## Embedding Defaults into Terminological Knowledge Representation Formalisms (1995)

Venue: | Journal of Automated Reasoning |

Citations: | 135 - 7 self |

### BibTeX

@INPROCEEDINGS{Baader95embeddingdefaults,

author = {Franz Baader and Bernhard Hollunder},

title = {Embedding Defaults into Terminological Knowledge Representation Formalisms},

booktitle = {Journal of Automated Reasoning},

year = {1995},

pages = {306--317},

publisher = {Morgan Kaufmann}

}

### Years of Citing Articles

### OpenURL

### Abstract

We consider the problem of integrating Reiter's default logic into terminological representation systems. It turns out that such an integration is less straightforward than we expected, considering the fact that the terminological language is a decidable sublanguage of first-order logic. Semantically, one has the unpleasant effect that the consequences of a terminological default theory may be rather unintuitive, and may even vary with the syntactic structure of equivalent concept expressions. This is due to the unsatisfactory treatment of open defaults via Skolemization in Reiter's semantics. On the algorithmic side, we show that this treatment may lead to an undecidable default consequence relation, even though our base language is decidable, and we have only finitely many (open) defaults. Because of these problems, we then consider a restricted semantics for open defaults in our terminological default theories: default rules are only applied to individuals that are explicitly presen...

### Citations

11502 |
Computers and Intractability, A Guide to the Theory of NPCompleteness
- Garey, Johnson
- 1979
(Show Context)
Citation Context ...ding minimal valuations that make a monotonic boolean formula / "true" is NP-complete. In fact, if / is in conjunctive normal form, this is just the well-known problem of finding minimal hit=-=ting sets [26, 9]-=-. On the other hand, if / is in disjunctive normal form, the minimal valuations can be found in polynomial time. However, transforming a given monotonic boolean formula into disjunctive normal form ma... |

1484 |
A logic for default reasoning
- Reiter
- 1980
(Show Context)
Citation Context ...minological systems community. However, these investigations may also be of interest for research in nonmonotonic reasoning itself. Most nonmonotonic reasoning formalisms (e.g. Reiter's default logic =-=[25]-=-, Circumscription [17]) use full first-order predicate logic as their base language. In this general form, the formalisms are usually highly undecidable (see e.g. [25] Theorem 4.9). For this reason, w... |

947 | A theory of diagnosis from first principles
- Reiter
- 1987
(Show Context)
Citation Context ...ding minimal valuations that make a monotonic boolean formula / "true" is NP-complete. In fact, if / is in conjunctive normal form, this is just the well-known problem of finding minimal hit=-=ting sets [26, 9]-=-. On the other hand, if / is in disjunctive normal form, the minimal valuations can be found in polynomial time. However, transforming a given monotonic boolean formula into disjunctive normal form ma... |

865 |
Circumscription—a form of non-monotonic reasoning
- McCarthy
- 1980
(Show Context)
Citation Context ...mmunity. However, these investigations may also be of interest for research in nonmonotonic reasoning itself. Most nonmonotonic reasoning formalisms (e.g. Reiter's default logic [25], Circumscription =-=[17]-=-) use full first-order predicate logic as their base language. In this general form, the formalisms are usually highly undecidable (see e.g. [25] Theorem 4.9). For this reason, work on decision proced... |

654 |
A Truth Maintenance System
- Doyle
- 1986
(Show Context)
Citation Context ...ating defaults of) all extensions more efficient. 5.1 Junker and Konolige's method Junker and Konolige [12] translate a closed default theory (A; D) into a Truth Maintenance Network (TMN) `a la Doyle =-=[8]-=-. The nodes of the TMN are the consequents CD , and the prerequisites and negated justifications LD of the defaults. A default ff : fi 1 ; . . . ; fi n =fl of D is translated into a nonmonotonic justi... |

621 | An Overview of the KL-ONE Knowledge Representation System
- Brachman, Schmolze
- 1985
(Show Context)
Citation Context ...e problem of integrating Reiter's default logic into a terminological representation formalism. This treatment of defaults in terminological systems has already been proposed by Brachman and Schmolze =-=[7]-=-, but to the best of our knowledge, this proposal was never followed up. Reiter's default rule approach seems to fit well into the philosophy of terminological systems because most of them already pro... |

