Valid attacks in argumentation frameworks with recursive attacks
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Valid attacks in argumentation frameworks with recursive attacks ˜ del Cerro1 · M.-C. Lagasquie-Schiex1 C. Cayrol1 · J. Fandinno1 · L. Farinas
© Springer Nature Switzerland AG 2020
Abstract The purpose of this work is to study a generalisation of Dung’s abstract argumentation frameworks that allows representing recursive attacks, that is, a class of attacks whose targets are other attacks. We do this by developing a theory of argumentation where the classic role of attacks in defeating arguments is replaced by a subset of them, which is “extensiondependent” and which, intuitively, represents a set of “valid attacks” with respect to the extension. The studied theory displays a conservative generalisation of Dung’s semantics (complete, preferred, stable and grounded) and also of its principles (conflict-freeness, acceptability and admissibility). Furthermore, despite its conceptual differences, we are also able to show that our theory agrees with the AFRA interpretation of recursive attacks for the complete, preferred, stable and grounded semantics and with a recent flattening method. Keywords Abstract argumentation · Higher-order attacks · Acceptability semantics Mathematics Subject Classification (2010) 68
The second author is funded by the Centre International de Math´e matiques et d’Informatique de Toulouse (CIMI) through contract ANR-11-LABEX-0040-CIMI within the program ANR-11-IDEX-0002-02. M.-C. Lagasquie-Schiex
[email protected] C. Cayrol [email protected] J. Fandinno [email protected] L. Fari˜nas del Cerro [email protected] 1
IRIT, Universit´e de Toulouse, CNRS, Toulouse, France
C. Cayrol et al.
1 Introduction Argumentation has become an essential paradigm for Knowledge Representation and, especially, for reasoning from contradictory information [1, 15] and for formalizing the exchange of arguments between agents in, e.g., negotiation [2]. Formal abstract frameworks have greatly eased the modelling and study of argumentation. For instance, a Dung’s argumentation framework (AF) [15] consists of a collection of arguments interacting with each other through an attack relation, enabling to determine “acceptable” sets of arguments called extensions. A natural generalisation of Dung’s argumentation frameworks consists in allowing higher-order attacks (also called recursive attacks in the relevant literature) that target other attacks. Here is an example from the legal domain, borrowed from [3]. Example 1 The lawyer says that the defendant did not have intention to kill the victim (Argument b). The prosecutor says that the defendant threw a sharp knife towards the victim (Argument a). So, there is an attack denoted by α from a to b. And the intention to kill should be inferred. Then the lawyer says that the defendant was in a habit of throwing the knife at his wife’s foot once drunk. This latter argument (Argument c) is better considered attacking the attack from a to b, than argument a itself (so there is now another attack denoted by β from c to α). Now the prosecutor’s argumentation seems no longer sufficient
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