## A Model-Theoretic Semantics for Defeasible Logic (2002)

Venue: | Proc. Workshop on Paraconsistent Computational Logic |

Citations: | 18 - 4 self |

### BibTeX

@INPROCEEDINGS{Maher02amodel-theoretic,

author = {M. J. Maher},

title = {A Model-Theoretic Semantics for Defeasible Logic},

booktitle = {Proc. Workshop on Paraconsistent Computational Logic},

year = {2002},

pages = {67--80}

}

### Years of Citing Articles

### OpenURL

### Abstract

Defeasible logic is an efficient logic for defeasible reasoning.

### Citations

1542 | The Stable Model Semantics for Logic Programming
- Gelfond, Lifschitz
- 1988
(Show Context)
Citation Context ...wing the pattern of this paper, but using the well-founded semantics in place of Kunen’s semantics and using a substantially different metaprogram. Other semantics, such as the stable model semantics =-=[9]-=-, give rise to several D-models for a defeasible theory in the corresponding defeasible logic. 6 Conclusion We have introduced an approach to defining an appropriate model theory for defeasible logics... |

789 | Constraint logic programming: a survey
- Jaffar, Maher
- 1994
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Citation Context ...Model-Theoretic Semantics for Defeasible Logic 3 of this work to other defeasible logics, including logics which admit pre-defined relations – constraints in the sense of constraint logic programming =-=[16]-=-. 2 The Defeasible Logic DL We begin by presenting the basic ingredients of defeasible logic. A defeasible theory contains five different kinds of knowledge: facts, strict rules, defeasible rules, def... |

237 |
1987], `Negation in logic programming
- Kunen
(Show Context)
Citation Context ...DL. If T is a defeasible theory, then MT is M augmented with a representation of T . It was shown in [20] that the consequences of T are characterized by MT under Kunen’s semantics for logic programs =-=[17]-=-. Theorem 2 ([20]). Let T be a defeasible theory and let MT denote its metaprogram counterpart. Let H be the Herbrand domain over which MT is defined. For each literal p, 1. T ⊢ +∆p iff MT , Th(H) ⊢K ... |

222 |
Unfounded sets and well-founded semantics for general logic programs
- Gelder, Ross, et al.
- 1991
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Citation Context ...ams provides an alternate form of failureto-prove. Indeed, [20] showed that Well-Founded Defeasible Logic is characterized by metaprogram of Section 4 and the well-founded semantics of logic programs =-=[30]-=-. In the well-founded semantics – and many other semantics of logic programs – the semantics rests on a single domain of values D. Thus, in these cases, the introduction of Th(D) is unnecessary. In th... |

197 | Autoepistemic logic - Marek, Truszczyfiski - 1991 |

195 | Defeasible logic
- Nute
- 1994
(Show Context)
Citation Context ... briefly outline how this approach extends to a wide range of defeasible logics. 1 Introduction Defeasible logic is a logic designed for efficient defeasible reasoning. The logic was designed by Nute =-=[23,24]-=- with the intention that it be efficiently implementable. This intention has been realised in systems that can process hundreds of thousands of defeasible rules quickly [21]. Over the years, Nute and ... |

146 | Representation results for defeasible logic
- Antoniou, Billington, et al.
(Show Context)
Citation Context ...feasible rules quickly [21]. Over the years, Nute and others have proposed many variants of defeasible logic [24,2]. In this paper we will address a particular defeasible logic, which we denote by DL =-=[5,1]-=-. However, this work is easily modified to address other defeasible logics. Defeasible logics are, in general, paraconsistent. The nature of defeasible reasoning, where one chain of reasoning may defe... |

122 | Constructive negation for constraint logic programming
- Stuckey
- 1991
(Show Context)
Citation Context ...ram M must now accommodate constraints and Theorem 2 must be extended. But such changes are not difficult. The extension of Kunen’s result, equating ⊢K and |=K, to arbitrary domains is due to Stuckey =-=[29]-=-. 5.2 Variants of DL As proposed in [2], the metaprogram presentation of DL can be generalized to a framework for the definition of many different defeasible logics. [2] presents some variants of DL w... |

