[GJW95]: Centering Theory

[Kam86] [GGG93] [Sid83]

Centering: A Framework for Modeling the Local Coherence of Discourse. Computational Linguistics 21(2): 203–225.

Each utterance has a set of forward-looking centers Cf (ranked by grammatical role: subject > object > other) and at most one backward-looking center Cb (the highest-ranked Cf element of the previous utterance that is also realized in the current one). Three transition types — continuation, retaining, shifting — classify adjacent-utterance pairs by whether the Cb is preserved and whether that Cb is the most-highly-ranked Cf.

Two normative rules govern coherent discourse: Rule 1 (pronominalization constraint — if any Cf element is pronominalized in the next utterance, the Cb must be); Rule 2 (transition preference — sequences of continuations preferred over sequences of retentions, which are preferred over sequences of shifts; the pair-of-utterances restriction is [BFP87]'s variant, per the paper's own footnote).

The empirical anchors are the paper's own discourses: the (1)/(2) coherence contrast, the (15)/(16) Rule-1 violation and repair, the (7)-(10) hamster variants, the (20) transition showcase, and the §9 comparison with [Sid83] on example (34). Examples use String entities and the substrate's Utterance String GrammaticalRole.

@[reducible, inline]

abbrev GroszJoshiWeinstein1995.Utt : Type

Utterance abbreviation specialized to the GJW use case (String entities, grammatical-role-ranked Cf).

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• GroszJoshiWeinstein1995.Utt = Discourse.Centering.Utterance String Discourse.Centering.GrammaticalRole

Discourses (1)-(2): the coherence contrast (paper §2)

def GroszJoshiWeinstein1995.D1.a : Utt

(1a) John went to his favorite music store to buy a piano.

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def GroszJoshiWeinstein1995.D1.b : Utt

(1b) He had frequented the store for many years.

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def GroszJoshiWeinstein1995.D1.c : Utt

(1c) He was excited that he could finally buy a piano.

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def GroszJoshiWeinstein1995.D1.d : Utt

(1d) He arrived just as the store was closing for the day.

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def GroszJoshiWeinstein1995.D2.a : Utt

(2a) John went to his favorite music store to buy a piano.

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def GroszJoshiWeinstein1995.D2.b : Utt

(2b) It was a store John had frequented for many years.

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def GroszJoshiWeinstein1995.D2.c : Utt

(2c) He was excited that he could finally buy a piano.

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def GroszJoshiWeinstein1995.D2.d : Utt

(2d) It was closing just as John arrived.

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Transition predictions

The Cb and transition sequences of both discourses follow from the
substrate's discourse-level scan. 

theorem GroszJoshiWeinstein1995.d1_cbs : Discourse.Centering.cbs [D1.a, D1.b, D1.c, D1.d] = [some "John", some "John", some "John"]

Discourse 1: John is the Cb throughout.

theorem GroszJoshiWeinstein1995.d1_transitions : Discourse.Centering.transitions [D1.a, D1.b, D1.c, D1.d] = [Discourse.Centering.Transition.continuation, Discourse.Centering.Transition.continuation, Discourse.Centering.Transition.continuation]

Discourse 1 is all continuations.

theorem GroszJoshiWeinstein1995.d2_cbs : Discourse.Centering.cbs [D2.a, D2.b, D2.c, D2.d] = [some "John", some "John", some "John"]

Discourse 2: the Cb is also John throughout. At (a→b), both John and the store are realized in D2.b and John outranks the store in Cf(D2.a) (subject > object).

theorem GroszJoshiWeinstein1995.d2_transitions : Discourse.Centering.transitions [D2.a, D2.b, D2.c, D2.d] = [Discourse.Centering.Transition.retaining, Discourse.Centering.Transition.continuation, Discourse.Centering.Transition.retaining]

