  In this paper we revisit the problem of computing the closure of a set of
attributes, given a set of Armstrong dependencies. This problem is of main
interest in logics, in the relational database model, in lattice theory and in
Formal Concept Analysis as well. We consider here three main closure
algorithms, namely Closure, LinClosure and Wild's Closure, which are combined
with implication bases which may have different characteristics, among which
being "minimal", e.g., the Duquenne-Guigues basis, and being "direct", e.g.,
the Canonical Basis and the D-basis. The impacts of minimality and directness
on the closure algorithms are then deeply studied also experimentally. The
results are extensively analyzed and propose a different and fresh look at
computing the closure of a set of attributes.
  This paper has been submitted to the International Journal of Approximate
Reasoning.