74 | Propositional defeasible logic has linear complexity. Theory and Practice of Logic Programming
- Maher
(Show Context)
Citation Context ...ina Goldin, Jørgen Villadsen, Toshiharu Waragai (http://floc02.diku.dk/PCL/).s2 Michael J. Maher as electronic commerce [14,11]. Indeed, propositional DL has been shown to have linear time complexity =-=[19]-=-. On the other hand, neither DL nor any other variant of modern defeasible logic has a model theory. DL is defined purely in proof-theoretic terms [24,5]. Furthermore, a model theory based on the idea... |

73 |
Some direct theories of nonmonotonic inheritance
- Horty
- 1994
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Citation Context ...) is likely to be inappropriate for defeasible logic, since the kind of scepticism that is developed from intersection of extensions in default logic is different from the kind of “direct” scepticism =-=[15]-=- that occurs in defeasible logic [27]. In early work on semantics for defeasible logics, Nute [23] defined a model theory for LDR, a substantially simpler precursor of DL, in terms of a minimal belief... |

71 | Argumentation semantics for defeasible logic
- Governatori, Maher, et al.
- 2004
(Show Context)
Citation Context ... reasoning, we will use this semantics as a key intermediate step in verifying the correctness of our model-theoretic semantics. We have described DL and its variants in argumentation-theoretic terms =-=[12,13]-=-. Such a characterization is useful for the applications of the logic that we have in mind, but the resulting semantics is again a meta-level treatment of the proof theory: proof trees are grouped tog... |

65 |
ter Hofstede
- Aalst, Dumas, et al.
- 2005
(Show Context)
Citation Context ...r – in further inferences, but no form of ex falso quodlibet reasoning is possible. DL, and similar logics, have been proposed as the appropriate language for executable regulations [4], negotiations =-=[10]-=-, contracts [26], and business rules [14]. The logics are considered to have satisfactory expressiveness and the efficiency of the implementations supports real-time response in applications such ⋆ Or... |

62 | Efficient defeasible reasoning systems - Maher, Rock, et al. |

61 |
Defeasible Logic is Stable
- Billington
- 1993
(Show Context)
Citation Context ...feasible rules quickly [21]. Over the years, Nute and others have proposed many variants of defeasible logic [24,2]. In this paper we will address a particular defeasible logic, which we denote by DL =-=[5,1]-=-. However, this work is easily modified to address other defeasible logics. Defeasible logics are, in general, paraconsistent. The nature of defeasible reasoning, where one chain of reasoning may defe... |

60 | 2000 A Flexible Framework for Defeasible Logic
- Antoniou, Billington, et al.
- 2000
(Show Context)
Citation Context ...e. This intention has been realised in systems that can process hundreds of thousands of defeasible rules quickly [21]. Over the years, Nute and others have proposed many variants of defeasible logic =-=[24,2]-=-. In this paper we will address a particular defeasible logic, which we denote by DL [5,1]. However, this work is easily modified to address other defeasible logics. Defeasible logics are, in general,... |

59 |
A Declarative Approach to Business Rules
- Grosof, Labrou, et al.
- 1999
(Show Context)
Citation Context ... ex falso quodlibet reasoning is possible. DL, and similar logics, have been proposed as the appropriate language for executable regulations [4], negotiations [10], contracts [26], and business rules =-=[14]-=-. The logics are considered to have satisfactory expressiveness and the efficiency of the implementations supports real-time response in applications such ⋆ Originally published in proc. PCL 2002, a F... |

49 | Negation as Failure, in Logic and Database (H - Clark - 1978 |

39 | On the Analysis of Regulations using Defeasible Rules
- Antoniou, Billington, et al.
- 1999
(Show Context)
Citation Context ... – or even together – in further inferences, but no form of ex falso quodlibet reasoning is possible. DL, and similar logics, have been proposed as the appropriate language for executable regulations =-=[4]-=-, negotiations [10], contracts [26], and business rules [14]. The logics are considered to have satisfactory expressiveness and the efficiency of the implementations supports real-time response in app... |