Discourse 2 is retain, continue, retain: at (a→b) and (c→d) the store is Cp while John stays Cb. (The paper's prose describes the flips informally as changes of "aboutness"; under the formal definitions the Cb remains John throughout, and the incoherence surfaces as retains rather than shifts.)

theorem GroszJoshiWeinstein1995.discourse1_more_coherent_than_discourse2 : Discourse.Centering.coherenceScore [D1.a, D1.b, D1.c, D1.d] > Discourse.Centering.coherenceScore [D2.a, D2.b, D2.c, D2.d]

The coherence contrast (paper §2): Discourse 1's all-continuation sequence outscores Discourse 2's mixed sequence under the sum-of-ranks measure (the sequence form of Rule 2).

Discourses (15)-(16): Rule 1 violation and shift repair (paper §7)

def GroszJoshiWeinstein1995.D15.a : Utt

(15a) He has been acting quite odd. (Cb = John, presumed in segment.)

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• GroszJoshiWeinstein1995.D15.a = { realizations := [{ entity := "John", role := Discourse.Centering.GrammaticalRole.subject, isPronoun := true }] }

def GroszJoshiWeinstein1995.D15.b : Utt

(15b) He called up Mike yesterday. (Cb = John, "He" = John.)

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def GroszJoshiWeinstein1995.D15.c : Utt

(15c) John wanted to meet him urgently. (Cb = John, "him" = Mike.) The Cf member Mike is pronominalized but the Cb John is not — a Rule 1 violation.

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theorem GroszJoshiWeinstein1995.d15_b_to_c_cb : Discourse.Centering.cb D15.b D15.c = some "John"

theorem GroszJoshiWeinstein1995.discourse15_violates_rule1 : ¬Discourse.Centering.PronominalizationConstraint D15.b D15.c

Rule 1 violation: in (15c), Mike is pronominalized but the Cb John is realized as a proper name. The paper's diagnosis.

theorem GroszJoshiWeinstein1995.d15_a_to_b_satisfies_rule1 : Discourse.Centering.PronominalizationConstraint D15.a D15.b

The (a→b) pair of the same discourse satisfies Rule 1 (the only Cf element from (a) is John, who is pronominalized in (b) — the Cb is also pronominalized). The violation is local to the (b→c) step.

Discourse (16) is the paper's minimal repair of (15): the same John–Mike sequence with an intervening utterance that shifts the center to Mike, "making the full sequence coherent" — Rule 1 "operates independently of the type of centering transition." (The paper's footnote tempers the contrast: per [GGG93], (16d) without the intervening (c) is not as bad as (15c).)

def GroszJoshiWeinstein1995.D16.a : Utt

(16a) John has been acting quite odd.

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• GroszJoshiWeinstein1995.D16.a = { realizations := [{ entity := "John", role := Discourse.Centering.GrammaticalRole.subject, isPronoun := false }] }

def GroszJoshiWeinstein1995.D16.b : Utt

(16b) He called up Mike yesterday. ("He" = John.)

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def GroszJoshiWeinstein1995.D16.c : Utt

(16c) Mike was studying for his driver's test. Mike is the only Cf(16b) element realized here, so the center shifts to Mike.

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• GroszJoshiWeinstein1995.D16.c = { realizations := [{ entity := "Mike", role := Discourse.Centering.GrammaticalRole.subject, isPronoun := false }] }

def GroszJoshiWeinstein1995.D16.d : Utt

(16d) He was annoyed by John's call. ("He" = Mike.)

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theorem GroszJoshiWeinstein1995.d16_cbs : Discourse.Centering.cbs [D16.a, D16.b, D16.c, D16.d] = [some "John", some "Mike", some "Mike"]

The intervening (16c) shifts the center from John to Mike, who then stays Cb through (16d).

theorem GroszJoshiWeinstein1995.d16_transitions : Discourse.Centering.transitions [D16.a, D16.b, D16.c, D16.d] = [Discourse.Centering.Transition.continuation, Discourse.Centering.Transition.shifting, Discourse.Centering.Transition.continuation]

theorem GroszJoshiWeinstein1995.d16_c_to_d_satisfies_rule1 : Discourse.Centering.PronominalizationConstraint D16.c D16.d

After the shift, (16d)'s pronoun realizes the new Cb Mike — Rule 1 is satisfied exactly where (15c) violated it.