269 | A scheme for integrating concrete domains into concept languages
- Baader, Hanschke
- 1991
(Show Context)
Citation Context ...es. In the following we shall describe a more efficient method of finding these minimal (maximal) sets. The method is an extension of the tableaux-based consistency algorithms for ABoxes described in =-=[1, 10]-=-. The idea of employing tableaux-based methods for such purposes was already used in [18, 28], but these papers restricted themselves to propositional logic, which is a much easier case. In order to d... |

238 |
Non-monotonic logic
- McDermott, Doyle
- 1980
(Show Context)
Citation Context ...imal) sets. The method is an extension of the tableaux-based consistency algorithms for ABoxes described in [1, 10]. The idea of employing tableaux-based methods for such purposes was already used in =-=[18, 28]-=-, but these papers restricted themselves to propositional logic, which is a much easier case. In order to decide whether an ABox A is consistent, the tableaux-based consistency algorithm tries to gene... |

116 |
Search Through Systematic Set Enumeration
- Rymon
- 1992
(Show Context)
Citation Context ...owever, transforming a given monotonic boolean formula into disjunctive normal form may cause an exponential blow-up. To optimize the search for minimal valuations one can use the method described in =-=[27]-=-. The rules of the labelled consistency algorithm as described have the unpleasant property that deciding whether or not a rule is applicable is an NP-hard problem. In fact, the preconditions of the r... |

81 |
Recursive unsolvability of a problem of Thue
- POST
- 1947
(Show Context)
Citation Context ... language ALCF , this treatment of open defaults also leads to an undecidable default consequence relation, even though ALCF is decidable. This is achieved by reducing the word problem for semigroups =-=[24]-=- to the consequence problem of a default theory. Let \Sigma be a finite alphabet, and let R = f(u 1 ; v 1 ); . . . , (u n ; v n )g be a finite set of relations presenting a semigroup over \Sigma. In t... |

66 | Subsumption algorithms for concept languages
- Hollunder, Nutt
- 1990
(Show Context)
Citation Context ...hods 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 illustrate why Reiter uses Skolemization in his seman... |

50 | How to prefer more specific defaults in terminological default logic
- Baader, Hollunder
- 1993
(Show Context)
Citation Context ...treated with a modified preferential approach. According to Reiter's semantics the specificity of prerequisites of rules has no influence on the order in which defaults rules are supposed to fire. In =-=[3]-=- we describe a modification of terminological default logic in which more specific defaults are preferred. Acknowledgements We should like to thank Bernhard Nebel and Peter Patel-Schneider for helpful... |

42 | On open defaults
- Lifschitz
- 1990
(Show Context)
Citation Context ...the Skolemized version of the first ABox. Consequently, we have a in 9R:C as a default consequence of the first ABox, but not of the second one, even though these two ABoxes are equivalent. Lifschitz =-=[15]-=- proposes a treatment of open defaults which avoids Skolemization by working with classes of models instead of sets of formulae in the definition of default extensions. Obviously, working with models ... |

36 |
Hybrid Inference in KL-ONEbased Knowledge Representation Systems.” German Workshop on
- Hollunder
- 1990
(Show Context)
Citation Context ...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 l... |

31 | I lied about the trees” or, defaults and definitions in knowledge representation
- Brachman
- 1985
(Show Context)
Citation Context ...andle such default assumptions, but does not destroy the definitional character of concept descriptions---because otherwise the advantage of automatic concept classification, etc., would be lost (see =-=[5]-=-). Besides the general arguments for the importance of reasoning with defaults, which can be found in the nonmonotonic reasoning literature, the need for embedding defaults into terminological represe... |

29 |
Computing the extensions of autoepistemic and default logics with a truth maintenance system
- Junker, Konolige
- 1990
(Show Context)
Citation Context ...on 3). A similar problem arises when considering the integration from the algorithmic point of view. In the abstract of their paper on how to compute extensions for default logic, Junker and Konolige =-=[12] write tha-=-t their method is applicable if the default theory "consists of a finite number of defaults and premises and classical derivability for the base language is decidable." A related formulation... |

21 |
Living with CLASSIC: When and How to Use a KL-ONE Like Language
- Brachman, McGuiness, et al.
- 1991
(Show Context)
Citation Context ...ated by the fact that this is an important item on the wish list of users of terminological representation systems (see e.g. [22]). Several existing terminological systems, such as back [20], classic =-=[6]-=-, k-rep [16], loom [19], or sb-one [14], have been or will be extended to provide the user with some kind of default reasoning facilities. However, as 1 We are taking this as our exceptional animal, i... |