38 | Toward a declarative language for negotiating executable contracts
- Reeves, Grosof, et al.
- 1999
(Show Context)
Citation Context ...nferences, but no form of ex falso quodlibet reasoning is possible. DL, and similar logics, have been proposed as the appropriate language for executable regulations [4], negotiations [10], contracts =-=[26]-=-, and business rules [14]. The logics are considered to have satisfactory expressiveness and the efficiency of the implementations supports real-time response in applications such ⋆ Originally publish... |

30 |
Defeasible reasoning and decision support systems. Decis
- Nute
- 1988
(Show Context)
Citation Context ... briefly outline how this approach extends to a wide range of defeasible logics. 1 Introduction Defeasible logic is a logic designed for efficient defeasible reasoning. The logic was designed by Nute =-=[23,24]-=- with the intention that it be efficiently implementable. This intention has been realised in systems that can process hundreds of thousands of defeasible rules quickly [21]. Over the years, Nute and ... |

24 | A semantic decomposition of defeasible logic
- Maher, Governatori
- 1999
(Show Context)
Citation Context ...nsequently – the logic is sound but not complete for this semantics. Although there is not a model theory for defeasible logic, there has been work on providing a semantics for DL in other styles. In =-=[20]-=- we showed that DL can be defined in terms of a metaprogram, defined to reflect the inference rules of the logic, and a semantics for the language of the metaprogram. This approach was successful in e... |

21 | Normal Forms for Defeasible Logic - Antoniou, Billington, et al. - 1998 |

17 | 2000).”An argumentation-theoretic characterization of defeasible logic
- Governatori, Maher
(Show Context)
Citation Context ... reasoning, we will use this semantics as a key intermediate step in verifying the correctness of our model-theoretic semantics. We have described DL and its variants in argumentation-theoretic terms =-=[12,13]-=-. Such a characterization is useful for the applications of the logic that we have in mind, but the resulting semantics is again a meta-level treatment of the proof theory: proof trees are grouped tog... |

10 |
Directly sceptical inheritance cannot capture the intersection of extensions
- Schlechta
- 1993
(Show Context)
Citation Context ...efeasible logic, since the kind of scepticism that is developed from intersection of extensions in default logic is different from the kind of “direct” scepticism [15] that occurs in defeasible logic =-=[27]-=-. In early work on semantics for defeasible logics, Nute [23] defined a model theory for LDR, a substantially simpler precursor of DL, in terms of a minimal belief state for each theory. LDR defines d... |

9 |
The Varieties of Programming Languages
- Scott, Strachey
- 1974
(Show Context)
Citation Context ...nd conflicting arguments are resolved by notions of argument defeat that reflect defeat in defeasible logic. Thus this work also fails to address model theory. Finally, a denotational-style semantics =-=[28]-=- has been given to DL [18]. The semantics is compositional, and fully abstract in all but one syntactic class. Although this semantics provides a useful analysis of DL, it does not provide a model the... |

7 | A Compositional Semantics for Logic Programs. Theoretical Computer Science - Bossi, Gabbrielli, et al. - 1994 |

5 | Defeasible Logic for Automated Negotiation
- Governatori, Hofstede, et al.
- 2000
(Show Context)
Citation Context ... Originally published in proc. PCL 2002, a FLoC workshop; eds. Hendrik Decker, Dina Goldin, Jørgen Villadsen, Toshiharu Waragai (http://floc02.diku.dk/PCL/).s2 Michael J. Maher as electronic commerce =-=[14,11]-=-. Indeed, propositional DL has been shown to have linear time complexity [19]. On the other hand, neither DL nor any other variant of modern defeasible logic has a model theory. DL is defined purely i... |

2 |
Soundness and Incompleteness for a Defeasible Logic
- Semantics
- 1999
(Show Context)
Citation Context ...lief state for each theory. LDR defines defeat only in terms of definite provability; this limitation is the main reason why the approach is successful [23]. Recently, this approach has been extended =-=[8,25]-=- to a defeasible logic that is closer to DL, and more general in some respects. However, the semantics is based on the idea of intersection of extensions and – perhaps consequently – the logic is soun... |