Language processing relies on memory. There exists a considerable body of literature on retrieval in sentence processing and, in particular, on cases involving recall of syntax-relevant information. There is no reason to doubt, however, that memory is involved in semantic aspects of language processing as well. In this work, we look at the case of additive presuppositions, such as those involved in interpreting the additive particle too. When one hears Mary went to the party, too, one should recall that someone other than Mary went to the party. We make the case that, as a starting hypothesis, it would be expected that the retrieval of this kind of information should share basic features of memory processes in language with the better-known cases of recall involved in syntactic parsing. In particular, we argue that, given certain assumptions and linking hypotheses, all prominent retrieval theories predict the existence of distance effects for the recall of previous information, independent of whether the recall is driven by syntactic or semantic, sentential or inter-sentential, considerations. As the distance increases, so does the difficulty of processing. We test this prediction in four experiments that investigate the role of retrieval in interpreting too. Using the Bayesian hierarchical modelling paradigm, we find evidence in two self-paced reading experiments that it takes more time to read sentences with too when the distance between the trigger and its antecedent is greater, compared to a baseline that lacks the presupposition trigger. This result shows that theories of the role of memory in language are just as relevant to the domain of discourse interpretation as they are to syntactic parsing. The fact that our evidence was relatively hard to find, however, suggests additionally that there are interesting differences to explore in the future.