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In English, a sentence like "The cat didn't eat the carrot or the pepper" typically receives a "neither" interpretation; in Japanese it receives a "not this or not that" interpretation. These two interpretations are in a subset/superset relation, such that the "neither" interpretation (strong reading) asymmetrically entails the "not this or not that" interpretation (weak reading). This asymmetrical entailment raises a learnability problem. According to the Semantic Subset Principle, all language learners, regardless of the language they are exposed to, start by assigning the strong reading, since this interpretation makes such sentences true in the narrowest range of circumstances.). If the "neither" interpretation is children's initial hypothesis, then children acquiring a superset language will be able to revise their initial hypothesis on the basis of positive evidence. The aim of the present study is to test an additional account proposed by Pagliarini, Crain, Guasti (2018) as a possible explanation for the earlier convergence to the adult grammar by Italian children. The hypothesis tested here is that the presence of a lexical form such as recursive "né" that unambiguously conveys a "neither" meaning, would lead children to converge earlier to the adult grammar due to a blocking effect of the recursive "né" form in the inventory of negated disjunction forms in a language. We compared data from Italian (taken from Pagliarini, Crain, Guasti, 2018), French, Hungarian and Dutch. Dutch was tested as baseline language. French and Hungarian have -- similarly to Italian -- a lexical form that unambiguously expresses the "neither" interpretation ("ni ni" and "sem sem," respectively). Our results did not support this hypothesis however, and are discussed in the light of language-specific particularities of the syntax and semantics of negation.