Discourses (7)-(10): Cf ranking and Rule 1 (paper §5)

[GJW95] §5 examples (7)-(10). All four variants share utterances (a) and (b); they differ only in (c)'s realization choices. Variants (7) and (8) satisfy Rule 1; variants (9) and (10) violate it. The paper notes (10) is "completely unacceptable" and (9) is also degraded — both more so than (7) and (8) — because of the Rule 1 violations.

Shared:
> a. Susan gave Betsy a pet hamster.
> b. She reminded her that such hamsters were quite shy. 

def GroszJoshiWeinstein1995.D7_10.a : Utt

(a) Susan gave Betsy a pet hamster. Cf = [Susan, Betsy, hamster].

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def GroszJoshiWeinstein1995.D7_10.b : Utt

(b) She reminded her ... "She" = Susan (subj), "her" = Betsy (obj).

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def GroszJoshiWeinstein1995.D7_10.c7 : Utt

(7c) She asked Betsy whether she liked the gift. — "She" = Susan, Betsy as proper name (object). Cb = Susan, Cp = Susan ⇒ CONTINUE. Susan is pronominalized; Rule 1 satisfied.

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def GroszJoshiWeinstein1995.D7_10.c8 : Utt

(8c) Betsy told her that she really liked the gift. — Betsy as proper name (subject), "her" = Susan. Cb = Susan (highest in Cf(b) realized in c), but Cp = Betsy ⇒ RETAIN. Susan as Cb pronominalized via "her"; Rule 1 satisfied.

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def GroszJoshiWeinstein1995.D7_10.c9 : Utt

(9c) Susan asked her whether she liked the gift. — Susan as proper name (subject), "her" = Betsy. Cb = Susan, Cp = Susan ⇒ would be CONTINUE, but Betsy is pronominalized while Cb (Susan) is a proper name ⇒ Rule 1 VIOLATION.

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def GroszJoshiWeinstein1995.D7_10.c10 : Utt

(10c) She told Susan that she really liked the gift. — "She" = Betsy (subj), Susan as proper name (obj). Cb = Susan (highest in Cf(b) realized in c). Cp = Betsy ⇒ RETAIN. Betsy is pronominalized while Cb (Susan) is a proper name ⇒ Rule 1 VIOLATION.

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theorem GroszJoshiWeinstein1995.d7_to_10_share_cb : Discourse.Centering.cb D7_10.b D7_10.c7 = some "Susan" ∧ Discourse.Centering.cb D7_10.b D7_10.c8 = some "Susan" ∧ Discourse.Centering.cb D7_10.b D7_10.c9 = some "Susan" ∧ Discourse.Centering.cb D7_10.b D7_10.c10 = some "Susan"

All four (c) variants share Cb = Susan: Susan is the highest-ranked Cf(b) element realized in each (c). The choice of variant does not change which entity is the Cb — only how that Cb is realized.

theorem GroszJoshiWeinstein1995.d7_satisfies_rule1 : Discourse.Centering.PronominalizationConstraint D7_10.b D7_10.c7

Variant 7 satisfies Rule 1 (Susan as Cb pronominalized).

theorem GroszJoshiWeinstein1995.d8_satisfies_rule1 : Discourse.Centering.PronominalizationConstraint D7_10.b D7_10.c8

Variant 8 satisfies Rule 1 (Susan as Cb pronominalized via "her").

theorem GroszJoshiWeinstein1995.d9_violates_rule1 : ¬Discourse.Centering.PronominalizationConstraint D7_10.b D7_10.c9

Variant 9 violates Rule 1: Betsy is pronominalized but Cb (Susan) is realized as a proper name.

theorem GroszJoshiWeinstein1995.d10_violates_rule1 : ¬Discourse.Centering.PronominalizationConstraint D7_10.b D7_10.c10

Variant 10 violates Rule 1: Betsy is pronominalized but Cb (Susan) is realized as a proper name. The paper calls this case "completely unacceptable"; the Rule-1 split (7, 8 satisfy; 9, 10 violate) tracks the paper's acceptability ordering.

