Language.Dung.Examples

This is the examples module accompanying the implementation of Dung's argumentation frameworks.

This module contains a collection of examples, showing how to define arguments, argumentation frameworks and how to use the standard definitions.

To run these examples, or your own: start GHCi and do the following:

:l Language.Dung.Examples

Example uses of the basic definitions

Given a = "A", b = "B", c = "C"

type AbsArg = String

The simplest abstract argument is an argument identifiable by its name

a :: AbsArg

b :: AbsArg

c :: AbsArg

exampleAF :: DungAF AbsArg

Example AF: A -> B -> C

exampleAF2 :: DungAF AbsArg

Example AF: A <-> B

Now follow a few example outputs using the above argumentation frameworks.

setAttacks:

[a,b] setAttacks c in the argumentation framework exampleAF:

>>> setAttacks exampleAF [a,b] c
True

>>> setAttacks exampleAF [b,c] a
False

>>> setAttacks exampleAF2 [] b
False

conflictFree:

[a,c] is conflictFree in the argumentation framework exampleAF:

>>> conflictFree exampleAF [a,c]
True

>>> conflictFree exampleAF [a,b,c]
False

>>> conflictFree exampleAF2 [a,b]
False

acceptable:

c is acceptable w.r.t. [a,b] in the argumentation framework exampleAF:

>>> acceptable exampleAF c [a,b]
True

>>> acceptable exampleAF c []
False

>>> acceptable exampleAF b [a,b,c]
False

admissible:

[a,b,c] is admissible in the argumentation framework exampleAF:

>>> admissible exampleAF [a,b,c]
False

>>> admissible exampleAF [a,c]
True

>>> admissible exampleAF [a]
True

grounded:

The grounded labelling of the argumentation frameworks exampleAF and exampleAF2:

>>> grounded exampleAF
[("A",In),("C",In),("B",Out)]

>>> grounded exampleAF2
[("A",Undecided),("B",Undecided)]

groundedExt:

The grounded extension of the argumentation frameworks exampleAF and exampleAF2:

>>> groundedExt exampleAF
["A", "C"]
>>> groundedExt exampleAF2
[]

Example uses of the fixpoint definitions

faf :: [AbsArg] -> [AbsArg]

fixed point function for a specific argumentation framework, faf = f exampleAF.

groundedF:

The grounded extension of the argumentation framework exampleAF using the fixpoint definition:

>>> groundedF faf
["A","C"]

>>> groundedF (f exampleAF2)
[]

Example uses of the basic labelling definitions

Given d = "D", e = "E"

d :: AbsArg

e :: AbsArg

exampleAF3 :: DungAF AbsArg

Left hand side of Fig1. in Caminada. Arguments are: {a,b,c,d}. Attacks: {(a, a), (a, c), (b, c), (c, d)}

exampleAF4 :: DungAF AbsArg

Right hand side of Fig1. in Caminada. Arguments are: {a,b,c,d,e}. Attacks: {(a, b), (b, a), (b, c), (c, d), (d, e), (e, c)}

complete:

The complete labellings of the argumentation framework exampleAF3 and exampleAF4:

>>> complete exampleAF3
[
  [("A",Undecided),("B",In),("C",Out),("D",In)]
]

>>> complete exampleAF4
[
  [("A",Out),("B",In),("C",Out),("D",In),("E",Out)],
  [("A",In),("B",Out),("C",Undecided),("D",Undecided),("E",Undecided)],
  [("A",Out),("B",In),("C",Out),("D",Undecided),("E",Undecided)]
]

completeExt:

The complete extensions of the argumentation frameworks exampleAF3 and exampleAF4:

>>> completeExt exampleAF3
[
  ["B","D"]
]
>>> completeExt exampleAF4
[
  ["B","D"],
  ["A"],
  ["B"]
]

semiStable:

The semi-stable labellings of the argumentation framework exampleAF3 and exampleAF4:

>>> semiStable exampleAF3
[
  [("A",Undecided),("B",In),("C",Out),("D",In)]
]

>>> semiStable exampleAF4
[
  [("A",Out),("B",In),("C",Out),("D",In),("E",Out)],
]

semiStableExt:

The complete extensions of the argumentation frameworks exampleAF3 and exampleAF4:

>>> semiStableExt exampleAF3
[
  ["B","D"]
]
>>> semiStableExt exampleAF4
[
  ["B","D"],
]

Example uses of the input functionality

exampleAF5 :: DungAF AbsArg

Parsed example as given on the CEGARTIX webpage: http://www.dbai.tuwien.ac.at/proj/argumentation/cegartix/.

arg(a).
arg(b).
arg(c).
arg(d).
arg(e).
arg(f).
arg(g).
att(a,b).
att(c,b).
att(c,d).
att(d,c).
att(d,e).
att(e,g).
att(f,e).
att(g,f).

This is given as a literal string to parseAF.

Example uses of the output functionality

output :: String

Output String corresponding to exampleAF, i.e. toCegartix exampleAF.

>>> putStr output
arg("A").
arg("B").
arg("C").
att("A","B").
att("B","C").

output2 :: String

Output String corresponding to exampleAF2, i.e. toCegartix exampleAF2.

>>> putStr output2
arg("A").
arg("B").
att("A","B").
att("B","A").

output3 :: String

Output String corresponding to exampleAF3, i.e. toCegartix exampleAF3.

>>> putStr output3
arg("A").
arg("B").
arg("C").
arg("D").
att("A","A").
att("A","C").
att("B","C").
att("C","D").

output4 :: String

Output String corresponding to exampleAF4, i.e. toCegartix exampleAF4.

>>> putStr output4
arg("A").
arg("B").
arg("C").
arg("D").
arg("E").
att("A","B").
att("B","A").
att("B","C").
att("C","D").
att("D","E").
att("E","C").

output5 :: String

Output String corresponding to exampleAF5, i.e. toCegartix exampleAF5.