Strong Equivalence for Argumentation Semantics Based on Conflict-Free Sets

Argumentation can be understood as a dynamic reasoning process, i.e. it is in particular useful to know the effects additional information causes with respect to a certain semantics. Accordingly, one can identify the information which does not contribute to the results no matter which changes are performed. In other words, we are interested in so-called

kernels

of frameworks, where two frameworks with the same kernel are then “immune” to all kind of newly added information in the sense that they always produce an equal outcome. The concept of

strong equivalence

for argumentation frameworks captures this intuition and has been analyzed for several semantics which are all based on the concept of admissibility. Other important semantics have been neglected so far. To close this gap, we give strong equivalence results with respect to naive, stage and

cf

2 extensions, and we compare the new results with the already existing ones. Furthermore, we analyze strong equivalence for symmetric frameworks and discuss local equivalence, a certain relaxation of strong equivalence.