## Robust Semantics for Argumentation Frameworks (1999)

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Venue: | Journal of Logic and Computation |

Citations: | 38 - 1 self |

### BibTeX

@ARTICLE{Jakobovits99robustsemantics,

author = {H. Jakobovits and D. Vermeir},

title = {Robust Semantics for Argumentation Frameworks},

journal = {Journal of Logic and Computation},

year = {1999},

volume = {9},

pages = {215--261}

}

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### Abstract

We suggest a so-called "robust" semantics for a model of argumentation which represents arguments and their interactions, called "argumentation frameworks". We study a variety of additional definitions of acceptability of arguments; we explore the properties of these definitions; we describe their inter-relationships: e.g. robust models can be characterized using the minimal (well-founded) models of a meta-framework. The various definitions of acceptability of argument sets can all deal with contradiction within an argumentation framework. Keywords: Argumentation framework, semantics 1 Introduction In this paper we present semantics for a formal model of argumentation. As in other works such as [Pol94] and [Dun95], we abstract from the actual contents and form of the arguments themselves, and rather concentrate on the analysis of interactions between arguments. Argumentation-theoretic interpretations and proof-procedures are applicable in practical reasoning, legal reasoning ([KT96]...

### Citations

831 | On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games
- Dung
- 1995
(Show Context)
Citation Context ...n an argumentation framework. Keywords: Argumentation framework, semantics 1 Introduction In this paper we present semantics for a formal model of argumentation. As in other works such as [Pol94] and =-=[Dun95]-=-, we abstract from the actual contents and form of the arguments themselves, and rather concentrate on the analysis of interactions between arguments. Argumentation-theoretic interpretations and proof... |

463 |
Algorithms in C
- Sedgewick
- 1998
(Show Context)
Citation Context ... Argumentation frameworks can be used to model a wide range of situations, some of which are not even linked to discussion. Here we present a variant of the stable marriage problem (see, for example, =-=[Sed90]-=-), which we call the stable-tennisdoublessproblem, and which we define as follows: suppose there is a given set S of available tennis players that are candidates for being paired up into teams to play... |

335 |
Introduction to Mathematical Logic
- Mendelson
- 1964
(Show Context)
Citation Context ...s to those arguments which are beyond dispute. It is defined by means of the so-called "minimal" complete labeling. This complete labeling shall be defined with the help of transfinite seque=-=nces (see [Men79]-=-), i.e. sequences on the class On of ordinal numbers, as follows: Definition 9 Let (A; ;) be an argumentation framework. Define the transfinite sequencessS ff ; T ff ; ff 2 On as follows: let S 0 = T ... |

180 | An abstract, argumentation-theoretic approach to default reasoning
- Bondarenko, Dung, et al.
- 1997
(Show Context)
Citation Context ...,[PS95]), mediation systems ([GK96],[BG94]), decision-making systems ([KPG96]), and are especially useful for reasoning among electronic agents and in deductive databases. Moreover, as pointed out in =-=[BDKT97]-=-, this approach unifies and generalizes many existing approaches to defeasible reasoning, including several systems of non-monotonic logic, default logic, and logic programming. For example, the appro... |

136 |
Abstract argumentation systems
- Vreeswijk
- 1997
(Show Context)
Citation Context ...which are true in any credulous approach. This type of reasoning exists in non-monotonic reasoning [Pol94] and logic programming [SZ90]. For argumentation, intersecting credulous sets is suggested in =-=[Vre97]-=-. In order to adapt this idea to the semantics which we have suggested here, we introduce the obligatory semantics as follows: Definition 26 Let AF = (A; ;) be an argumentation framework. A robust set... |

131 | Stable models and non-determinism in logic programs with negation
- Saccá, Zaniolo
- 1990
(Show Context)
Citation Context ... of all credulous approaches. Such a semantics accepts those arguments which are true in any credulous approach. This type of reasoning exists in non-monotonic reasoning [Pol94] and logic programming =-=[SZ90]-=-. For argumentation, intersecting credulous sets is suggested in [Vre97]. In order to adapt this idea to the semantics which we have suggested here, we introduce the obligatory semantics as follows: D... |

127 | The zeno argumentation framework
- Gordon, Karacapilidis
- 1997
(Show Context)
Citation Context ...is preferred iff it is maximal admissible. A consistent set S of arguments is said to be stable iff S attacks every argument that does not belong to S. Example 1 Consider the discussion, presented in =-=[GK96]-=-, between a husband and wife about which car to buy. The husband, who has wanted a fast sports car ever since he finished law school, wants to buy a Porsche. The wife, whose priority is the safety of ... |

