Turco, Braun and Dimroth (2014): When Contrasting Polarity, the Dutch Use Particles, Germans Intonation

Turco, Braun and Dimroth study how Dutch and German speakers mark a switch from a negative to a positive claim in two discourse contexts. In a polarity contrast, (1), the positive claim is about a different topic situation, in Klein's sense, than the negative one, so the two claims are compatible; in a polarity correction, (2), it is about the same topic situation, so they exclude each other. These are Umbach's contrast and correction. German speakers produced Höhle's Verum focus, a high-falling pitch accent on the finite verb, and never a sentence-internal affirmative particle, whereas Dutch speakers mostly produced the accented affirmative particle wel (Dutch.Particles.wel). The paper's claim is that the two devices are functionally equivalent but operate on different levels. A sentence contains a polarity operator and, above it, an assertion operator carried by the finite verb; wel is the overt affirmative value of the polarity operator, the counterpart of niet, as Sudhoff has it, whereas Verum focus marks the assertion operator. An overt polarity value fixes the polarity of its sentence, so wel cannot occur in a negated sentence while Verum focus can, which is why the assertion operator takes effect above polarity, as in Blühdorn. The paper sets this against Sudhoff, for whom focus on wel is itself an instance of Verum focus: that the two devices do the same work does not put them on the same level.

Main definitions

• Sentence: a property of a topic situation, asserted through a polarity operator (Sentence.polarityOp) and an assertion operator that Verum focus marks (Sentence.verumFocus).
• Switch, IsContrast, IsCorrection: a negative claim followed by a positive one, about a different or the same topic situation.

Main results

• Switch.disjoint_iff, IsCorrection.disjoint, exists_isContrast_not_disjoint: corrected claims exclude each other and contrasted ones need not.
• denotation_verumFocus, denotation_affirmation: neither device changes truth conditions.
• pol_of_polarityOp_eq_some, exists_verumFocus_negative: wel makes its sentence positive, and Verum focus occurs in a negated sentence.

Implementation notes

The polarity operator is a single slot of the sentence holding its overt value, if any, with unmarked affirmation as the default, so a sentence with the affirmative particle is positive by construction and Het kind heeft wel niet gehuild is not a Sentence. The production results are not formalized. Dutch speakers used wel in most utterances of both contexts, fewer in correction, an effect the paper leaves unexplained, and Verum focus never in contrast and rarely in correction; German speakers used Verum focus in more than 70% of the utterances of both contexts and never a sentence-internal particle. In correction only, some German speakers produced the polarity particle doch, German.PolarityParticle.doch, as a separate utterance before a Verum focus utterance; the paper codes the combination as another realization, not an affirmative particle, since doch never carried the correction by itself. Wel was mostly accented, as a downstepped fall in contrast and as a fall in correction, and the pitch range of German Verum focus was larger in correction than in contrast; the paper attributes the greater prominence of correction either to the strength of undoing a denial, as Hogeweg has it, or to the absence of a contrastive topic accent before the comment. The examples are the rows of Data.Examples.TurcoBraunDimroth2014.

References

• [TBD14]
• [Umb04]
• [Kle08]
• [Hoh92]
• [Sud12a]
• [Blu12]
• [Hog09]
• [Hog09]
• [DABV10]

The polarity operator and the assertion operator

structure TurcoBraunDimroth2014.Sentence (S : Type u_1) (W : Type u_2) : Type (max u_1 u_2)

A sentence predicates a descriptive property, given per topic situation as the set of worlds where it holds there, of a topic situation, through a polarity operator and, above it, the assertion operator carried by the finite verb, which Verum focus accents.

• property : S → Set W
• situation : S
• polarityOp : Option Polarity

  The overt value of the polarity operator: negation, or an affirmative particle such as Dutch wel; none when affirmation is unmarked.

• verumFocus : Focus.Mark

  The mark on the assertion operator, F-marked under Verum focus.

def TurcoBraunDimroth2014.Sentence.pol {S : Type u_1} {W : Type u_2} (s : Sentence S W) : Polarity

The polarity of a sentence, the value of its polarity operator, positive by default.

