  Abstract Dialectical Frameworks (ADFs) are argumentation frameworks where
each node is associated with an acceptance condition. This allows us to model
different types of dependencies as supports and attacks. Previous studies
provided a translation from Normal Logic Programs (NLPs) to ADFs and proved the
stable models semantics for a normal logic program has an equivalent semantics
to that of the corresponding ADF. However, these studies failed in identifying
a semantics for ADFs equivalent to a three-valued semantics (as partial stable
models and well-founded models) for NLPs. In this work, we focus on a fragment
of ADFs, called Attacking Dialectical Frameworks (ADF$^+$s), and provide a
translation from NLPs to ADF$^+$s robust enough to guarantee the equivalence
between partial stable models, well-founded models, regular models, stable
models semantics for NLPs and respectively complete models, grounded models,
preferred models, stable models for ADFs. In addition, we define a new
semantics for ADF$^+$s, called L-stable, and show it is equivalent to the
L-stable semantics for NLPs. This paper is under consideration for acceptance
in TPLP.