91 | Abstract argumentation
- Kowalski, Toni
- 1996
(Show Context)
Citation Context ...mselves, and rather concentrate on the analysis of interactions between arguments. Argumentation-theoretic interpretations and proof-procedures are applicable in practical reasoning, legal reasoning (=-=[KT96]-=-,[PS95]), mediation systems ([GK96],[BG94]), decision-making systems ([KPG96]), and are especially useful for reasoning among electronic agents and in deductive databases. Moreover, as pointed out in ... |

82 |
A lattice theoretical fixed point theorem and its applications
- Tarski
(Show Context)
Citation Context ...nd we consider therefore the following function: OE : 2 An(S[T ) ! 2 An(S[T ) OE(X) = fag [ fd j d ; X and S [ T 6; dg This function is clearly monotonic with respect to set inclusion so, as shown in =-=[Tar55]-=-, OE has a least fixpoint \Phi. It is straightforward to show that T [ \Phi is a supporting defence of S, which contradicts the maximality of T . 2. Let a be such that + 2 l(a). We must show that 8b ;... |

63 | Justification and defeat
- Pollock
- 1994
(Show Context)
Citation Context ...iction within an argumentation framework. Keywords: Argumentation framework, semantics 1 Introduction In this paper we present semantics for a formal model of argumentation. As in other works such as =-=[Pol94]-=- and [Dun95], we abstract from the actual contents and form of the arguments themselves, and rather concentrate on the analysis of interactions between arguments. Argumentation-theoretic interpretatio... |

39 | A system for defeasible argumentation, with defeasible priorities
- Prakken, Sartor
- 1996
(Show Context)
Citation Context ...cteria. This situation could be modeled by an argumentation framework, where the arguments are rules of the type used in logic programming, and the attack relation used is undercutting. As defined in =-=[PS96]-=-, a rule a undercuts a rule b iff the consequent of rule a states that the antecedent of rule b does not hold. (By stating that the consequent of rule b is not fulfilled, rule a shows that rule b is n... |

36 | On the relation between legal language and legal argument: assumptions, applicability and dynamic priorities
- Prakken, Sartor
- 1995
(Show Context)
Citation Context ..., and rather concentrate on the analysis of interactions between arguments. Argumentation-theoretic interpretations and proof-procedures are applicable in practical reasoning, legal reasoning ([KT96],=-=[PS95]-=-), mediation systems ([GK96],[BG94]), decision-making systems ([KPG96]), and are especially useful for reasoning among electronic agents and in deductive databases. Moreover, as pointed out in [BDKT97... |

32 | How to buy a Porsche: An approach to defeasible decision making. In: Working Notes of the AAAI-94 Workshop on Computational Dialectics - Brewka, Gordon - 1994 |

16 | An argumentation based framework for defeasible and qualitative reasoning - KARACAPILIDIS, PAPADIAS, et al. - 1996 |

13 | Dialectical proof theory for defeasible argumentation with defeasible priorities - Prakken - 1996 |

9 | On the theory of argumentation frameworks
- Jakobovits
- 2000
(Show Context)
Citation Context ...le reasoning, including several systems of non-monotonic logic, default logic, and logic programming. For example, the approach presented in this paper generates, by a simple and natural mapping (see =-=[JV96]-=-), a new semantics for logic programs. Within a given framework of interacting arguments, there might be one or several sets of conclusions that are deemed acceptable. The selected set(s) must satisfy... |

6 |
Phan Minh Dung. The acceptability semantics for logic programs
- Kakas, Mancarella
- 1994
(Show Context)
Citation Context ...uced in this paper with previous proposals, most of which have a natural formulation in terms of labelings. Section 6 contains a discussion of three related approaches, those of [BDKT97], [Pol94] and =-=[KMD94]-=-, and their relationship with our semantics. Finally, in section 7, we present conclusions and directions for further research. All the proofs of the theorems in this paper are included in the appendi... |

2 |
A theory of argumentation and its application to semantics for logic programs
- Jakobovits
- 1995
(Show Context)
Citation Context ...pt. The theory of argumentation which we have presented in this paper, due to its high level of abstraction, can be applied to many branches of science, including logic programming. We have shown, in =-=[Jak95]-=- and [JV96], how to map literals in a logic program onto arguments of an argumentation framework. In [JV97] we are examining the application of the semantics defined in the present paper, to logic pro... |

2 |
Argumentation and logic programming semantics
- Jakobovits, Vermeir
- 1997
(Show Context)
Citation Context ... can be applied to many branches of science, including logic programming. We have shown, in [Jak95] and [JV96], how to map literals in a logic program onto arguments of an argumentation framework. In =-=[JV97]-=- we are examining the application of the semantics defined in the present paper, to logic programs. Another area in which argumentation frameworks are particularly useful is to model reasoning among e... |