Discourse (20): CONTINUE / RETAIN / SHIFT (paper §7)

def GroszJoshiWeinstein1995.D20.a : Utt

(20a) John has been having a lot of trouble arranging his vacation.

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• GroszJoshiWeinstein1995.D20.a = { realizations := [{ entity := "John", role := Discourse.Centering.GrammaticalRole.subject, isPronoun := false }] }

def GroszJoshiWeinstein1995.D20.b : Utt

(20b) He cannot find anyone to take over his responsibilities.

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• GroszJoshiWeinstein1995.D20.b = { realizations := [{ entity := "John", role := Discourse.Centering.GrammaticalRole.subject, isPronoun := true }] }

def GroszJoshiWeinstein1995.D20.c : Utt

(20c) He called up Mike yesterday to work out a plan.

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def GroszJoshiWeinstein1995.D20.d : Utt

(20d) Mike has annoyed him a lot recently.

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def GroszJoshiWeinstein1995.D20.e : Utt

(20e) He called John at 5 AM on Friday last week.

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theorem GroszJoshiWeinstein1995.discourse20_transitions : Discourse.Centering.transitions [D20.a, D20.b, D20.c, D20.d, D20.e] = [Discourse.Centering.Transition.continuation, Discourse.Centering.Transition.continuation, Discourse.Centering.Transition.retaining, Discourse.Centering.Transition.shifting]

The paper-annotated transition labels b→c, c→d, d→e — CONTINUE, RETAIN, SHIFT — preceded by an unannotated a→b continuation.

theorem GroszJoshiWeinstein1995.discourse20_rule1_a_b : Discourse.Centering.PronominalizationConstraint D20.a D20.b

Rule 1 holds throughout Discourse 20 (the paper's claim).

theorem GroszJoshiWeinstein1995.discourse20_rule1_b_c : Discourse.Centering.PronominalizationConstraint D20.b D20.c

theorem GroszJoshiWeinstein1995.discourse20_rule1_c_d : Discourse.Centering.PronominalizationConstraint D20.c D20.d

theorem GroszJoshiWeinstein1995.discourse20_rule1_d_e : Discourse.Centering.PronominalizationConstraint D20.d D20.e

Comparison with [Sid83]: example (34) (paper §9)

This section mechanizes the Sidner-comparison the paper makes in its own §9 (p. 222) — the example is Sidner's own, cited from her 1979 dissertation — on the discourse:

(34) a. I haven't seen Jeff for several days.
     b. Carl thinks he's studying for his exams,
     c. but I think he went to the Cape with Linda.

GJW summarize Sidner's prediction: "On Sidner's account, Carl is
the actor focus after (34b) and Jeff is the discourse focus.
Because the actor focus is preferred as the referent of pronominal
expressions, Carl is the leading candidate for the entity referred
to by *he* in (34c)." Then: "On our account, Jeff is the C_b at
(34b) and there is no problem."

Both theories must commit to a referent for *he* in (34c). The
formalization picks the one that is **coherence-preferred** under
each theory:

- Sidner: agent-position pronoun → actor focus (Carl). See
  `Sidner1983.resolvePronoun` and the focus-state computation in
  `Studies/Sidner1983.lean`.
- GJW: pick the resolution that yields the higher-ranked Rule-2
  transition. With "he" = Jeff the Cb is preserved (Jeff → Jeff)
  but the matrix subject "I" becomes the new Cp, so this is a
  RETAIN. With "he" = Carl, the Cb shifts (Jeff → Carl), so this
  is a SHIFT. RETAIN outranks SHIFT under Rule 2, so GJW predict
  Jeff. 

def GroszJoshiWeinstein1995.D34.a : Utt

(34a) I haven't seen Jeff for several days.

