Poesio, Stevenson, Di Eugenio and Hitzeman (2004): Centering: A Parametric Theory and Its Instantiations #
This file formalizes the parametric reading of centering theory in [PSDEH04]. The claims of [GJW95], Constraint 1 on the uniqueness of the backward-looking center, Rule 1 on its pronominalization, and Rule 2 on the preference among transitions, can only be evaluated once the notions they quantify over are fixed, and the literature has fixed them in several ways: what an utterance is, which utterance counts as the previous one, when an entity is realized, which noun phrases introduce forward-looking centers, how the centers are ranked, and which pronouns Rule 1 governs. Each setting is an instantiation of the theory, and the paper's corpus study finds that different instantiations make different claims true.
The instantiations are the substrate's parameters: the realization relation is the Membership
instance, the ranking is the LinearOrder on roles, the CF filter is cfFilter, the utterance
unit is merge, and the previous utterance is the argument of cb. The paper's illustrations
of each parameter are worked as such: the associative reference of (5) is a Bridged
realization (ex5), the second-person pronoun of (7) a filtered forward-looking center (ex7),
the egg vases of (9) recovered either by sentence units or by indirect realization (ex9), the
tie of (10) two backward-looking centers under grammatical-function ranking and one under its
linear disambiguation (ex10), and the adjunct clauses of (14) and (16) the two definitions of
the previous utterance pulling in opposite directions (ex14, ex16). Constraint 1 is
unpacked into CB uniqueness and entity continuity (strong_iff), uniqueness holds under any
ranking that separates the previous utterance's realizations (cbAll_length_le_one), the three
forms of Rule 1 are ordered (CbPronominalized.rule1Original), and the four-way transition
classification of [BFP87] refines the three-way one with its
preference order (bfp_toTransition, toTransition_mono).
Implementation notes #
The corpus statistics of Tables 1 to 15, the statistical tests, and the trade-off they reveal between Rule 1 on the one hand and Constraint 1 and Rule 2 on the other are not formalized; the examples carry the mechanisms the statistics measure. Utterance identification, segmentation, and the Walker heuristics are corpus-operational choices and are represented only by the way the examples are cut into utterances.
References #
Constraint 1 unpacked (§5.3.2, §5.3.4) #
The backward-looking centers of cur after prev under a partial ranking: the entities of
the highest-ranked realizations in prev that cur realizes, each once. Under a ranking that
separates the realizations there is at most one.
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- One or more equations did not get rendered due to their size.
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CB uniqueness: at most one backward-looking center, the weak form of Constraint 1.
Equations
- PoesioEtAl2004.CBUniqueness prev cur = ((PoesioEtAl2004.cbAll prev cur).length ≤ 1)
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Entity continuity: the utterance realizes some forward-looking center of the previous one.
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- PoesioEtAl2004.EntityContinuity prev cur = (1 ≤ (PoesioEtAl2004.cbAll prev cur).length)
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The strong form of Constraint 1: exactly one backward-looking center.
Equations
- PoesioEtAl2004.Constraint1Strong prev cur = ((PoesioEtAl2004.cbAll prev cur).length = 1)
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Equations
- PoesioEtAl2004.instDecidableCBUniqueness prev cur = { decide := (PoesioEtAl2004.cbAll prev cur).length.ble 1, reflects_decide := ⋯ }
Equations
- PoesioEtAl2004.instDecidableEntityContinuity prev cur = { decide := Nat.ble 1 (PoesioEtAl2004.cbAll prev cur).length, reflects_decide := ⋯ }
Equations
- PoesioEtAl2004.instDecidableConstraint1Strong prev cur = { decide := (PoesioEtAl2004.cbAll prev cur).length.beq 1, reflects_decide := ⋯ }
Strong Constraint 1 is CB uniqueness together with entity continuity.
CB uniqueness holds under any ranking that separates the realizations of the previous utterance, which a partial ranking such as grammatical function becomes once a disambiguating factor such as linear order is added.
Rule 1 in its three forms (§2.3.2) #
Rule 1 in its original form: a backward-looking center kept from the previous utterance is
pronominalized. The form of [GJW95] is PronominalizationConstraint, and
the unconditional form is CbPronominalized.
Equations
- PoesioEtAl2004.Rule1Original prev cur prevCb = ((∃ (c : E), Discourse.Centering.cb prev cur = some c ∧ prevCb = some c) → Discourse.Centering.CbPronominalized prev cur)
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The unconditional form implies the original one, as it implies the 1995 form.
