Object of this study is the analysis of the Indicative and Subjunctive morphological mood marking, with special reference to Italian. I claim that the occurrence of these moods triggers a presupposition of assertibility and non-assertibility of the clauses that contain them: a clause counts as assertible just in case it leads to an effective elimination of possible worlds from the input context it gets added to. I show how these considerations can correctly account for the interpretation of hypothetical statements (indicative and counterfactual conditionals), and for the phenomenon of mood alternation in the domain of subordinated clauses.