Actuality effects as conversational implicatures

•Past perfective on the Spanish possibility modal can trigger either an actuality or a counterfactuality inference with respect to the prejacent.•Actuality arises through application of Relevance reasoning.•Counterfactuality arises through application of Quantity reasoning.•Past imperfective on the possibility modal does not necessarily trigger these effects due to the presence of genericity. Past perfective on the Spanish possibility modal poder (“can”, “be able to”) can trigger either an actuality or a counterfactuality effect on the prejacent. This is surprisingly different from other languages with an overt perfective vs. imperfective distinction (French, Hindi, Greek, etc.), where past perfective morphology on a possibility modal leads to actuality entailments (Bhatt, 1999; Hacquard, 2006). Contrary to previous work (Borgonovo and Cummins, 2007; Borgonovo, 2011), in this paper I argue that the effects observed in Spanish are best characterized as arising pragmatically from the interaction between the discourse model of the Question Under Discussion (Büring, 2003) and the Levinsonian maxims of Quantity and Informativeness. I propose that constructions with past perfective poder can be potentially ambiguous between the two readings, whereas those with past imperfective poder are just vague.