The contribution presents a generative grammar for Greimas’ semiotic square, designed to represent modal syntax. In particular: (1) the grammar will generate both modal syntagms and their structural descriptions; (2) the articulation of the immanent narrative structure will be clarified; (3) structural features which are not manifested on the linear surface will become easier to examine. This model contributes to computational narratology theory, aiming at merging post-structuralist narratology with formal language theory.