  The covariant canonical formalism for four-dimensional BF theory is
performed. The aim of the paper is to understand in the context of the
covariant canonical formalism both the reducibility that some first class
constraints have in Dirac's canonical analysis and also the role that
topological terms play. The analysis includes also the cases when both a
cosmological constant and the second Chern character are added to the pure BF
action. In the case of the BF theory supplemented with the second Chern
character, the presymplectic 3-form is different to the one of the BF theory in
spite of the fact both theories have the same equations of motion while on the
space of solutions they both agree to each other. Moreover, the analysis of the
degenerate directions shows some differences between diffeomorphisms and
internal gauge symmetries.