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def GroszJoshiWeinstein1995.D34.b : Utt

(34b) Carl thinks he's studying for his exams. The matrix subject is Carl (full name); the embedded subject "he" co-specifies Jeff (continuing from 34a).

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def GroszJoshiWeinstein1995.D34.c_he_is_jeff : Utt

(34c) under the resolution "he" = Jeff: continues the Cb.

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def GroszJoshiWeinstein1995.D34.c_he_is_carl : Utt

(34c) under the resolution "he" = Carl: shifts the Cb.

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theorem GroszJoshiWeinstein1995.d34_cb_b : Discourse.Centering.cb D34.a D34.b = some "Jeff"

Cb of (34b) given (34a) is Jeff — paper's own claim ("Jeff is the C_b at (34b)", §9 p. 222).

theorem GroszJoshiWeinstein1995.d34_cb_c_jeff : Discourse.Centering.cb D34.b D34.c_he_is_jeff = some "Jeff"

Under the Jeff-resolution of (34c), the Cb continues as Jeff.

theorem GroszJoshiWeinstein1995.d34_cb_c_carl : Discourse.Centering.cb D34.b D34.c_he_is_carl = some "Carl"

Under the Carl-resolution of (34c), the Cb shifts to Carl.

theorem GroszJoshiWeinstein1995.d34_jeff_retaining : Discourse.Centering.classifyTransitionExtended D34.b D34.c_he_is_jeff (Discourse.Centering.cb D34.a D34.b) = Discourse.Centering.Transition.retaining

Jeff-resolution: Cb stable (Jeff → Jeff), but the matrix "I" becomes the new Cp, so this is a RETAIN, not a CONTINUE.

theorem GroszJoshiWeinstein1995.d34_carl_shift : Discourse.Centering.classifyTransitionExtended D34.b D34.c_he_is_carl (Discourse.Centering.cb D34.a D34.b) = Discourse.Centering.Transition.shifting

Carl-resolution: Cb shifts from Jeff to Carl.

def GroszJoshiWeinstein1995.gjwPredictedHe : Option String

GJW prediction for (34c): by Rule 2 (RETAIN outranks SHIFT here), the Jeff-resolution is preferred. Returns Option String: none if the candidate Rule-2 ranks coincide and the framework cannot adjudicate; otherwise some "Jeff" or some "Carl".

Caveat about overclaim. GJW themselves do not commit to a unique referent in §9 p. 222 — they only say "Jeff is the C_b at (34b) and there is no problem." Rule 2 in their paper is a constraint over speaker production, not an interpreter resolution algorithm. This function operationalizes "GJW's prediction" as "the resolution Rule 2 would prefer if a speaker had to choose between the two transitions"; it is closer to the Brennan-Friedman-Pollard 1987 resolution algorithm than to GJW 1995 as published. The headline disagreement theorem is honest about this gap — see its docstring.

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theorem GroszJoshiWeinstein1995.gjw_prefers_jeff : gjwPredictedHe = some "Jeff"

theorem GroszJoshiWeinstein1995.sidner_gjw_disagree_on_d34c : Sidner1983.D34.sidnerPredictedHe ≠ gjwPredictedHe

The disagreement on what "he" in (34c) refers to.

Sidner's prediction (§5.2.6 step 3): agent-position pronoun → actor focus = Carl.

GJW's Rule-2 preference (with the caveat above that GJW themselves don't claim uniqueness): RETAIN > SHIFT under Rule 2 ⇒ Jeff.

Each side commits to a named prediction; the inequality follows by decide from the witnesses.