18 |
The SB-ONE knowledge representation workbench
- Kobsa
- 1989
(Show Context)
Citation Context ...tant item on the wish list of users of terminological representation systems (see e.g. [22]). Several existing terminological systems, such as back [20], classic [6], k-rep [16], loom [19], or sb-one =-=[14]-=-, have been or will be extended to provide the user with some kind of default reasoning facilities. However, as 1 We are taking this as our exceptional animal, in view of the fact that last IJCAI was ... |

15 |
Attribute description formalisms ... and the rest of the world
- Nebel, Smolka
- 1991
(Show Context)
Citation Context ...idable, if classic applied rules not only to individuals explicitly present in the ABox, but also to implicit individuals. This result for classic rules has already been mentioned by Nebel and Smolka =-=[21]-=-, but without proof. In the next section we shall see that the restriction to explicit individuals leads to a decidable consequence relation even if one allows nonmonotonic default rules instead of cl... |

4 |
A semantics for open normal defaults via a modified preferential approach. DFKI research report RR-93-13
- Baader, Schlechta
- 1993
(Show Context)
Citation Context ...sistent sets of assertional facts) can be solved by an extension of the tableaux-based algorithm for assertional reasoning. As an alternative to the pragmatic solution described in the present paper, =-=[4]-=- proposes a new semantics for open defaults, in which defaults are also applied to implicit individuals. To make this possible without encountering the problems pointed out in Section 3, open defaults... |

4 |
A tableau-based characterisation for default logic
- Schwind, Risch
- 1991
(Show Context)
Citation Context ...inite number of defaults and premises and classical derivability for the base language is decidable." A related formulation can be found in the abstract of Schwind and Risch's paper on the same t=-=opic [28]-=-. Since our base language is decidable, and we certainly do not want to have infinitely many default rules, these methods seem to apply in our case. However, a closer look at the papers reveals that b... |

3 |
Making KR systems useful
- Mays, Dionne
- 1991
(Show Context)
Citation Context ... fact that this is an important item on the wish list of users of terminological representation systems (see e.g. [22]). Several existing terminological systems, such as back [20], classic [6], k-rep =-=[16]-=-, loom [19], or sb-one [14], have been or will be extended to provide the user with some kind of default reasoning facilities. However, as 1 We are taking this as our exceptional animal, in view of th... |

3 |
System presentation
- BACK
- 1991
(Show Context)
Citation Context ...also substantiated by the fact that this is an important item on the wish list of users of terminological representation systems (see e.g. [22]). Several existing terminological systems, such as back =-=[20]-=-, classic [6], k-rep [16], loom [19], or sb-one [14], have been or will be extended to provide the user with some kind of default reasoning facilities. However, as 1 We are taking this as our exceptio... |

2 | Statement of interest
- McGregor
- 1991
(Show Context)
Citation Context ...this is an important item on the wish list of users of terminological representation systems (see e.g. [22]). Several existing terminological systems, such as back [20], classic [6], k-rep [16], loom =-=[19]-=-, or sb-one [14], have been or will be extended to provide the user with some kind of default reasoning facilities. However, as 1 We are taking this as our exceptional animal, in view of the fact that... |

2 |
Org.). Terminological logic users workshop -- Proceedings
- Peltason, Luck, et al.
- 1991
(Show Context)
Citation Context ...ng defaults into terminological representation formalisms is also substantiated by the fact that this is an important item on the wish list of users of terminological representation systems (see e.g. =-=[22]-=-). Several existing terminological systems, such as back [20], classic [6], k-rep [16], loom [19], or sb-one [14], have been or will be extended to provide the user with some kind of default reasoning... |

1 |
problems for simple defaults
- Hard
- 1989
(Show Context)
Citation Context ..., the formalisms are usually highly undecidable (see e.g. [25] Theorem 4.9). For this reason, work on decision procedures for decidable subcases was mostly restricted to propositional logic (see e.g. =-=[13]-=-), thus leaving the wide gap between propositional logic and full first-order logic almost unexplored. Since most terminological representation languages can be viewed as decidable subclasses of first... |

1 |
Variables in hypothesis
- Poole
- 1987
(Show Context)
Citation Context ...ly contains a female spouse of Tom. As already pointed out by Poole, the reason for this strange behaviour comes from that fact that "we have lost the context of what the Skolem constants represe=-=nt" ([23]-=-, p.907), in our case the context that Gordy was originally introduced to stand for a female spouse of Tom. Poole proposes to keep track of this context by using Hilbert's ffl-symbol. Although Poole's... |