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... first to show satisfaction of [18]’s rationality postulates for Tarskian logic instantiations with and without preferences. Following this, we reconstruct classical logic approaches to argumentation =-=[12, 13, 26]-=-, including those that additionally accommodate preferences [5]. To the best of our knowledge, we are the first to prove [18]’s postulates for classical logic approaches with preferences. Finally, we ...

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...few intuitive postulates. 1 Introduction There are two major categories of instantiations of Dung’s abstract argumentation framework [4]. A category uses deductive logics (such as propositional logic =-=[2, 6]-=- or Tarskian logics [1]). The second category uses rule-based languages [3, 5, 7] which distinguish between facts, strict rules (they encode strict information), and defeasible rules (they describe ge...

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.... A study on how to choose an appropriate attack relation was recently carried out by Amgoud and Besnard [1]. Some basic properties of an attack relation were also discussed by Gorogiannis and Hunter =-=[8]-=-. Examples of such properties are recalled below. C1 ∀a, b, c ∈ A, if Conc(a) ≡ Conc(b) then aRc iff bRc C2 ∀a, b, c ∈ A, if Supp(a) = Supp(b) then cRa iff cRb The first property says that two argumen...

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... of new attacks between existing arguments may occur if the underlying attack definition is changed and the abstract AF has to re-instantiated. A detailed analysis of attack-relations can be found in =-=[27]-=-. 3.4. Preliminary Relations Now we present some preliminary relations between the mentioned notions of equivalence. The presented implications follow directly from Definitions 3, 4 and 6. Figure 1 su...

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...: logic–based and abstract approaches. The former (see for instance [16]) takes the logical structure of arguments into account and defines notions like attack, undercut, defensibility etc. (see e.g. =-=[43]-=-) in terms of logical properties of the chosen argument structures. In contrast, abstract approaches - which will be the topic of this paper - consider arguments as atomic items, focusing entirely on ...

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... applied for reasoning about inconsistent information, this relation captures the logical inconsistency of a knowledge base. An example of relation is the so-called undercut and proposed in [30] (see =-=[31]-=- for more attack relations in case of systems built over propositional knowledge bases). Definition 3 (Undercut). An argument (H,h) undercuts an argument (H ′, h′) iff ∃h′′ ∈ H ′ such that h ≡ ¬h′′. T...

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...ever, are relevant for more than just the connection between logic programming and formal argumentation. They also shed light on specific aspects of instantiated argumentation theory in general (e.g. =-=[3, 11, 10]-=-). In particular we show 1 the connection between argument-labellings at the abstract level and conclusion-labellings at the instantiated level. With one notable exception, we are able to show that ma...

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...ions naturally appear. For instance, normal and local expansions correspond to re-instantiations if a new piece of information is added [3] or if we change to a less restrictive notion of attack (see =-=[13]-=- for different attack relations). In this paper we study the most general form of a dynamic scenario, so-called update where adding as well as deleting of arguments and attacks is allowed. Furthermore...

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...emantically equivalent. This restriction comes with a disadvantage however, as the set of pre-defined claims must be chosen with care, since inconsistent conclusions might be drawn otherwise. Indeed, =-=[17]-=- identify conditions for rational and consistent end results, which require the existence of specific arguments, which must be included in C. On the other hand, this restriction is in line with the co...

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...ion is based on the abstract argumentation theory proposed by Dung [11]. This paper studies the case when Dung’s framework is instantiated by building arguments in classical propositional logic (e.g. =-=[4, 12]-=-). The advantages of such an approach are that it can benefit from all the results proved in the case of abstract argumentation, and in addition, it allows for using some important and useful notions ...