argumentation frameworks have played a major role as a way of understanding argumentbased inference, resulting in different argumentbased semantics. In order to make such semantics computationally attractive, suitable proof procedures are required, in which a search space of arguments is examined to find out which arguments are warranted or ultimately acceptable. This paper introduces a novel approach to model warrant ion in a skeptical abstract argumentation framework. We show that such search space can be defined as a lattice, and illustrate how the so-called dialectical constraints can play a role for guiding the efficient computation of warranted arguments.