Proposition Sets or Structured Meanings: That’s the Question.

1. Proposition Setsor Structured Meanings:That’s the Question. • Manfred Krifka • Humboldt-Universität &Zentrum für Allgemeine Sprachwissenschaft (ZAS)Berlin • http://amor.rz.hu-berlin.de/~h2816i3x

2. Two Approaches to Questions • The Proposition Set Approach(e.g., Hamblin 1958, 1973; Karttunen 1977; Groenendijk & Stokhof 1984, ...): • The meaning of a question is a set of propositions;a congruent answer to the question identifies one of them. [[Which novel did Mary read?]] = { read(ulysses)(mary), read(moby-dick)(mary)... } • The Functional (= Structured Meaning, Categorial) Approach(e.g., Ajdukiewicz 1928, Cohen 1929, Hull 1975, Tichy 1978, Hausser & Zaefferer 1979, Stechow & Zimmermann 1984, Reich 2001): • The meaning of a question is an unsaturated proposition;a congruent answer to the question saturates it. [[ Which novel did Mary read?]] a. read(xnovel)(mary) b. xnovel [read(x)(mary)] c. x[read(x)(mary)], novelQ-Function, Q-Restriction [[ Ulysses.]] = ulysses, x[read(x)(mary)](ulysses) = read(mary)(ulysses).

3. The Proposition Set Approach to Questions • [[Which novel did Mary read?]]= { Mary read Ulysses, Mary read Moby-Dick, Mary read Dr. Faust } Set of all possible worlds

4. The Proposition Set Approach to Questions • [[Which novel did Mary read?]]= { Mary read Ulysses, Mary read Moby-Dick, Mary read Dr. Faust } Set of all possible worlds PropositionMary read Ulysses

5. The Proposition Set Approach to Questions • [[Which novel did Mary read?]]= { Mary read Ulysses, Mary read Moby-Dick, Mary read Dr. Faust } Set of all possible worlds PropositionMary read Ulysses PropositionMary read Moby-Dick

6. The Proposition Set Approach to Questions • [[Which novel did Mary read?]]= { Mary read Ulysses, Mary read Moby-Dick, Mary read Dr. Faust } Set of all possible worlds PropositionMary read Ulysses PropositionMary read Moby-Dick PropositionMary read Dr. Faust

7. The Proposition Set Approach to Questions • [[Which novel did Mary read?]]= { Mary read Ulysses, Mary read Moby-Dick, Mary read Dr. Faust } Set of all possible worlds PropositionMary read Ulysses PropositionMary read Moby-Dick PropositionMary read Dr. Faust Exhaustive coreof propositions:Mary read only UlyssesMary read only Moby-DickMaryread only Dr. Faust Exhaustive core: EXH([[Q]]): {p| p’[p’[[Q]]  p = p’ — {p”[[Q]] | p”  p’}] }

8. The Proposition Set Approach to Questions • [[Which novel did Mary read?]]= { Mary read Ulysses, Mary read Moby-Dick, Mary read Dr. Faust} Specification ofquestion meaningby exhaustivecore of propositions(built intoquestion semanticsin Groenendijk & Stokhof, here just a didacticdevice)

9. The Proposition Set Approach to Questions • [[Who read Ulysses?]]= { Mary read Ulysses, John read Ulysses, Kai read Ulysses}

10. The Proposition Set Approach to Questions • [[Who read which novel?]]= { Mary read Ulysses, John read Ulysses, Kai read Ulysses, Mary read Dr. Faust, John read Dr. Faust, Kai read Dr. Faust, Mary read Moby-Dick, John read Moby-Dick, Kai read Moby-Dick}

11. Relationship between the PS and SM approach • We can derive proposition set meanings from structured meanings:[[Q]]PS = { [[Q]]SM(y) | yDOM([[Q]]SM) } • e.g. [[Which novel did Mary read?]]PS • = [[Which novel did Mary read?]]SM(y) | yDOM([[Which novel did Mary read?]]SM) } = { xnovel[Mary read x](y) | y novel } • = { Mary read Ulysses, Mary read Moby-Dick, ... } • We cannot derive structured meanings from proposition set meanings(at least if propositions are not expressions in a representation language) • Hence:The PS approach is the null hypothesis; adherents for the SM approach have to provide for arguments for it. • Question:Are there linguistic phenomena that cannot be handled by the PS approach,but can be handled by the SM approach?

