%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Encoding for semi-stable extensions % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% an argument x defeats an argument y if x attacks y defeat(X,Y) :- att(X,Y), not vaf. %% Guess a set S \subseteq A in(X) :- not out(X), arg(X). out(X) :- not in(X), arg(X). %% S has to be conflict-free :- in(X), in(Y), defeat(X,Y). %% The argument x is defeated by the set S defeated(X) :- in(Y), defeat(Y,X). %% The argument x is not defended by S not_defended(X) :- defeat(Y,X), not defeated(Y). %% All arguments x \in S need to be defended by S (admissibility) :- in(X), not_defended(X). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % For the remaining part we need to put an order on the domain. % Therefore, we define a successor-relation with infinum and supremum % as follows %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% lt(X,Y) :- arg(X),arg(Y), X