Proposition Sets or Structured Meanings: Thats the Question. Manfred Krifka Humboldt-Universität & Zentrum für Allgemeine Sprachwissenschaft (ZAS) Berlin

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

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. xnovel [read(x)(mary)]

c. x[read(x)(mary)], novel Q-Function, Q-Restriction

[[ Ulysses. ]] = ulysses, x[read(x)(mary)](ulysses) = read(mary)(ulysses).

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



Mary read Ulysses


PropositionMary read Ulysses



Mary read Ulysses

Mary readMoby-Dick



PropositionMary read Moby-Dick



Mary read Ulysses

Mary readDr. Faust

Mary readMoby-Dick




PropositionMary read Dr. Faust



Mary read Ulysses

Mary readDr. Faust

Mary readMoby-Dick




PropositionMary read Dr. Faust

Exhaustive core of 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’}] }


[[ Which novel did Mary read? ]]= { Mary read Ulysses, Mary read Moby-Dick, Mary read Dr. Faust}

Kai readUlysses

Kai readMoby-Dick

Kai readDr. Faust

John readUlysses

John readDr. Faust

John readMoby-Dick

Mary read Ulysses

Mary readDr. Faust

Mary readMoby-Dick

Specification ofquestion meaningby exhaustivecore of propositions(built intoquestion semanticsin Groenendijk & Stokhof, here just a didacticdevice)


[[ Who read Ulysses? ]]= { Mary read Ulysses, John read Ulysses, Kai read Ulysses}

Kai readUlysses

Kai readMoby-Dick

Kai readDr. Faust

John readUlysses

John readDr. Faust

John readMoby-Dick

Mary read Ulysses

Mary readDr. Faust

Mary readMoby-Dick

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}

Kai readUlysses

Kai readMoby-Dick

Kai readDr. Faust

John readUlysses

John readDr. Faust

John readMoby-Dick

Mary read Ulysses

Mary readDr. Faust

Mary readMoby-Dick

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) }

= { xnovel[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?

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

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 Q iff [[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 Q iff there is a unique p EXH([[Q]]) such that p [[A]]


Congruent answer:Q: Which novel did Mary read?A: Mary read Ulysses.

Kai readUlysses

Kai readMoby-Dick

Kai readDr. Faust

John readUlysses

John readDr. Faust

John readMoby-Dick

Mary read Ulysses

Mary readDr. Faust

Mary readMoby-Dick

Mary read Exiles


Incongruent answers:

Q: Which novel did Mary read?#A’: Mary read Exiles.

Kai readUlysses

Kai readMoby-Dick

Kai readDr. Faust

John readUlysses

John readDr. Faust

John readMoby-Dick

Mary read Ulysses

Mary readDr. Faust

Mary readMoby-Dick

Mary read Exiles

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.

Focus in Answers in the PS AccountOptimally 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) | xnovel}corresponds to alternatives: {read(x)(mary) | xALT(ulysses)}

not: MAryF read Ulysses, as question meaning does not correspond to alternatives: {read(ulysses)(x) | xALT(mary)}

But what does “correspond” mean?

Q/A pairs in PS: What does “correspond” mean?

Rooth (1992): Alternatives = all possible denotations of the appropriate typeCongruence 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}

Kai readUlysses

Kai readMoby-Dick

Kai readDr. Faust

Kai readExiles

John readUlysses

John readDr. Faust

John readMoby-Dick

John readExiles

Mary read Ulysses

Mary readDr. Faust

Mary readMoby-Dick

Mary readExiles

Question meaning:Q: Which noveldid Mary read?




(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}

Kai readUlysses

Kai readMoby-Dick

Kai readDr. Faust

Kai readExiles

John readUlysses

John readDr. Faust

John readMoby-Dick

John readExiles

Mary read Ulysses

Mary readDr. Faust

Mary readMoby-Dick

Mary readExiles


Answer alternatives:A: Mary read ULYSsesF.

