(= p) (16) a. ScalAlt(p) = {John spilt wine and broke all glasses, John spilt wine and broke some glasses, John spilt wine, John broke all glasses, John broke some glasses, p} The assumption of the operators L and R has the effect of projecting a local implicature from each disjunct into the main context.
the statement implicates the following: (17) ¬(John spilt wine and broke all glasses) ¬(John spilt wine and broke some glasses) ¬(John broke all glasses) Here the SI that John did not break all glasses arises from a stronger alternative of the second disjunct.