12. Aims of this talk • Krifka (2001), “For a structured meaning account of questions and answers”:There are such phenomena, hence we need an SM approach to questions.(In particular, alternative questions, multiple questions, focus marking in answers) • Büring (2002), “Question-Answer-Congruence: Unstructured”:gives arguments that try to refute the arguments of Krifka (2001), arguing that the PS approach to questions is sufficient. • Aims of this talk:- Restate the arguments of Krifka (2001)- Discuss the counterarguments of Büring (2002)- Conclude that the PS approach to questions is insufficient, and that the SM approach does better. • Here: Restricted to an argument concerning focus marking

13. Congruent Answers to Questions • Congruent and incongruent answers:Q: Which novel did Mary read?A: Mary read Ulysses.#A’: Mary read Exiles.#A’’: Mary danced. • Congruence criterion, first version:An answer A is congruent to a question Qiff [[A]] [[Q]] • [[Which novel did Mary read?]] = {read(x)(mary) | novel(x)}, = Q • [[Mary read Ulysses.]] = read(ulysses)(mary),  Q • [[Mary read Exiles.]] = read(exiles)(mary),  Q • With exhaustive cores of question meanings:An answer A is congruent to a question Qiff there is a unique p  EXH([[Q]]) such that p  [[A]]

14. Congruent Answers to Questions • Congruent answer: • Q: Which novel did Mary read?A: Mary read Ulysses.

15. Congruent Answers to Questions • Incongruent answers: • Q: Which novel did Mary read?#A’: Mary read Exiles.

16. Congruent Answers and Focus • Question-answer congruence; first systematic observation: Hermann Paul 1889. • Congruent question / answer pairs indicated by focus of the answer:Q: What did Mary read?A: Mary read ULYSsesF. Focus o.k. • Wrong focus placements:A: *MAryF read Ulysses. Focus in wrong place.

17. Focus in Answers in the PS Account • Optimally matched: Proposition set theory of questions / Alternative Semantics to focuscf. Rooth 1985, Rooth 1992, von Stechow 1990. • Alternative semantics to focus:Two levels of interpretation: Meaning proper, Alternatives. • Focus marking introduces alternatives;the meaning proper is an element of the set of alternatives. • Examples: [[Mary read ULYSsesF.]] = read(ulysses)(mary)[[Mary read ULYSsesF.]]A= {read(x)(mary) | x  ALT(ulysses)} • [[MAryF read Ulysses. ]] = read(ulysses)(mary)[[MAryF read Ulysses. ]]A = {read(ulysses)(x) | x  ALT(mary)} • Conditions for congruent Q/A-pairs:Question meaning corresponds to the alternatives of the answer. • Examples:[[Which novel did Mary read?]] = {read(x)(mary) | x  novel}o.k.: Mary read ULYSsesF, as question meaning {read(x)(mary) | xnovel}corresponds to alternatives: {read(x)(mary) | xALT(ulysses)} • not: MAryF read Ulysses, as question meaning does not correspond to alternatives: {read(ulysses)(x) | xALT(mary)} • But what does “correspond” mean?

18. Q/A pairs in PS: What does “correspond” mean? • Rooth (1992): Alternatives = all possible denotations of the appropriate type • Congruence criterion, second version:An answer A is congruent to a question Q iff (i) [[A]] [[Q]] • (ii) [[Q]][[A]]A • Example:Q: Which novel did Mary read? A: Mary read ULYSsesF.as {read(x)(mary) | x  novel} {read(x)(mary) | x  De} Question meaning:Q: Which noveldid Mary read?

19. Q/A pairs in PS: What does “correspond” mean? • Rooth (1992): Alternatives = all possible denotations of the appropriate type • Congruence criterion, second version:An answer A is congruent to a question Q iff (i) [[A]] [[Q]] • (ii) [[Q]][[A]]A • Example:Q: Which novel did Mary read? A: Mary read ULYSsesF.as {read(x)(mary) | x  novel} {read(x)(mary) | x  De} Question meaning:Q: Which noveldid Mary read? Answer alternatives:A: Mary read ULYSsesF. [[Q]][[A]]A ,shown in terms of exhaustive cores:EXH([[Q]])  EXH([[A]]A)

20. Q/A pairs in PS: What does “correspond” mean? • Rooth (1992): Alternatives = all possible denotations of the appropriate type • Congruence criterion, second version:An answer A is congruent to a question Q iff (i) [[A]] [[Q]] • (ii) [[Q]][[A]]A • Example:Q: Which novel did Mary read? *A: MAryF read Ulysses.as {read(x)(mary) | x  novel} {read(ulysses)(y) | y  De} Question meaning:Q: Which noveldid Mary read? Answer alternatives:A: MAryF read Ulysses. EXH([[Q]])  EXH([[A]]A)

