Alternative vs Polar questions: the cornering effect

The problem: The standard Hamblin/Karttunen semantics for Polar Questions (PolQ), (1a), and alternative questions composed of two polar alternatives (AltQ∨N), (1b), induces equivalent partitions: (1a-i) and (1b-i) (the canonical intonation is as indicated ([7, 5])). (1) a. Are you making pasta L * H-H% ? (final raising) [PolQ] i. (1a)(w 0)= λq[q = λw.make(pasta, you, w) ∨q = λw.¬make(pasta, you, w)] b. Are you making pasta L * H-or not H * L-L% ? (final fall) [AltQ∨N] i. (1b)(w 0) = λq[q = (λw.make(pasta, you, w) ∨ λw.¬make(pasta, you, w))] The denotations in (1a-i) and (1b-i) do not explain the differences pointed out by [2]: in requests, (2a), rethorical questions,(2b), invitations, (2c), and conversation starters, (2d) it is only appropriate to use a PolQ (in those cases, using AltQ∨Ns, as in (2), is inappropriate). (2) a. Will you marry me or not?(odd) b. Are you crazy or not? (odd) c.Do you want a beer or not? (odd) d.Do you like to play golf or not?(odd) [8] have recently provided a purely pragmatic account of PolQs vs. AltQ∨Ns according to which PolQs are special because their positive answer has a higher utility value for the questioner. However, there are problematic examples as well as new data that remains unexplained (3): the cornering effect.