Class Realizability

java.lang.Object
org.tweetyproject.arg.dung.util.Realizability
public abstract class Realizability extends Object
Contains some methods for checking realizability of extension sets, see e.g. [Dunne, Dvorak, Linsbichler, Woltran: Characteristics of multiple viewpoints in abstract argumentation. Artificial Intelligence 228: 153-178, 2015]

  • Constructor Details

    • Realizability

      public Realizability()

  • Method Details

    • args

      public static Collection<Argument> args(Collection<Extension<DungTheory>> exts)
      Returns the set of all arguments appearing in some extension.
      Parameters:
      exts - some set of extensions
      Returns:
      the set of all arguments appearing in some extension.

    • isPair

      public static boolean isPair(Collection<Extension<DungTheory>> exts, Argument a, Argument b)
      Checks whether the given pair of arguments is a pair in the extension set, i.e. whether there is an extension that contains both arguments.
      Parameters:
      exts - some set of extensions
      a - some argument
      b - some argument
      Returns:
      true, if the two arguments are a pair.

    • pairs

      public static Collection<Set<Argument>> pairs(Collection<Extension<DungTheory>> exts)
      Returns the set of sets of arguments {a,b}, s.t. both a and b appear in at least one extension.
      Parameters:
      exts - some set of extensions
      Returns:
      the set of all arguments appearing in some extension.

    • isDownwardClosed

      public static boolean isDownwardClosed(Collection<Extension<DungTheory>> exts)
      Checks whether the set is downward-closed, i.e., if it contains each subset of each contained set.
      Parameters:
      exts - some set of extensions
      Returns:
      true if the set is downward-closed

    • isTight

      public static boolean isTight(Collection<Extension<DungTheory>> exts)
      Checks whether the given set is tight, i.e., whether for all extensions ext and each argument a, if (ext with a) is not in the set, there there is an argument b in ext such that (a,b) is not a pair.
      Parameters:
      exts - some set of extensions
      Returns:
      true if the set is tight.

    • isIncomparable

      public static boolean isIncomparable(Collection<Extension<DungTheory>> exts)
      Checks whether the given set is incomparable, i.e., whether for each pair ext1, ext2 of extensions we have that neither is a proper subset of the other.
      Parameters:
      exts - some set of extensions
      Returns:
      true if the set is incomparable.

    • isAdmClosed

      public static boolean isAdmClosed(Collection<Extension<DungTheory>> exts)
      Checks whether the given set is adm-closed, i.e., whether for each pair ext1, ext2 of extensions we have that if all a in ext1 and b in ext2 are a pair, then (ext1 union ext2) is also an extension.
      Parameters:
      exts - some set of extensions
      Returns:
      true if the set is adm-closed.

    • isPrefClosed

      public static boolean isPrefClosed(Collection<Extension<DungTheory>> exts)
      Checks whether the given set if pref-closed, i.e., whether it is incomparable and adm-closed.
      Parameters:
      exts - a set of extensions
      Returns:
      true if the set is pref-closed.