21. Over- and Underfocused Answers • Congruent question / answer pairs indicated by focus of the answer:Q: What did Mary read?A: Mary read ULYSsesF. Focus o.k. • Wrong focus placements: • A: *MAryF read Ulysses. Focus on wrong place. • Over-and underfocused answers:A: *MAryF read ULYSsesF.Overfocused; too many foci.A: Mary read Ulysses. Underfocused; no focus. • Q: Which student read which novel?A: MAryF read ULYSsesF. Focus o.k. (except for list answer)A: Mary read ULYSsesF. Underfocused; too few foci. • Q: What did Mary do?A: Mary [read ULYSses]F. Focus o.k.; focus projectionA: *Mary READF Ulysses. Underfocused; focus too narrow. • Q: What did Mary do with Ulysses?A: Mary READF Ulysses. Focus o.k.A: *Mary [read ULYsses]F. Overfocused; focus too wide.

22. Banning Underfocused Answers • Example: No focus at all.Q: Which novel did Mary read? *A: Mary read Ulysses.as {read(x)(mary) | x  novel} {read(ulysses)(mary)}

23. Banning Underfocused Answers • Example: Too few foci.Q: Who read which novel? *A: MAryF read Ulysses.as {read(x)(y) | yperson, xnovel} {read(ulysses)(x) | x  De}

24. No Banning of Overfocused Answers • Example: Too many foci.Q: Which novel did Mary read? *A: MAryF read ULYSsesF.but {read(x)(mary) | x  novel} {read(x)(y) | x, y  De}

25. A Preference for Minimal Focus? • Congruence criterion, third version:An answer A is congruent to a question Q iff (i) [[A]][[Q]](ii) [[Q]][[A]]A ( or EXH([[Q]])  EXH([[A]]A) )(iii) There is no A’ that is like A with the exception that it has less focus marking than A, that satisfies (i) and (ii). • Preference for minimal focus: Avoid Focus, Schwarzschild 1999. • Example: Q: Which novel did Mary read?A: Mary read ULYSsesF. *A’: MAryF read ULYSsesF.*A”: Mary read Ulysses. • Both A, A’ satsfy (i) and (ii), but A has less focus marking, so A’ is ruled out. • A” has less focus marking than A’, but it doesn’t have enough to satisfy (ii). • In general:Have enough focus marking to express congruence with answer (ii),but use focus marking sparingly (iii).Can be formulated as antagonistic constraints in OT.

26. But what is less focus marking? • Example: VP focus • Q: What did John do?{P(john) | PDet, P: activity} • a. A: John [read ULYSses]F. (focus projection / accent percolation) • b. *A’: John read ULYSsesF. (narrow focus, realized like A) • c. *A”: John READF Ulysses. (narrow focus on verb) • *A”’: [John read ULYSses]F. (sentence focus, realized like A) • All answers satisfy clause (i), as [[A]][[Q]] • Answers (b) and (c) are ruled out due to clause (ii), as [[Q]][[A]]A • Answer (d) should be ruled out due to clause (iii), as there is a possible answer with less focus marking, (a),that satisfies clauses (i) and (ii)and has less (= smaller) focus marking. • Hence: Less focus marking can meanfocus marking on a smaller constituent; [ X [U VF W] Y] has less focus marking than [X [U V W]F Y]

27. Less Focus Marking • It is quite natural to interpret “less” focus marking as “smaller” focus marking,because it leads to a reduction of alternative setsin terms of exhaustive cores: • EXH([[Mary read ULYSsesF]]A)  EXH([[Mary [read ULYSses]F]]), • EXH([[Mary [read ULYSses]F]]A)  EXH([[[Mary read ULYSses]F]]) • This suggests to replace clause (iii) of congruence criterion by:(iii’) There is no A’ that satisfies (i) and (ii) and EXH([[A’]]A)  EXH([[A]]A)

