACE-complete. In the second part, we amalgamate the kernel language with feature descriptions as used in computational linguistics. We show that feature descriptions do not increase the complexity of the subsumption problem. Contents 1 Introduction 3 2 Concept Languages 7 3 Checking Satisfiability 10 4 PSPACE-Complete Languages 13 4.1 Satisf...

### Citations

584 | An Overview of the KL-ONE Knowledge Representation System, in
- Brachman, Schmolze
- 1985
(Show Context)
Citation Context ...on, and agreement and disagreement of feature chains. Selection corresponds to existential quantification of roles. Agreement and disagreement are counterparts of kl-one's so-called "role value m=-=aps" [BS85]-=-. Smolka shows that a feature language that contains intersection, union and complement of feature descriptions, as well as selection, agreement and disagreement on features, has an NP-complete satisf... |

421 | An Introduction to Unification-Based Approaches to Grammar
- Shieber
- 1986
(Show Context)
Citation Context ...oncepts and Feature Logic Feature descriptions emerged in computational linguistics as a device to describe constituents of sentences in terms of attributes, which are called features in this context =-=[Sh86]. Examples-=- for such features may be gender, number, or voice. The main operation on feature descriptions is a test for consistency. In his paper on "Feature Logic", Smolka gave a Tarsky style semantic... |

347 | CLASSIC: A Structural Data Model for Objects
- Borgida, Brachman, et al.
- 1989
(Show Context)
Citation Context ...ntences are described in terms of attributes (so-called features) and their values [Sh86, Smo88]. Recently, concept languages have been investigated as a means to describe object oriented data models =-=[BBMR89]-=-. A concept is built up of two kinds of primitive symbols, concepts and roles. An interpretation interprets them as subsets of a domain and binary relations over the domain. These primitives can be co... |

281 |
First-order logic
- Smullyan
- 1968
(Show Context)
Citation Context ...mula 9x:OE C (x) is a model of the concept C and vice versa. In particular, C is unsatisfiable if and only if 9x:OE C (x) is unsatisfiable. A careful analysis shows that first order tableaux calculus =-=[Sm68]-=- always terminates for such formulas, and exhibits a model if the formula is satisfiable, or produces obvious contradictions if the formula is not satisfiable. In particular it follows that a formula ... |

201 | Reasoning and Revision in Hybrid Representation Systems - Nebel - 1990 |

137 |
Combinatorial algorithms
- Nijenhuis, Wilf
- 1979
(Show Context)
Citation Context ...e function sat1 in Figure 1 is called with arguments x and S = fx: Cg. Then sat1 returns true if and only if there exists a clash free quasi-complete constraint system extending S. Nijenhuis and Wilf =-=[NW75]-=- give a linear space algorithm that enumerates all partitions of a finite set. We can use a slightly modified version of their algorithm enumerating only k-partitions to find an appropriate k-partitio... |

117 | Expressiveness and tractability in knowledge representation and reasoning - Brachman, Levesque - 1987 |

111 | The Loom Knowledge Representation Language - MacGregor, Bates - 1987 |

74 | An essential hybrid reasoning system: knowledge and symbol level accounts of KRYPTON - Brachman, Pigman, et al. - 1985 |

61 | Computational complexity of terminological reasoning in BACK - Nebel - 1988 |

53 | The restricted language architecture of a hybrid representation system - Vilain - 1985 |

50 | Small can he Beautiful in Knowledge Representation - Patel-Schneider - 1984 |

44 | Undecidability of subsumption in NIKL - Patel-Schneider - 1989 |

42 |
Subsumption in KL-ONE is undecidable
- Schmidt-Schau
- 1989
(Show Context)
Citation Context ... expression father first name : = father father first name: Interestingly, agreements of feature chains are computationally tractable, whereas agreements of arbitrary role chains cause undecidability =-=[Sch89]-=-. Concepts implicitly form a hierarchy: a concept C is subsumed by a concept D if in every interpretation the set denoted by C is a subset of the set denoted by D. The basic reasoning facility provide... |

30 | Recent Developments in NIKL - Kaczmarek, Bates, et al. - 1986 |

27 |
Attributive concept descriptions with unions and complements
- Schmidt-Schauß, Smolka
- 1988
(Show Context)
Citation Context ...o-NP-hard [LB87, Neb88]. Other work identified languages with undecidable subsumption problem [Pat89, Sch89, Sch88]. The first nontrivial subsumption algorithm was given by Schmidt-Schau�� and Smo=-=lka [SS88]-=- for the language ALC, which extends FL \Gamma by allowing for arbitrary logical connectives and role quantification as constructs. The algorithm is even optimal, since it requires linear space and th... |

16 |
A feature logic with subsorts. LILOG Report 33
- Smolka
- 1988
(Show Context)
Citation Context ...le quantification, number restrictions and role conjunction that captures the intuitive meaning. Only recently, the close relation between kl-one-languages and feature formalisms has been pointed out =-=[Smo88]-=-. In this paper we introduce a language that encorporates both kl-one-one constructs and features. Features are functional roles, that is they are supposed to have at most one filler. Natural examples... |

15 | Hybrid Reasoning in BACK - Nebel, vonLuck - 1988 |

9 | Undecidability of U - Schild - 1988 |

8 |
The tractability of subsumption in frame based description languages
- Brachmann, Levesque
- 1984
(Show Context)
Citation Context ...epresentation formalisms like frames and semantic networks, kl-one languages have the advantage of a Tarski style declarative semantics that allows to conceive them as sublanguages of predicate logic =-=[BL84]-=-. Concepts are intended to be descriptions of classes of objects. Essentially, such a description is given in terms of primitive classes and attributes of objects. A related family of formalisms emerg... |

3 | Subsumption Algorithms for Some Attributive Concept Description Languages - Hollunder - 1989 |