[[Q]] [[A]]A ,shown in terms of exhaustive cores:EXH([[Q]]) EXH([[A]]A)




(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}

Kai readUlysses

Kai readMoby-Dick

Kai readDr. Faust

Kai readExiles

John readUlysses

John readDr. Faust

John readMoby-Dick

John readExiles

Mary read Ulysses

Mary readDr. Faust

Mary readMoby-Dick

Mary readExiles


Answer alternatives:A: MAryF read Ulysses.

EXH([[Q]]) EXH([[A]]A)

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.

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)}

Kai readUlysses

Kai readMoby-Dick

Kai readDr. Faust

Kai readExiles

John readUlysses

John readDr. Faust

John readMoby-Dick

John readExiles

Mary read Ulysses

Mary readDr. Faust

Mary readMoby-Dick

Mary readExiles

Banning Underfocused Answers

Example: Too few foci.Q: Who read which novel? *A: MAryF read Ulysses.as {read(x)(y) | yperson, xnovel} {read(ulysses)(x) | x De}

Kai readUlysses

Kai readMoby-Dick

Kai readDr. Faust

Kai readExiles

John readUlysses

John readDr. Faust

John readMoby-Dick

John readExiles

Mary read Ulysses

Mary readDr. Faust

Mary readMoby-Dick

Mary readExiles

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}

Kai readUlysses

Kai readMoby-Dick

Kai readDr. Faust

Kai readExiles

John readUlysses

John readDr. Faust

John readMoby-Dick

John readExiles

Mary read Ulysses

Mary readDr. Faust

Mary readMoby-Dick

Mary readExiles

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.

But what is less focus marking?

Example: VP focusQ: What did John do?

{P(john) | PDet, 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)

d. *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]

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)

A Conflict for Less Focus Marking

Q: What did Mary do with which novel?{R(x)(mary) | novel(x), RDeet, R: activity }

a. A: Mary READF ULYSsesF (and BURNEDF [Finnegan’s WAKE]F).{R(x)(mary) | xDe, RDeet }

b. *A’: Mary [read ULYSses]F

{P(mary) | PDet }

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)

Another Conflict for Less Focus Marking

Q: What did Mary do?{P(mary) | PDet, P: activity }

a. A: Mary [read ULYSses]F

{P(mary) | PDet }

b. *A’: Mary READF ULYSsesF (and BURNEDF [Finnegan’s WAKE]F).{R(x)(mary) | xDe, RDeet }

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, PDet we can take an arbitrary xand define R as: R = xy[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!

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:

a. John [read ULYSsesF]. (focus licensed by accent)

b. John [readF ULYSsesF]. (focus of head licensed by focus on argument)

c. John [readF ULYSsesF]F. (focus on VP licensed by focus on head)

Compare this with focus on verb and object NP:

d. 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)

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), novelo.k.: [[ Mary read ULYSsesF. ]], = x[read(x)(mary)], ulyssesidentical backgrounds, ulysses novel

not ok: [[ MAryF read Ulysses. ]], = x[read(ulysses)], maryBackground condition violated.

not o.k: [[ Mary read ExilesF. ]], = x[read(x)(mary)], exilesFocus condition violated, exiles novel

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)], studentnovelo.k.: [[ MAryF read ULYSsesF ]], = xy[read(y)(x)], mary, ulysses ,identical backgrounds, mary, ulysses studentnovel not 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)], activityo.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)], readBackground condition (and focus condition) violated.

Overfocusation:[[ What did Mary do with Ulysses? ]], = R[R(ulysses)(mary)], transitive_activityo.k.: [[ Mary READF Ulysses. ]], = R[R(ulysses)(mary)], readidentical backgrounds, read transitive activitynot o.k.: [[ Mary [read ULYSsesF]. ]], = P[P(mary)], x[read(ulysses)(x)]Background and focus condition violated.

Documents

Proposition Sets or Structured Meanings: Thats the Question. Manfred Krifka Humboldt-Universität & Zentrum für Allgemeine Sprachwissenschaft (ZAS) Berlin