## Logic of Violations: A Gentzen system for reasoning with contrary-to-duty obligations (2005)

Venue: | Australasian Journal of Logic |

Citations: | 46 - 28 self |

### BibTeX

@ARTICLE{Governatori05logicof,

author = {Guido Governatori and Antonino Rotolo},

title = {Logic of Violations: A Gentzen system for reasoning with contrary-to-duty obligations},

journal = {Australasian Journal of Logic},

year = {2005},

volume = {4},

pages = {193--215}

}

### Years of Citing Articles

### OpenURL

### Abstract

In this paper we present a Gentzen system for reasoning with contrary-to-duty obligations. The intuition behind the system is that a contrary-to-duty is a special kind of normative exception. The logical machinery to formalise this idea is taken from substructural logics and it is based on the definition of a new non-classical connective capturing the notion of reparational obligation. Then the system is tested against well-known contrary-to-duty paradoxes. 1

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Citation Context ...he structural rules of exchange, duplication and contraction. Otherwise, the introduction and elimination rules have to be supplemented by rules for the “structural” meaning of the operators involved =-=[8, 21]-=-. According to Definition 1 the usual rules of contraction, duplication and exchange hold trivially for the formulas in the antecedent. However, they do not make any sense for the consequent so we nee... |

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Citation Context ...nite (possibly empty) set of formulas and A is a formula. As usual in Gentzen systems the meaning of operators and connectives is given by the rules for their introduction and elimination (cf., e.g., =-=[20]-=-). More precisely, this is true in the presence of the structural rules of exchange, duplication and contraction. Otherwise, the introduction and elimination rules have to be supplemented by rules for... |

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Citation Context ...s not the case, then B is a not a consequence of the normative system. This task can be done within a labelled deductive system based on the so-called Input-Output logic developed by L. van der Torre =-=[23, 16, 17]-=-. Basically, our system starts from this last conception of normative reasoning. First, it is based on a purely syntactic view of deontic logic so that all the machinery consists of defining a suitabl... |

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Representing business contracts in RuleML
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Citation Context ...of the system by means of non-monotonic patterns such as cumulativity, restricted transitivity, etc. • Combining the logic of ⊗ with a logic able to cope with normative conflicts. Preliminary results =-=[10, 9]-=- show that the logic of ⊗ can be easily combined with Defeasible Logic. This combination has proved very successful in the representation of Business contracts where CTD are very frequent. To sum up w... |

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Citation Context ...nd so forth. 6 Dealing with CTD Paradoxes Now, let us see how our system deals with some of the most infamous paradoxes of CTD reasoning. In particular, we want to give a formal account of Chisholm’s =-=[6]-=- and Forrester’s [7] paradoxes, Belzer’s [4] “Reykjavik scenario” and Makinson’s [15] “Möbius strip example”. Since these puzzles are well-known in the deontic logic community we shall not recall any ... |

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Citation Context ...unt of CTD obligations and consequently solutions to the just mentioned paradoxes of deontic logic. In a wide sense, significant examples in this direction are some papers by H. Prakken and M. Sergot =-=[18, 19]-=-. Basically, they regard CTD structures as contextual obligations, that is obligations strictly relative to a certain context of application. Accordingly, they are not just conditional obligations whi... |

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Citation Context ... Makinson and L. van der Torre. Their main idea, as pointed out by Makinson [15] himself, can be traced back to a pioneering work by Stenius [22] and it was later improved by Alchourrón and Bu2slygin =-=[2, 1]-=-. This line of investigation is based on the intuition that any obligation can be explained in terms of a consequence relation of what is explicitly stated as obligatory in a normative system. Actuall... |

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Citation Context ...ng with CTD Paradoxes Now, let us see how our system deals with some of the most infamous paradoxes of CTD reasoning. In particular, we want to give a formal account of Chisholm’s [6] and Forrester’s =-=[7]-=- paradoxes, Belzer’s [4] “Reykjavik scenario” and Makinson’s [15] “Möbius strip example”. Since these puzzles are well-known in the deontic logic community we shall not recall any of their intuitive e... |

43 |
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Citation Context ...tial violations) between norms. A different approach, inspired by similar intuitions, has been developed in particular by D. Makinson and L. van der Torre. Their main idea, as pointed out by Makinson =-=[15]-=- himself, can be traced back to a pioneering work by Stenius [22] and it was later improved by Alchourrón and Bu2slygin [2, 1]. This line of investigation is based on the intuition that any obligation... |

39 |
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Citation Context ... Makinson and L. van der Torre. Their main idea, as pointed out by Makinson [15] himself, can be traced back to a pioneering work by Stenius [22] and it was later improved by Alchourrón and Bu2slygin =-=[2, 1]-=-. This line of investigation is based on the intuition that any obligation can be explained in terms of a consequence relation of what is explicitly stated as obligatory in a normative system. Actuall... |