Transitions (§2.2.3, §2.3.3) #
The four transitions of [BFP87]: the center is kept, or the previous utterance had none, and is the preferred center (continue) or not (retain); or the center changes and is the preferred center (smooth shift) or not (rough shift).
- continue : BFPTransition
- retain : BFPTransition
- smoothShift : BFPTransition
- roughShift : BFPTransition
Instances For
Equations
- PoesioEtAl2004.instDecidableEqBFPTransition x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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Rule 2 on single transitions: continue over retain over smooth shift over rough shift.
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The three-way transition each four-way one refines.
Equations
- PoesioEtAl2004.BFPTransition.continue.toTransition = Discourse.Centering.Transition.continuation
- PoesioEtAl2004.BFPTransition.retain.toTransition = Discourse.Centering.Transition.retaining
- PoesioEtAl2004.BFPTransition.smoothShift.toTransition = Discourse.Centering.Transition.shifting
- PoesioEtAl2004.BFPTransition.roughShift.toTransition = Discourse.Centering.Transition.shifting
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The four-way preference order refines the three-way one.
The four-way classification of an utterance after an utterance with center prevCb, none
for an utterance with no center.
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An utterance is unclassified exactly when it has no backward-looking center: the null and zeroing transitions of a segment.
The four-way classification refines the three-way one.
The parameters (§2.4, §3.4) #
The CF filter: only the entities satisfying p introduce forward-looking centers, as when
first- and second-person pronouns or predicative noun phrases are excluded.
Equations
- PoesioEtAl2004.cfFilter p u = { realizations := List.filter (fun (r : Discourse.Centering.Realization E R) => p r.entity) u.realizations }
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The utterance unit: clauses merged into one sentence-sized utterance.
Equations
- PoesioEtAl2004.merge us = { realizations := (List.map (fun (x : Discourse.Centering.Utterance E R) => x.realizations) us).flatten }
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An utterance with the anchors of its associative references, each mention paired with the entity it indirectly realizes.
- utt : Discourse.Centering.Utterance E R
- anchors : List (E × E)
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Indirect realization: an entity is realized when mentioned or when anchored by a mention.
Equations
- PoesioEtAl2004.instMembershipBridged = { mem := fun (b : PoesioEtAl2004.Bridged E R) (e : E) => e ∈ b.utt ∨ ∃ a ∈ b.anchors, a.2 = e ∧ a.1 ∈ b.utt }
Equations
- PoesioEtAl2004.instDecidableMemBridgedOfDecidableEq b e = { decide := decide (e ∈ b.utt) || decide (∃ a ∈ b.anchors, a.2 = e ∧ a.1 ∈ b.utt), reflects_decide := ⋯ }
Grammatical function with linear-order disambiguation: the role together with the surface position, an earlier mention outranking a later one of the same function.
Equations
- PoesioEtAl2004.GFLin n = Lex (Discourse.Centering.GrammaticalRole × (Fin n)ᵒᵈ)
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A realization by a name in role r at surface position i.
Equations
- PoesioEtAl2004.GFLin.name e r i = { entity := e, role := toLex (r, OrderDual.toDual i), isPronoun := false }
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The three tiers of information status of [SH99], the ranking of §4.4.3.
- hearerOld : InfoStatus
- mediated : InfoStatus
- hearerNew : InfoStatus
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Equations
- PoesioEtAl2004.instDecidableEqInfoStatus x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Equations
- PoesioEtAl2004.instReprInfoStatus = { reprPrec := PoesioEtAl2004.instReprInfoStatus.repr }
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- One or more equations did not get rendered due to their size.
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Hearer-old entities outrank mediated ones, which outrank hearer-new ones.
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The illustrations #
Equations
- PoesioEtAl2004.instDecidableEqEnt5 x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Equations
- PoesioEtAl2004.instReprEnt5 = { reprPrec := PoesioEtAl2004.instReprEnt5.repr }
Equations
- PoesioEtAl2004.instReprEnt5.repr PoesioEtAl2004.Ent5.john prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "PoesioEtAl2004.Ent5.john")).group prec✝
- PoesioEtAl2004.instReprEnt5.repr PoesioEtAl2004.Ent5.house prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "PoesioEtAl2004.Ent5.house")).group prec✝
- PoesioEtAl2004.instReprEnt5.repr PoesioEtAl2004.Ent5.door prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "PoesioEtAl2004.Ent5.door")).group prec✝
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(5): John walked toward the house. The door was open. Under direct realization the second utterance has no backward-looking center; with the door anchored to the house it has one.
Equations
- PoesioEtAl2004.instDecidableEqEnt7 x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Equations
- PoesioEtAl2004.instReprEnt7 = { reprPrec := PoesioEtAl2004.instReprEnt7.repr }
Equations
- One or more equations did not get rendered due to their size.
