Language.Dung.AF

This module implements Dung's argumentation frameworks.

Basic definitions

data DungAF arg

An abstract argumentation framework is a set of arguments (represented as a list) and an attack relation on these arguments.

Constructors

AF [arg] [(arg, arg)]

Instances

Eq arg => Eq (DungAF arg)

Show arg => Show (DungAF arg)

setAttacks :: Eq arg => DungAF arg -> [arg] -> arg -> Bool

Given an argumentation framework, determines whether args (subset of the arguments in the AF), attacks an argument arg (in the AF).

conflictFree :: Eq arg => DungAF arg -> [arg] -> Bool

Given an argumentation framework, determines whether args (subset of the arguments in the AF) is conflict-free.

acceptable :: Eq arg => DungAF arg -> arg -> [arg] -> Bool

Given an argumentation framework, determines whether an argument is acceptable with respect to a list of args (subset of the arguments in the AF).

f :: Eq arg => DungAF arg -> [arg] -> [arg]

Given an argumentation framework, determines whether an argument is acceptable with respect to args (subset of the arguments in the AF).

admissible :: Eq arg => DungAF arg -> [arg] -> Bool

Given an argumentation framework, determines whether the set of arguments args (subset of the arguments in the AF) is admissible, i.e. if args is conflictFree and args is a subset of f af args

unattacked :: Eq arg => [arg] -> DungAF arg -> arg -> Bool

Given a list of arguments that are Out in an argumentation framework af, an argument arg is unattacked if the list of its attackers, ignoring the outs, is empty.

attacked :: Eq arg => [arg] -> DungAF arg -> arg -> Bool

Given a list of arguments that are In in an argumentation framework af, an argument arg is attacked if there exists an attacker that is In.

Grounded semantics through fixpoints and labelling

groundedF :: Eq arg => ([arg] -> [arg]) -> [arg]

Given a characteristic function f, computes the grounded extension by iterating on the empty set (list) until it reaches a fixpoint.

data Status

Labelling of arguments.

Constructors

In

Out

Undecided

Instances

Eq Status

Show Status

grounded :: Eq arg => DungAF arg -> [(arg, Status)]

Computes the grounded labelling for a Dung argumentation framework, returning a list of arguments with statuses.

Based on section 4.1 of Proof Theories and Algorithms for Abstract Argumentation Frameworks by Modgil and Caminada

groundedExt :: Eq arg => DungAF arg -> [arg]

The grounded extension of an argumentation framework is just the grounded labelling, keeping only those arguments that were labelled In.