## Another perspective on Default Reasoning (1992)

Venue: | Ann. Math. Artif. Intell |

Citations: | 85 - 0 self |

### BibTeX

@ARTICLE{Lehmann92anotherperspective,

author = {Daniel Lehmann},

title = {Another perspective on Default Reasoning},

journal = {Ann. Math. Artif. Intell},

year = {1992},

volume = {15},

pages = {61--82}

}

### Years of Citing Articles

### OpenURL

### Abstract

The lexicographic closure of any given finite set D of normal defaults is defined. A conditional assertion a b is in this lexicographic closure if, given the defaults D and the fact a, one would conclude b. The lexicographic closure is essentially a rational extension of D, and of its rational closure, defined in a previous paper. It provides a logic of normal defaults that is different from the one proposed by R. Reiter and that is rich enough not to require the consideration of non-normal defaults. A large number of examples are provided to show that the lexicographic closure corresponds to the basic intuitions behind Reiter's logic of defaults. 1 Plan of this paper Section 2 is a general introduction, describing the goal of this paper, in relation with Reiter's Default Logic and the program proposed in [12] by Lehmann and Magidor. Section 3 first discusses at length some general principles of the logic of defaults, with many examples, and, then, puts this paper in perspe...

### Citations

1518 |
A Logic for Default Reasoning
- Reiter
- 1980
(Show Context)
Citation Context ...n. In other terms, lexicographic closure is, in the terminology of [13], consistency preserving. This is indeed one of the hallmarks of Default Reasonings`a la Reiter as attested by the discussion in =-=[16]-=-, and in particular Corollary 2.2 there. Since there has been a lot of discussion in the literature, in particular in [5] and [3], of the principle of Transitivity, it is probably worth a short discus... |

571 | Nonmonotonic reasoning, preferential models and cumulative logics
- Kraus, Lehmann, et al.
- 1990
(Show Context)
Citation Context ...is a syntactic construction in the sense of [14], i.e., it is sensitive to the presentation of the default information. 3 Nonmonotonic Reasoning 3.1 The Rational Enterprise We shall briefly summarize =-=[8]-=- and [12] and set up the stage. This section was prepared in collaboration with David Makinson. Some nonmonotonic inference relations are better behaved than others. In particular, there are some simp... |

388 |
A logical framework for default reasoning
- Poole
- 1988
(Show Context)
Citation Context ...that have the same rank (or strength). We propose that, in the case of contradictory defaults of the same rank, we try to satisfy as many as possible. This proposal is in disagreement with D. Poole's =-=[15]-=-, but in agreement with the Maximal Entropy approach of [6]. It is shown that this idea guarantees rationality. In Section 9 a formal description of our complete proposal is given. First, a model-theo... |

246 | M.Magidor.What does a conditional knowledge base entail
- Lehmann
- 1992
(Show Context)
Citation Context ...ll be called the order of the set D. The set D may be partitioned into D1 \Phi D k\Gamma1 \Phi D k\Gamma2 \Phi : : : \Phi D 0 . We remind the reader that the rational closure of the set D, defined in =-=[10]-=- and studied in depth in [12] (see Theorem 5.17 and Lemma 2.24) is the set of defaults D that consists of all defaults (a : b) such that the rank of a is strictly less than the rank of as:b (equivalen... |

167 | Inconsistency management and prioritized syntaxbased entailment
- Benferhat, Cayrol, et al.
- 1993
(Show Context)
Citation Context ... superset of the rational closure of a knowledge base. The answer provided here, the lexicographic closure, is almost such a set, and a simple variation meets the condition in full. Independently, in =-=[1]-=-, Benferhat&al. proposed a similar lexicographic construction based on an unspecified ordering of single defaults. When one applies their construction to the ordering on single defaults defined in [12... |

161 |
General patterns in non-monotonic reasoning
- Makinson
- 1994
(Show Context)
Citation Context ...ll propositional models appear, at some level. An assertion of the form asfalse will appear in D l only if a is a logical contradition. In other terms, lexicographic closure is, in the terminology of =-=[13]-=-, consistency preserving. This is indeed one of the hallmarks of Default Reasonings`a la Reiter as attested by the discussion in [16], and in particular Corollary 2.2 there. Since there has been a lot... |

