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

Each normal logic program has a 2-valued Minimal Hypotheses semantics