  Posibilistic logic is the most extended approach to handle uncertain and
partially inconsistent information. Regarding normal forms, advances in
possibilistic reasoning are mostly focused on clausal form. Yet, the encoding
of real-world problems usually results in a non-clausal (NC) formula and
NC-to-clausal translators produce severe drawbacks that heavily limit the
practical performance of clausal reasoning. Thus, by computing formulas in its
original NC form, we propose several contributions showing that notable
advances are also possible in possibilistic non-clausal reasoning.
  {\em Firstly,} we define the class of {\em Possibilistic Horn Non-Clausal
Knowledge Bases,} or $\mathcal{\overline{H}}_\Sigma$, which subsumes the
classes: possibilistic Horn and propositional Horn-NC.
$\mathcal{\overline{H}}_\Sigma $ is shown to be a kind of NC analogous of the
standard Horn class.
  {\em Secondly}, we define {\em Possibilistic Non-Clausal Unit-Resolution,} or
$ \mathcal{UR}_\Sigma $, and prove that $ \mathcal{UR}_\Sigma $ correctly
computes the inconsistency degree of $\mathcal{\overline{H}}_\Sigma $members.
$\mathcal{UR}_\Sigma $ had not been proposed before and is formulated in a
clausal-like manner, which eases its understanding, formal proofs and future
extension towards non-clausal resolution.
  {\em Thirdly}, we prove that computing the inconsistency degree of
$\mathcal{\overline{H}}_\Sigma $ members takes polynomial time. Although there
already exist tractable classes in possibilistic logic, all of them are
clausal, and thus, $\mathcal{\overline{H}}_\Sigma $ turns out to be the first
characterized polynomial non-clausal class within possibilistic reasoning.
