  In this paper we explore a unifying approach --- that of hypotheses
assumption --- as a means to provide a semantics for all Normal Logic Programs
(NLPs), the Minimal Hypotheses (MH) semantics. This semantics takes a positive
hypotheses assumption approach as a means to guarantee the desirable properties
of model existence, relevance and cumulativity, and of generalizing the Stable
Models in the process. To do so we first introduce the fundamental semantic
concept of minimality of assumed positive hypotheses, define the MH semantics,
and analyze the semantics' properties and applicability. Indeed, abductive
Logic Programming can be conceptually captured by a strategy centered on the
assumption of abducibles (or hypotheses). Likewise, the Argumentation
perspective of Logic Programs also lends itself to an arguments (or hypotheses)
assumption approach. Previous works on Abduction have depicted the atoms of
default negated literals in NLPs as abducibles, i.e., assumable hypotheses. We
take a complementary and more general view than these works to NLP semantics by
employing positive hypotheses instead.
