This paper addresses the two interpretations that a combination of negative\ud indefinites can get in concord languages like French: a concord reading, which amounts to\ud a single negation, and a double negation reading. We develop an analysis within a polyadic\ud framework, where a sequence of negative indefinites can be interpreted as an iteration\ud of quantifiers or via resumption. The first option leads to a scopal relation, interpreted\ud as double negation. The second option leads to the construction of a polyadic negative\ud quantifier corresponding to the concord reading. Given that sentential negation participates\ud in negative concord, we develop an extension of the polyadic approach which can deal with\ud non-variable binding operators, treating the contribution of negation in a concord context\ud as semantically empty. Our semantic analysis, incorporated into a grammatical analysis\ud formulated in HPSG, crucially relies on the assumption that quantifiers can be combined\ud in more than one way upon retrieval from the quantifier store. We also consider crosslinguistic\ud variation regarding the participation of sentential negation in negative concord
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