- PoesioEtAl2004.instReprEnt7.repr PoesioEtAl2004.Ent7.you prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "PoesioEtAl2004.Ent7.you")).group prec✝
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(7): with the second-person pronoun introducing a forward-looking center every utterance has one; without it the if-clause has none, and the third utterance has one only when the if-clause is treated as embedded and the first utterance is its previous utterance.
Equations
- PoesioEtAl2004.instDecidableEqEnt9 x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Equations
- PoesioEtAl2004.instReprEnt9 = { reprPrec := PoesioEtAl2004.instReprEnt9.repr }
Equations
- One or more equations did not get rendered due to their size.
- PoesioEtAl2004.instReprEnt9.repr PoesioEtAl2004.Ent9.vases prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "PoesioEtAl2004.Ent9.vases")).group prec✝
- PoesioEtAl2004.instReprEnt9.repr PoesioEtAl2004.Ent9.bases prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "PoesioEtAl2004.Ent9.bases")).group prec✝
- PoesioEtAl2004.instReprEnt9.repr PoesioEtAl2004.Ent9.bodies prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "PoesioEtAl2004.Ent9.bodies")).group prec✝
- PoesioEtAl2004.instReprEnt9.repr PoesioEtAl2004.Ent9.straw prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "PoesioEtAl2004.Ent9.straw")).group prec✝
- PoesioEtAl2004.instReprEnt9.repr PoesioEtAl2004.Ent9.eggs prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "PoesioEtAl2004.Ent9.eggs")).group prec✝
- PoesioEtAl2004.instReprEnt9.repr PoesioEtAl2004.Ent9.nests prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "PoesioEtAl2004.Ent9.nests")).group prec✝
- PoesioEtAl2004.instReprEnt9.repr PoesioEtAl2004.Ent9.finial prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "PoesioEtAl2004.Ent9.finial")).group prec✝
- PoesioEtAl2004.instReprEnt9.repr PoesioEtAl2004.Ent9.lid prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "PoesioEtAl2004.Ent9.lid")).group prec✝
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(9): with finite clauses as utterances none of the four clauses after the first has a backward-looking center; with sentences as utterances the second sentence continues the egg vases, as does the second clause once its bases and bodies are anchored to the vases.
Equations
- PoesioEtAl2004.instDecidableEqEnt10 x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- PoesioEtAl2004.instReprEnt10 = { reprPrec := PoesioEtAl2004.instReprEnt10.repr }
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- One or more equations did not get rendered due to their size.
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(10): the corner cupboard and Branicki tie under grammatical-function ranking, so both are backward-looking centers of the next utterance, against CB uniqueness; with linear-order disambiguation the earlier mention, the cupboard, is the unique one.
Equations
- PoesioEtAl2004.instDecidableEqEnt14 x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Equations
- One or more equations did not get rendered due to their size.
- PoesioEtAl2004.instReprEnt14.repr PoesioEtAl2004.Ent14.john prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "PoesioEtAl2004.Ent14.john")).group prec✝
- PoesioEtAl2004.instReprEnt14.repr PoesioEtAl2004.Ent14.bill prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "PoesioEtAl2004.Ent14.bill")).group prec✝
- PoesioEtAl2004.instReprEnt14.repr PoesioEtAl2004.Ent14.door prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "PoesioEtAl2004.Ent14.door")).group prec✝
- PoesioEtAl2004.instReprEnt14.repr PoesioEtAl2004.Ent14.you prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "PoesioEtAl2004.Ent14.you")).group prec✝
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Equations
- PoesioEtAl2004.instReprEnt14 = { reprPrec := PoesioEtAl2004.instReprEnt14.repr }
(14) and (16): the two definitions of the previous utterance of a clause after an adjunct clause pull in opposite directions. In (14) the main clause supplies the center John that the when-clause lacks, in (16) the adjunct clause supplies the center the patch that the main clause lacks.
Equations
- PoesioEtAl2004.instDecidableEqEnt23 x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- One or more equations did not get rendered due to their size.
- PoesioEtAl2004.instReprEnt23.repr PoesioEtAl2004.Ent23.info prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "PoesioEtAl2004.Ent23.info")).group prec✝
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Equations
- PoesioEtAl2004.instReprEnt23 = { reprPrec := PoesioEtAl2004.instReprEnt23.repr }
(23): with the second-person pronoun excluded, no utterance realizes a forward-looking center of the previous one, so entity coherence is absent throughout a coherent text.