Solving Advanced Argumentation Problems with Answer Set Programming

12/05/2019
by   Gerhard Brewka, et al.
0

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-labelled 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. Under consideration in Theory and Practice of Logic Programming (TPLP).

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/20/2013

The DIAMOND System for Argumentation: Preliminary Report

Abstract dialectical frameworks (ADFs) are a powerful generalisation of ...
research
08/09/2021

Harnessing Incremental Answer Set Solving for Reasoning in Assumption-Based Argumentation

Assumption-based argumentation (ABA) is a central structured argumentati...
research
07/23/2015

Improved Answer-Set Programming Encodings for Abstract Argumentation

The design of efficient solutions for abstract argumentation problems is...
research
03/31/2016

Characterizing Realizability in Abstract Argumentation

Realizability for knowledge representation formalisms studies the follow...
research
12/12/2012

ConArg: a Tool to Solve (Weighted) Abstract Argumentation Frameworks with (Soft) Constraints

ConArg is a Constraint Programming-based tool that can be used to model ...
research
12/22/2016

Solving Set Optimization Problems by Cardinality Optimization via Weak Constraints with an Application to Argumentation

Optimization - minimization or maximization - in the lattice of subsets ...
research
06/20/2018

Weighted Abstract Dialectical Frameworks: Extended and Revised Report

Abstract Dialectical Frameworks (ADFs) generalize Dung's argumentation f...

Please sign up or login with your details

Forgot password? Click here to reset