Probabilistic epistemic argumentation allows for reasoning about argumentation problems in a way that is well founded by probability theory. Epistemic states are represented by probability functions over possible worlds and can be adjusted to new beliefs using update operators. While the use of probability functions puts this approach on a solid foundational basis, it also causes computational challenges as the amount of data to process depends exponentially on the number of arguments. This leads to bottlenecks in applications such as modelling opponent's beliefs for persuasion dialogues. We show how update operators over probability functions can be related to update operators over much more compact representations that allow polynomial-time updates. We discuss the cognitive and probabilistic-logical plausibility of this approach and demonstrate its applicability in computational persuasion.
One limitation when restricting to probability labellings is that we cannot compute the probabilities of complex formulas over arguments anymore without adding further assumptions. However, as we demonstrated, we can sometimes do without complex formulas. In this context, probability labellings can be seen as an alternative to weighted argumentation frameworks that also assign a strength value between @math and @math to arguments @cite_1 @cite_2 @cite_26 @cite_19 @cite_35 . What makes probability labellings an interesting alternative is their well-defined relationship to probability functions and probability theory.
@cite_35 @cite_26 @cite_1 @cite_19 @cite_2
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The paper tackled the issue of arguments evaluation in weighted bipolar argumentation graphs (i.e., graphs whose arguments have basic strengths, and may be both supported and attacked). We introduce axioms that an evaluation method (or semantics) could satisfy. Such axioms are very useful for judging and comparing semantics. We then analyze existing semantics on the basis of our axioms, and finally propose a new semantics for the class of acyclic graphs. This paper presents a novel argumentation framework to support Issue-Based Information System style debates on design alternatives, by providing an automatic quantitative evaluation of the positions put forward. It also identifies several formal properties of the proposed quantitative argumentation framework and compares it with existing non-numerical abstract argumentation formalisms. Finally, the paper describes the integration of the proposed approach within the design Visual Understanding Environment software tool along with three case studies in engineering design. The case studies show the potential for a competitive advantage of the proposed approach with respect to state-of-the-art engineering design methods. This paper addresses the semantics of weighted argumentation graphs that are bipolar, i.e. contain both attacks and supports for arguments. It builds on previous work by Amgoud, Ben-Naim et. al. We study the various characteristics of acceptability semantics that have been introduced in these works, and introduce the notion of a modular acceptability semantics. A semantics is modular if it cleanly separates aggregation of attacking and supporting arguments (for a given argument @math ) from the computation of their influence on @math 's initial weight. We show that the various semantics for bipolar argumentation graphs from the literature may be analysed as a composition of an aggregation function with an influence function. Based on this modular framework, we prove general convergence and divergence theorems. We demonstrate that all well-behaved modular acceptability semantics converge for all acyclic graphs and that no sum-based semantics can converge for all graphs. In particular, we show divergence of Euler-based semantics () for certain cyclic graphs. Further, we provide the first semantics for bipolar weighted graphs that converges for all graphs. IBIS (Issue Based Information System) provides a widely adopted approach for knowledge representation especially suitable for the challenging task of representing wicked decision problems. While many tools for visualisation and collaborative development of IBIS graphs are available, automated decision support in this context is still underdeveloped, even though it would benefit several applications. QuAD (Quantitative Argumentation Debate) frameworks are a recently proposed IBIS-based formalism encompassing automated decision support by means of an algorithm for quantifying the strength of alternative decision options, based on aggregation of the strength of their attacking and supporting arguments. The initially proposed aggregation method, however, may give rise to discontinuities. In this paper we propose a novel, discontinuity-free algorithm for computing the strength of decision options in QuAD frameworks. We prove that this algorithm features several desirable properties and we compare the two aggregation methods, showing that both may be appropriate in the context of different application scenarios.