The author briefly discusses three theoretical constructs: a) possible worlds of modal logicians, expanded into b) text worlds ad c) discourse worlds of literary linguistics and practitioners of cognitive poetics, as well as theoreticians of literature. Since discourse worlds are also cultural concepts (Dolezel, Eco), the author postulates to extrapolate them onto all kinds of artistic texts, in the spirit of the broad semiotic approach originating with J.M. Lotman and B. Uspiensky. The author analyses those genres of figural painting in which narrativity helps in the creation of a fictional visual world. These are: 1) among the icons of the Eastern-Orthodox tradition those depicting hagiographical stories, scenes of the Passion and the Last Judement; 2) painted cycles, of which M. Chagall's oeuvre is an exemplar with a consistently constructed fictional-oneiric world. The most exciting interpretative game of the reader/viewer is Ingardenian concretization - the filling in of the missing material in the texture of a fictional world, both verbal and visual.