## Normal Forms for Defeasible Logic (1998)

Venue: | In Proc. Joint International Conference and Symposium on Logic Programming |

Citations: | 21 - 13 self |

### BibTeX

@INPROCEEDINGS{Antoniou98normalforms,

author = {G. Antoniou and D. Billington and M.J. Maher},

title = {Normal Forms for Defeasible Logic},

booktitle = {In Proc. Joint International Conference and Symposium on Logic Programming},

year = {1998},

pages = {160--174},

publisher = {MIT Press}

}

### OpenURL

### Abstract

Defeasible logic is an important logic-programming based nonmonotonic reasoning formalism which has an efficient implementation. It makes use of facts, strict rules, defeasible rules, defeaters, and a superiority relation. Representation results are important because they can help the assimilation of a concept by confining attention to its critical aspects. In this paper we derive some representation results for defeasible logic. In particular we show that the superiority relation does not add to the expressive power of the logic, and can be simulated by other ingredients in a modular way. Also, facts can be simulated by strict rules. Finally we show that we cannot simplify the logic any further in a modular way: Strict rules, defeasible rules, and defeaters form a minimal set of independent ingredients in the logic. 1 Introduction Normal forms play an important role in computer science. Examples of areas where normal forms have proved fruitful include logic [10], where normal forms o...

### Citations

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(Show Context)
Citation Context ...ptical reasoning approach. This should be contrasted with other approaches in which sceptical reasoning is realized using the intersection of credulous reasoning chains. For example, in default logic =-=[14] sceptical-=- reasoning is obtained by considering the intersection of all extensions. The two fundamental approaches lead to different behaviours, as pointed out by [16] in their "clash of intuitions" p... |

184 | Defeasible logic
- Nute
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(Show Context)
Citation Context ...concept by confining attention to its critical aspects. It is the third kind of benefit that we expect from the results of this paper. We will prove some representational results for Defeasible Logic =-=[11, 12]-=-, following the presentation of [4]. Defeasible Logic is an approach to nonmonotonic reasoning [1] that has a very distinctive feature: It was designed to be easily implementable right from the beginn... |

167 |
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(Show Context)
Citation Context ...ample, they can be instrumental in the implementation of a logic because assuming that formulae have a specific form can actually simplify and facilitate the development of algorithms (see resolution =-=[15]-=-). Normal forms can help to classify objects according to some criteria; for example, in relational database theory, a normal form characterizes those databases that don't allow specific kinds of anom... |

134 | Representation results for defeasible logic - Antoniou, Billington, et al. |

125 | A clash of intuitions: the current state of nonmonotonic multiple inheritance systems
- Touretzky, Horty, et al.
- 1987
(Show Context)
Citation Context ...s. For example, in default logic [14] sceptical reasoning is obtained by considering the intersection of all extensions. The two fundamental approaches lead to different behaviours, as pointed out by =-=[16] in their -=-"clash of intuitions" paper. For example, in default logic ambiguity in one predicate may be propagated to other predicates, but in defeasible logic this is not true. Priority logic [17, 18]... |

115 |
Nonmonotonic Reasoning
- Antoniou
- 1997
(Show Context)
Citation Context ...from the results of this paper. We will prove some representational results for Defeasible Logic [11, 12], following the presentation of [4]. Defeasible Logic is an approach to nonmonotonic reasoning =-=[1]-=- that has a very distinctive feature: It was designed to be easily implementable right from the beginning, unlike most other approaches. In fact it has an implementation as a straightforward extension... |

97 |
Further Normalization of the Data Base Relational Model
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(Show Context)
Citation Context ...of areas where normal forms have proved fruitful include logic [10], where normal forms of formulae are used both for the proof of theoretical results and in theorem proving, and relational databases =-=[5]-=-, where normal forms have been the driving force in the development of database theory and principles of good data modeling. There are several potential benefits of normal forms. For example, they can... |

