Examples showing the non-compatibility in the general case

We give examples for each usual valuation (the global valuation with tuples and 2 instances of the generic local valuation: [4,13]) and for the most classical semantics for acceptability (preferred semantics and stable semantics of [9]).

Cleanly-accepted argument but not well-defended: There are 3 examples (each using a distinct valuation: one for the global valuation and two for the two well-known instances of the local valuation):

• the argument $A$ is cleanly-accepted but it is not well-defended:
  

• the argument $A$ is cleanly-accepted but it is not well-defended:
  

• the argument $I$ is cleanly-accepted but it is not well-defended:
  

Well-defended argument but not cleanly-accepted: Similarly, for the same three valuations, we have:

• the argument $C$ is well-defended but it is not cleanly-accepted:
  

• the argument $F$ is well-defended but it is not cleanly-accepted:
  

• the argument $G$ is well-defended but it is not cleanly-accepted: