Multi-valued GRAPPA

Brewka, Gerhard; Pührer, Jörg; Woltran, Stefan

doi:10.1007/978-3-030-19570-0_6

Cited by 2 publications

(2 citation statements)

References 15 publications

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“…Beyond boosting performance of our system, future work is to apply our approach to alternative ADF semantics (Polberg 2014) as well as more recent generalizations of ADFs and GRAPPA such as weighted ADFs ) and multi-valued GRAPPA (Brewka et al . 2019); for dealing with possibly infinitely many values in this context, recent advances in ASP (Janhunen et al .…”

Section: Discussionmentioning

confidence: 99%

Solving Advanced Argumentation Problems with Answer Set Programming

Brewka

Diller

Heissenberger

et al. 2020

Theory and Practice of Logic Programming

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Powerful formalisms for abstract argumentation have been proposed, among them abstract dialectical frameworks (ADFs) that allow for a succinct and flexible specification of the relationship between arguments and the GRAPPA framework which allows argumentation scenarios to be represented as arbitrary edge-labeled graphs. The complexity of ADFs and GRAPPA is located beyond NP and ranges up to the third level of the polynomial hierarchy. The combined complexity of Answer Set Programming (ASP) exactly matches this complexity when programs are restricted to predicates of bounded arity. In this paper, we exploit this coincidence and present novel efficient translations from ADFs and GRAPPA to ASP. More specifically, we provide reductions for the five main ADF semantics of admissible, complete, preferred, grounded, and stable interpretations, and exemplify how these reductions need to be adapted for GRAPPA for the admissible, complete, and preferred semantics.

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Section: Discussionmentioning

confidence: 99%

Solving Advanced Argumentation Problems with Answer Set Programming

Brewka

Diller

Heissenberger

et al. 2020

Theory and Practice of Logic Programming

Self Cite

View full text Add to dashboard Cite

show abstract

“…Since this initial work on bipolar argumentation can capture all of Dung-style argumentation, it can be viewed as a generalization, and subsequent work has generalized it further. For example, Brewka et al (Brewka & Woltran, 2014;Brewka, Pührer, & Woltran, 2019) introduced the GRAPPA frameworkitself based on abstract dialectical frameworks (Brewka & Woltran, 2010) which are another generalization of Dung-style systems -which can express a range of classes of argument that expand on just "support" and "attack" 9 . Most recently, Escañuela Gonzalez et al (2021) have provided a general means of expressing information about support and attack that allows features such as numerical labels, and elements that allow the combination of strengths of arguments to propagate to those arguments that are supported or attacked.…”

Section: Computational Argumentationmentioning

confidence: 99%

A Model to Support Collective Reasoning: Formalization, Analysis and Computational Assessment

Ganzer

Criado

López-Sánchez

et al. 2023

jair

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In this paper we propose a new model to represent human debates and methods to obtain collective conclusions from them. This model overcomes two drawbacks of existing approaches. First, our model does not assume that participants agree on the structure of the debate. It does this by allowing participants to express their opinion about all aspects of the debate. Second, our model does not assume that participants’ opinions are rational, an assumption that significantly limits current approaches. Instead, we define a weaker notion of rationality that characterises coherent opinions, and we consider different scenarios based on the coherence of individual opinions and the level of consensus. We provide a formal analysis of different opinion aggregation functions that compute a collective decision based on the individual opinions and the debate structure. In particular, we demonstrate that aggregated opinions can be coherent even if there is a lack of consensus and individual opinions are not coherent. We conclude with an empirical evaluation demonstrating that collective opinions can be computed efficiently for real-sized debates.

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Multi-valued GRAPPA

Cited by 2 publications

References 15 publications

Solving Advanced Argumentation Problems with Answer Set Programming

Solving Advanced Argumentation Problems with Answer Set Programming

A Model to Support Collective Reasoning: Formalization, Analysis and Computational Assessment

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