## Abstract

Our starting point is to vieW argumentation networks (of the form pS, Rq) as representing a survival game. The players are the elements of S and the relation R is the attack relation. The various traditional Dung semantics for subset of S can be viewed as defining extensions in the form of possible survival groups E (formula presented) S. The survival sets E (which are the traditional extensions) are groups of players Which are conflict free and able to protect themselves. So far We have a different point of vieW on extensions Which is compatible With the traditional Dung formal mathematical machinery. However, given the survival point of vieW We can generalise and add additional features to the traditional argumentation networks: 1. The New features are: (a) We can add to each x in S a many lives value Mpxq, meaning hoW many live attackers are needed to force x to be out (i.e. x to become dead). (b) We associate With each attack pair py, xq in R a value Kpy, xq, meaning hoW many lives are taken out of Mpxq should the attack of y on x be successful (i.e. y is alive). The value Kpy, xq may be, or may not be, correlated or even related to the number of lives Mpyq Which y has. (c) The traditional concept of conflict free set is that of a set Whose members do not attack one another. With many lives available We look at “living together” sets, using a concept of being able to stay alive together. Members can attack but not able to kill one another. In fact We could introduce different strengths of attack, one When attacking inside a “living together” set and possibly another When a “living together” set protects itself. (d) We can noW investigate semantics for such systems pS,R,M,Kq. 2. The ideas of adding M and K arise from our research into the argumentation/logic behaviour of mulitiple complaints. Thus the semantics and additional features of argumentation that We study are inspired by real life applications. In fact, to protect an alleged oﬀender x against attacks from a group of complainers/victims E, x needs to present much stronger counter attacks,andfurthermorethepublicwilltoleratealittlebitofinconsistencies among E (i.e. E need not be completely conﬂict free). This observation led us to the idea that to present a formal argumentation system We need to deﬁne three types of attacks, α_{a},α_{d}, and α_{p}, in increasing strength. For E to attack x We use the αa attack. For Z to protect x, Z must use the αp attack and for E (resp. for Z) to be considered conﬂict free its members must not αd attack one another (though We may tolerate them αa attacking one another). Furthermore, the attacks can be deﬁned using the basic attack relation R in a more complex manner. For example z αa attacking x can be deﬁned as (formula presented). 3. We discuss our results and compare With other papers on the numerical and ranking aspects of argumentation.

Original language | English |
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Pages (from-to) | 295-335 |

Number of pages | 41 |

Journal | Journal of Applied Logics |

Volume | 7 |

Issue number | 3 |

State | Published - Jun 2020 |

Externally published | Yes |

### Bibliographical note

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