Equations

• s.pol = s.polarityOp.getD Polarity.positive

def TurcoBraunDimroth2014.Sentence.denotation {S : Type u_1} {W : Type u_2} (s : Sentence S W) : Set W

The proposition a sentence asserts.

Equations

• s.denotation = s.pol • s.property s.situation

theorem TurcoBraunDimroth2014.Sentence.denotation_verumFocus {S : Type u_1} {W : Type u_2} (s : Sentence S W) (m : Focus.Mark) : { property := s.property, situation := s.situation, polarityOp := s.polarityOp, verumFocus := m }.denotation = s.denotation

Accenting the assertion operator leaves the truth conditions unchanged.

theorem TurcoBraunDimroth2014.Sentence.denotation_affirmation {S : Type u_1} {W : Type u_2} (s : Sentence S W) : { property := s.property, situation := s.situation, polarityOp := some Polarity.positive, verumFocus := s.verumFocus }.denotation = { property := s.property, situation := s.situation, polarityOp := none, verumFocus := s.verumFocus }.denotation

An overt affirmative particle leaves the truth conditions of the unmarked affirmative sentence unchanged: wel and Verum focus are functionally equivalent on a positive sentence.

theorem TurcoBraunDimroth2014.Sentence.pol_of_polarityOp_eq_some {S : Type u_1} {W : Type u_2} {s : Sentence S W} {p : Polarity} (h : s.polarityOp = some p) : s.pol = p

An overt value of the polarity operator is the polarity of the sentence: a sentence with the affirmative particle is positive, so the particle cannot occur in a negated sentence.

theorem TurcoBraunDimroth2014.Sentence.exists_verumFocus_negative {S : Type u_1} {W : Type u_2} [Nonempty S] : ∃ (s : Sentence S W), s.verumFocus = Focus.Mark.focused ∧ s.pol = Polarity.negative

Verum focus can occur in a negated sentence, Das Kind HAT nicht geweint.

Polarity contrast and polarity correction

def TurcoBraunDimroth2014.Switch {S : Type u_1} {W : Type u_2} (a b : Sentence S W) : Prop

A polarity switch from a to b is a negative claim followed by a positive claim of the same descriptive property.

Equations

• TurcoBraunDimroth2014.Switch a b = (a.property = b.property ∧ a.pol = Polarity.negative ∧ b.pol = Polarity.positive)

def TurcoBraunDimroth2014.IsContrast {S : Type u_1} {W : Type u_2} (a b : Sentence S W) : Prop

A polarity contrast is a switch between claims about different topic situations.

Equations

• TurcoBraunDimroth2014.IsContrast a b = (TurcoBraunDimroth2014.Switch a b ∧ a.situation ≠ b.situation)

def TurcoBraunDimroth2014.IsCorrection {S : Type u_1} {W : Type u_2} (a b : Sentence S W) : Prop

A polarity correction is a switch between claims about the same topic situation.

Equations

• TurcoBraunDimroth2014.IsCorrection a b = (TurcoBraunDimroth2014.Switch a b ∧ a.situation = b.situation)

theorem TurcoBraunDimroth2014.Switch.disjoint_iff {S : Type u_1} {W : Type u_2} {a b : Sentence S W} (h : Switch a b) : Disjoint a.denotation b.denotation ↔ b.property b.situation ⊆ a.property a.situation

The claims of a switch exclude each other exactly when the property's holding of the second topic situation entails its holding of the first.

theorem TurcoBraunDimroth2014.IsCorrection.disjoint {S : Type u_1} {W : Type u_2} {a b : Sentence S W} (h : IsCorrection a b) : Disjoint a.denotation b.denotation

The claims of a correction exclude each other.

theorem TurcoBraunDimroth2014.exists_isContrast_not_disjoint {S : Type u_1} {W : Type u_2} [Nonempty W] {s₁ s₂ : S} (h : s₁ ≠ s₂) : ∃ (a : Sentence S W) (b : Sentence S W), IsContrast a b ∧ ¬Disjoint a.denotation b.denotation

The claims of a contrast need not exclude each other: any two topic situations carry a contrast whose claims are jointly true.