Using data from the understudied language Gιsιɖa Anii, we provide a formal analysis of irrealis that builds on the framework of modality proposed in Giannakidou and Mari. In particular, we propose that Anii has an irrealis modal morpheme whose meaning is that the speaker does not believe that the proposition is true at a particular time. This gives irrealis, at least in Anii, a negatively biased meaning. Giannakidou and Mari propose that the subjunctive in European languages is a positively biased modal but find no evidence in their data for a corresponding negatively biased one. However, in expanding their approach to a completely unrelated language, we show that modal bias can also be negative, filling in the paradigmatic gap left open by Giannakidou and Mari’s work. We also illustrate the utility of analyzing irrealis (in relation to the concept of veridicality) as a morphosyntactic and semantic category with a status similar to tense and aspect. Our formal analysis accounts for the obligatory realization of irrealis in a wide range of semantic contexts in Anii, including future tense, negation, and wishes, and shows how irrealis can be composed with other clausal elements. We suggest that reality status, which we analyze as (non)-veridicality, is obligatorily present in the Anii clause and discuss the implications of this for other languages.