We discuss explanations for formal (abstract and structured) argumentationthe question of whether and why a certain argument or claim can be accepted (or not) under various extension-based semantics. We introduce a flexible framework, which can act as the basis for many different types of explanations. For example, we can have simple or comprehensive explanations in terms of arguments for or against a claim, arguments that (indirectly) defend a claim, the evidence (knowledge base) that supports or is incompatible with a claim, and so on. We show how different types of explanations can be captured in our basic framework, discuss a real-life application and formally compare our framework to existing work.

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We study properties related to relevance in non-monotonic consequence relations obtained by systems of structured argumentation. Relevance desiderata concern the robustness of a consequence relation under the addition of irrelevant information. For an account of what (ir)relevance amounts to we use syntactic and semantic considerations. Syntactic criteria have been proposed in the domain of relevance logic and were recently used in argumentation theory under the names of non-interference and crashresistance. The basic idea is that the conclusions of a given argumentative theory should be robust under adding information that shares no propositional variables with the original database. Some semantic relevance criteria are known from non-monotonic logic. For instance, cautious monotony states that if we obtain certain conclusions from an argumentation theory, we may expect to still obtain the same conclusions if we add some of them to the given database. In this paper we investigate properties of structured argumentation systems that warrant relevance desiderata.Our attack form is sometimes called premise-attack [20] or directed undercut [6]. In Section 4 we will show that by adjusting · and · adequately we are able to accommodate many other attack forms defined in the literature.Definition 4 (Attack Diagram). Given a setting AF ⊢ (S), its attack diagram is the directed graph with the set of nodes Arg ⊢ (S) and edges between a and b iff a attacks b.Definition 5 (Dung Semantics, [12]). Where AF ⊢ (S) is a setting and A ⊆ Arg ⊢ (S) we define: A is conflict-free iff there are no a, b ∈ A such that a attacks b. A defends a ∈ Arg ⊢ (S) iff for each attacker b ∈ Arg ⊢ (S) of a there is a c ∈ A that attacks b. A is admissible iff it is conflict-free and it defends every a ∈ A. A is complete iff it is admissible and it contains every a ∈ Arg ⊢ (S) it defends. A is preferred iff it is ⊆-maximal complete. A is grounded iff it is ⊆-minimal complete. A is stable iff it is admissible and for all a ∈ Arg ⊢ (S) \ A there is a b ∈ A that attacks a.We denote the set of all admissible [complete, preferred, stable] sets A (also called "extensions") by Adm(AF ⊢ (S)) [Cmp(AF ⊢ (S)), Prf(AF ⊢ (S)), Stb(AF ⊢ (S))] and the grounded set by Grd(AF ⊢ (S)).Definition 6 (Consequence Relations). Where Sem ∈ {Grd, Prf, Stb}, and given a setting AF ⊢ we define:Where the setting AF ⊢ is clear from the context we will simply write |∼ Sem to avoid clutter.Remark 2. For reasons of space we restrict our focus in this paper on skeptical consequence as defined in Definition 6. Note that |∼ AF ⊢ Cmp coincides with |∼ AF ⊢ Grd .3 The Relevance Properties Syntactic RelevanceA syntactical relevance property that has been proposed in the context of structured argumentation is noninterference [9]. Let us call two sets of formulas syntactically disjoint if no atom that occurs in a formula

Recent studies of scientific interaction based on agent-based models (ABMs) suggest that a crucial factor conducive to efficient inquiry is what Zollman, 2010 has dubbed 'transient diversity'. It signifies a process in which a community engages in parallel exploration of rivaling theories lasting sufficiently long for the community to identify the best theory and to converge on it. But what exactly generates transient diversity? And is transient diversity a decisive factor when it comes to the efficiency of inquiry? In this paper we examine the impact of different conditions on the efficiency of inquiry, as well as the relation between diversity and efficiency. This includes certain diversity-generating mechanisms previously proposed in the literature (such as different social networks and cautious decision-making), as well as some factors that have so far been neglected (such as evaluations underlying theory-choice performed by scientists). This study is obtained via an argumentation-based ABM (Borg et al., 2017, 2018). Our results suggest that cautious decision-making does not always have a significant impact on the efficiency of inquiry while different evaluations underlying theory-choice and different social networks do. Moreover, we find a correlation between diversity and a successful performance of agents only under specific conditions, which indicates that transient diversity is sometimes not the primary factor responsible for efficiency. Altogether, when comparing our results to those obtained by structurally different ABMs based on Zollman's work, the impact of specific factors on efficiency of inquiry, as well as the role of transient diversity in achieving efficiency, appear to be highly dependent on the underlying model.

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