39 | Dyadic deontic logic and contrary-to-duty obligations
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(Show Context)
Citation Context ...unt of CTD obligations and consequently solutions to the just mentioned paradoxes of deontic logic. In a wide sense, significant examples in this direction are some papers by H. Prakken and M. Sergot =-=[18, 19]-=-. Basically, they regard CTD structures as contextual obligations, that is obligations strictly relative to a certain context of application. Accordingly, they are not just conditional obligations whi... |

33 |
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Citation Context ...he structural rules of exchange, duplication and contraction. Otherwise, the introduction and elimination rules have to be supplemented by rules for the “structural” meaning of the operators involved =-=[8, 21]-=-. According to Definition 1 the usual rules of contraction, duplication and exchange hold trivially for the formulas in the antecedent. However, they do not make any sense for the consequent so we nee... |

31 | The many faces of defeasibility in defeasible deontic logic
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Citation Context ... A ⊗ B as “B is the reparation of A”, the connective ⊗ permits the combination of primary and CTD obligations into unique regulations. It has been argued that violations are different from exceptions =-=[18, 24]-=-. We think this analysis is correct insofar as it maintains that a norm is still in force even when it is violated, whereas a default like ‘birds fly’ is cancelled, e.g., by the fact that Tweety does ... |

28 |
General Theory of Norms
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Citation Context ... law) we realise that the obligation not to kill is usually rendered as a norm stating an appropriate sanction which ought to follow in case of violation. Actually, it is not by chance that H. Kelsen =-=[14]-=- talks about legal obligations, called by him primary norms, as norms stipulating sanctions. A similar approach can be found in the analysis of deontic logicians like A.R. Anderson [3] who define ough... |

25 | Qualitative choice logic
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Citation Context ...possible solution for this problem is to supplement the definition of satisfiability by adding a degree of violation similar to the degree of disappointment proposed by Brewka, Benferhat and Le Berre =-=[5]-=- for their logic of ordered disjunction. However a careful analysis of this topic is left as a matter of future work. 19sJones and Pörn’s analysis such as the necessity of introducing hierarchies of s... |

16 |
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(Show Context)
Citation Context ...”. This confirms van der Torre and Tan’s [24] thesis that violability has to be read as a special kind of defeasibility. In very general terms, our formulation follows the intuition of Jones and Pörn =-=[12, 13]-=- insofar as it permits us to represent the real (actual) obligations expressed by the system. However, our approach is based on purely syntactical notion of ideality and is strictly related to the rol... |

15 | A Gentzen system for reasoning with contrary-to-duty obligations. A preliminary study - Governatori, Rotolo - 2002 |

12 |
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(Show Context)
Citation Context ... similar intuitions, has been developed in particular by D. Makinson and L. van der Torre. Their main idea, as pointed out by Makinson [15] himself, can be traced back to a pioneering work by Stenius =-=[22]-=- and it was later improved by Alchourrón and Bu2slygin [2, 1]. This line of investigation is based on the intuition that any obligation can be explained in terms of a consequence relation of what is e... |

11 |
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(Show Context)
Citation Context ...that H. Kelsen [14] talks about legal obligations, called by him primary norms, as norms stipulating sanctions. A similar approach can be found in the analysis of deontic logicians like A.R. Anderson =-=[3]-=- who define ought-assertions as obligations to do something or to repair their violations by means of sanctions. We are aware that this is one of the most discussed issues in contemporary philosophy o... |

11 |
Legal reasoning in 3-D
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- 1987
(Show Context)
Citation Context ...w, let us see how our system deals with some of the most infamous paradoxes of CTD reasoning. In particular, we want to give a formal account of Chisholm’s [6] and Forrester’s [7] paradoxes, Belzer’s =-=[4]-=- “Reykjavik scenario” and Makinson’s [15] “Möbius strip example”. Since these puzzles are well-known in the deontic logic community we shall not recall any of their intuitive examples but we will conf... |

7 | The logic of reusable propositional output with the fulfilment constraint
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- 2000
(Show Context)
Citation Context ...s not the case, then B is a not a consequence of the normative system. This task can be done within a labelled deductive system based on the so-called Input-Output logic developed by L. van der Torre =-=[23, 16, 17]-=-. Basically, our system starts from this last conception of normative reasoning. First, it is based on a purely syntactic view of deontic logic so that all the machinery consists of defining a suitabl... |

2 |
Modelling contracts in RuleML
- Governatori, Rotolo
- 2004
(Show Context)
Citation Context ...of the system by means of non-monotonic patterns such as cumulativity, restricted transitivity, etc. • Combining the logic of ⊗ with a logic able to cope with normative conflicts. Preliminary results =-=[10, 9]-=- show that the logic of ⊗ can be easily combined with Defeasible Logic. This combination has proved very successful in the representation of Business contracts where CTD are very frequent. To sum up w... |

2 |
Norma e condizione. Uno studio dell’implicazione normativa
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- 2001
(Show Context)
Citation Context ... to do something or to repair their violations by means of sanctions. We are aware that this is one of the most discussed issues in contemporary philosophy of norms (for a recent overview, see, e.g., =-=[25]-=-) since it concerns hard problems such as the very nature of conditional obligations. However, besides the plethora of different opinions on this matter, a point seems intuitively clear: ff a norm is ... |