112 | Belief revision and default reasoning: Syntax-based approaches
- Nebel
- 1991
(Show Context)
Citation Context ...d in this paper. Its computational complexity has been studied in [2] and [9]: it is in \Delta p 2 and is NP-hard and co-NP-hard. The lexicographic closure is a syntactic construction in the sense of =-=[14]-=-, i.e., it is sensitive to the presentation of the default information. 3 Nonmonotonic Reasoning 3.1 The Rational Enterprise We shall briefly summarize [8] and [12] and set up the stage. This section ... |

91 |
Counterfactuals
- Ginsberg
- 1986
(Show Context)
Citation Context ...qs:r holds. This is the common wisdom and the present perspective subscribes to it. Suppose now that our specific information is cs:d, or, equivalently, psqs:rs:ps:qsr. The common wisdom, defended in =-=[4]-=-, would like to convince us that we should not presume q to be true. The position defended here, presumes that q is true (and also p and :r) because this situation violates only one default (: r) wher... |

79 |
A maximum entropy approach to nonmonotonic reasoning
- Goldszmidt, Morris, et al.
- 1990
(Show Context)
Citation Context ...he case of contradictory defaults of the same rank, we try to satisfy as many as possible. This proposal is in disagreement with D. Poole's [15], but in agreement with the Maximal Entropy approach of =-=[6]-=-. It is shown that this idea guarantees rationality. In Section 9 a formal description of our complete proposal is given. First, a model-theoretic construction is presented: given a finite set D of no... |

33 |
and Menachem Magidor. What does a conditional knowledge base entail
- Lehmann
- 1992
(Show Context)
Citation Context ...ons behind Reiter's logic of defaults. 1 Plan of this paper Section 2 is a general introduction, describing the goal of this paper, in relation with Reiter's Default Logic and the program proposed in =-=[12]-=- by Lehmann and Magidor. Section 3 first discusses at length some general principles of the logic of defaults, with many examples, and, then, puts this paper in perspective relatively to previous work... |

14 |
Some Representational Issues in Default Reasoning
- Reiter, Criscuolo
- 1980
(Show Context)
Citation Context ...mal Entropy approach. Section 11 is a concluding discussion. 2 Introduction In [16], R. Reiter proposed a formal framework for Default Reasoning. Its focal point is the definition of an extension. In =-=[17]-=-, R. Reiter and G. Criscuolo found that, in this framework, one must consider non-normal defaults. Nonnormal defaults have, since then, been taken as the basic piece of default information by the logi... |

12 |
Rationality, transitivity, and contraposition
- Freund, Lehmann, et al.
- 1991
(Show Context)
Citation Context ...ks of Default Reasonings`a la Reiter as attested by the discussion in [16], and in particular Corollary 2.2 there. Since there has been a lot of discussion in the literature, in particular in [5] and =-=[3]-=-, of the principle of Transitivity, it is probably worth a short discussion. The question of Transitivity is: should we accept (a : c) on the basis of the two defaults (a : b) and (b : c)? The answer ... |

5 |
What is a nonmonotonic consequence relation
- Stalnaker
- 1992
(Show Context)
Citation Context ... material counterparts of D c , then d should be presumed true iff d is a logical consequence of c [ M c , i.e., M c ; c j= d. This semantics fits well into the implicit content framework proposed in =-=[18]-=-. 6 Single Defaults Let D be the singleton set f(a : b)g, where a and b are arbitrary formulas. We propose the following meaning to D: ffl if the information at hand c is consistent with a ! b, i.e., ... |

1 |
Private Communication
- Lagasquie-Schiex
- 1993
(Show Context)
Citation Context ... applies their construction to the ordering on single defaults defined in [12], one obtains the lexicographic closure presented in this paper. Its computational complexity has been studied in [2] and =-=[9]-=-: it is in \Delta p 2 and is NP-hard and co-NP-hard. The lexicographic closure is a syntactic construction in the sense of [14], i.e., it is sensitive to the presentation of the default information. 3... |