65 |
Prioritized conflict handling for logic programs
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(Show Context)
Citation Context ...e logic is the same as that between default and defeasible logic mentioned above: Priority logic is extension based, thus it propagates ambiguity. Courteous logic programs were introduced recently in =-=[8]-=- as a simple and efficient form of default reasoning, to be used as the reasoning basis for intelligent agents. The approach shares some basic ideas of defeasible logic. In particular, it is logic pro... |

62 |
Defeasible reasoning
- Nute
- 1987
(Show Context)
Citation Context ...concept by confining attention to its critical aspects. It is the third kind of benefit that we expect from the results of this paper. We will prove some representational results for Defeasible Logic =-=[11, 12]-=-, following the presentation of [4]. Defeasible Logic is an approach to nonmonotonic reasoning [1] that has a very distinctive feature: It was designed to be easily implementable right from the beginn... |

60 |
Defeasible Logic is Stable
- Billington
- 1993
(Show Context)
Citation Context ...itical aspects. It is the third kind of benefit that we expect from the results of this paper. We will prove some representational results for Defeasible Logic [11, 12], following the presentation of =-=[4]-=-. Defeasible Logic is an approach to nonmonotonic reasoning [1] that has a very distinctive feature: It was designed to be easily implementable right from the beginning, unlike most other approaches. ... |

58 |
Kakas, Logic programming without negation as failure
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(Show Context)
Citation Context ...g rules without negation as failure, and the priority relation. Using this observation we showed that courteous logic programs are strictly a special case of defeasible logic. LPwNF was introduced in =-=[7]-=- as an approach to default reasoning in which negation as failure is simulated by the use of a priority relation ?. The paper introduced a proof theory and a corresponding argumentation framework. LPw... |

11 | Nonmonotonic reasoning by monotonic inferences with priority constraints
- Wang, You, et al.
- 1996
(Show Context)
Citation Context ... by [16] in their "clash of intuitions" paper. For example, in default logic ambiguity in one predicate may be propagated to other predicates, but in defeasible logic this is not true. Prior=-=ity logic [17, 18]-=- is a knowledge representation language where a theory consists of logic programming-like rules, and a priority relation among them. The meaning of the priority relation is that once a rule r is inclu... |

10 |
A decidable quantified defeasible logic
- Nute
- 1994
(Show Context)
Citation Context ... requires an acyclic superiority relation. Using these elements it is straightforward to express knowledge in the form of defeasible theories. A series of examples in Defeasible Logic can be found in =-=[13, 6]-=-. 2.2 Technical details In this paper we restrict attention to propositional defeasible logic, and assume that the reader is familiar with the notation and basic notions of propositional logic. If q i... |

10 | Logic programming without default negation revisited
- Wang, You, et al.
- 1997
(Show Context)
Citation Context ... by [16] in their "clash of intuitions" paper. For example, in default logic ambiguity in one predicate may be propagated to other predicates, but in defeasible logic this is not true. Prior=-=ity logic [17, 18]-=- is a knowledge representation language where a theory consists of logic programming-like rules, and a priority relation among them. The meaning of the priority relation is that once a rule r is inclu... |

7 |
Introduction to Mathematical Logic, 3rd Edition
- Mendelson
- 1987
(Show Context)
Citation Context ... a minimal set of independent ingredients in the logic. 1 Introduction Normal forms play an important role in computer science. Examples of areas where normal forms have proved fruitful include logic =-=[10]-=-, where normal forms of formulae are used both for the proof of theoretical results and in theorem proving, and relational databases [5], where normal forms have been the driving force in the developm... |

1 |
Sceptical logic programming without negation as failure
- Antoniou, Billington, et al.
- 1997
(Show Context)
Citation Context ...tonic logic, one of many in the literature. The several features of defeasible logic provide for a very natural expression of many of the standard examples used to motivate other non-monotonic logics =-=[12, 3]-=-. Non-monotonic behaviour occurs only when a theory is altered by, for example, adding new facts. In such situations, we should not think of a theory as a stand-alone representation of knowledge, but ... |