Scalar Implicatures in Complex Sentences

The paper splits Gazdar's scalar implicatures into two tiers. A scalar alternative ψ that asymmetrically entails the assertion yields the primary implicature ¬Kψ (42), and K¬ψ is a secondary implicature when it is consistent with the assertion and all primary implicatures (43); these are NeoGricean.primaryImplicatures and NeoGricean.IsSecondaryImplicature. Disjunction sits on the scale (40) of or, the operators L and R of (39) that keep one disjunct, and and, and the scalar alternatives of a sentence are all substitutions of scale-mates for its scalar items (19).

Of A or B only the exclusiveness implicature K¬(A and B) is secondary, the strengthenings K¬A and K¬B being blocked (46). Of Kai had the broccoli or some of the peas they are K¬(broccoli and some) and K¬(all) (49), with K¬(broccoli and all), which K¬(all) entails, so the scalar item under disjunction gets the implicature earlier accounts missed. Of A or (B or C) they are the three pairwise exclusiveness implicatures and two that these entail (52).

Implementation notes

A world is a valuation of the atoms, or for (47) whether Kai had the broccoli and whether he had none, some but not all, or all of the peas. Alternatives are indexed by the scale-mates substituted, so one proposition can carry several indices, as A does in (51).

Errata

(51) lists nine primary implicatures of A or (B or C), but the cross product (19) of the two disjunctions' scales also yields A or B, A or C and A or (B and C), which asymmetrically entail the assertion. Their primary implicatures block no secondary implicature, so (52) holds over all twelve stronger alternatives (isSecondaryImplicature_abc_iff).

References

• Sauerland 2004, Scalar Implicatures in Complex Sentences