Modalized Questions and Exhaustivity

They show that the acceptability of a sentence of the form [....only.....dF.....], where d is a focused degree-denoting expression, correlates with the availability of a scalar implicature for the very same sentence without only: for instance, Jack has to read more than three books by Balzac generally implicates that Jack does not have to read more than four books by Balzac, while Jack read more than three books by Balzac does not generally implicate that Jack did not read more than four books by Balzac (i.e. does not implicate that Jack read exactly four books). Fox and Hackl (2006) furthermore show that these contrasts (as well as many other facts) follow from the following assumptions:

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