28. A Conflict for Less Focus Marking • Q: What did Mary do with which novel?{R(x)(mary) | novel(x), RDeet, R: activity} • a. A: Mary READF ULYSsesF (and BURNEDF [Finnegan’s WAKE]F).{R(x)(mary) | xDe, RDeet } • *A’: Mary [read ULYSses]F{P(mary) | PDet } • Both (a) and (b) satisfy clauses (i) and (ii) of congruence criterion,as[[A]][[Q]] and [[Q]][[A]]A • Which answer is excluded by (iii)? • (a) has smaller foci, but • (b) has fewer foci. • As (a) is the congruent answer, the size of foci appears to violate Avoid Focus less than the number of foci. • This is consonant with the revised criterion (iii), as e.g. EXH([[Mary READF ULYSsesF ]]A)  EXH([[Mary [read ULYSses]F]]A)

29. Another Conflict for Less Focus Marking • Q: What did Mary do?{P(mary) | PDet, P: activity} • A: Mary [read ULYSses]F{P(mary) | PDet } • b. *A’: Mary READF ULYSsesF (and BURNEDF [Finnegan’s WAKE]F).{R(x)(mary) | xDe, RDeet } • Both (a) and (b) satisfy clauses (i) and (ii) of congruence criterion,as[[A]][[Q]] and [[Q]][[A]]A • Notice: [[Q]][[A]]A holds for (b), as x, R are completely unrestricted;for every P, PDet we can take an arbitrary xand define R as: R = xy[P(y)] • Which answer is excluded by (iii)? • (a) has fewer foci, but • (b) has smaller foci. • As (a) is the congruent answer, the number of foci now appears to violate Avoid Focus less than the size of foci. • Hence: We cannot fix, in general,whether it is better to have fewer foci, or to have smaller foci: • A serious problem for the proposition set account of questions!

30. A Problem for Focus Projection • Selkirk (1984): Focus on the larger constituent is licensed by focus projection. • Focus on an argument licenses focus on the head. • Focus on the head licenses focus on the whole constituent. • This is how VP focus is generated, step by step: • John [read ULYSsesF]. (focus licensed by accent) • John [readF ULYSsesF]. (focus of head licensed by focus on argument) • John [readF ULYSsesF]F. (focus on VP licensed by focus on head) • Compare this with focus on verb and object NP: • John [READF ULYSsesF]. • Notice that (d) has fewer focus features than (c), hence everything else (d) should be preferred over (c), and in general multiple focus should be preferred over broad focus. • False prediction:Q: What did John do?*A: John READF ULYSsesF. (2 F-features)A’: John [readF ULYSsesF]F. (3 F-features, should be dispreferred)

31. Focus in Answers in the SM Account • Focus in the SM approach (von Stechow 1981, 1990; Jacobs 1984):Focus marking induces a partition between background and focus; the background applied to the focus yields the standard proposition. • Examples:[[Mary read ULYSsesF.]] = x[read(x)(mary)], ulysses[[MAryF read Ulysses.]] = x[read(ulysses)], mary • Conditions for congruent Q/A pairs:Background condition: Background of the answer = Question functionFocus condition: Focus of the answer  Question restriction • Examples:[[Which novel did Mary read?]] = x[read(x)(mary), novel • o.k.: [[Mary read ULYSsesF.]], = x[read(x)(mary)], ulyssesidentical backgrounds, ulysses  novel • not ok: [[MAryF read Ulysses.]], = x[read(ulysses)], maryBackground condition violated. • not o.k: [[Mary read ExilesF.]], = x[read(x)(mary)], exilesFocus condition violated, exiles  novel

32. Under / Overfocusation in the SM Account • Cases of underfocusation and overfocusation are excluded: • Underfocusation, too few foci: • [[Which student read which novel?]], = xy[read(y)(x)], studentnovel • o.k.: [[ MAryF read ULYSsesF]], = xy[read(y)(x)], mary, ulysses,identical backgrounds, mary, ulysses  studentnovelnot o.k.: [[Mary read ULYSsesF.]], = x[read(x)(mary)], ulysses,Background condition and focus condition violated • Underfocusation, focus too small:[[What did Mary do?]], = P[P(mary)], activity • o.k.: [[Mary [read ULYSses]F.]], = P[P(mary)], x[read(ulysses)(x)]identical backgrounds, x[read(ulysses)(x)]  activity • not o.k: [[ Mary READF Ulysses. ]], = R[R(ulysses)(mary)], readBackground condition (and focus condition) violated. • Overfocusation: • [[ What did Mary do with Ulysses? ]], = R[R(ulysses)(mary)], transitive_activity • o.k.: [[ Mary READF Ulysses. ]], = R[R(ulysses)(mary)], readidentical backgrounds, read  transitive activitynot o.k.: [[ Mary [read ULYSsesF]. ]], = P[P(mary)], x[read(ulysses)(x)]Background and focus condition violated.