Documentation

Studies.CoonKeine2021

Coon and Keine 2021: feature gluttony #

Coon and Keine argue that hierarchy effects, the Person Case Constraint on clitic clusters, the person restriction on Icelandic dative-nominative agreement and the person and number restrictions on German assumed-identity copulas, come not from failed Agree but from too much of it. A probe is a hierarchy of segments, each of which agrees on its own with the closest accessible DP bearing it and copies that DP's whole geometry back, so when the lower of two DPs bears segments the higher lacks, distinct segments agree with distinct DPs and the probe is gluttonous, which happens in inverse configurations only. Gluttony is harmless in itself: a clitic-doubling probe crashes because every DP it agreed with must cliticize and binary Merge cannot move two heads at once, while an agreement probe crashes only if the values it carries demand different Vocabulary items, so syncretism or the absence of an item lets a gluttonous probe converge. Articulating the person probe further along the speaker and addressee leaves of the person geometry derives the Weak, Ultrastrong and Me-First constraints, datives that expose their person node alone turn the Weak pattern into the Strong one, and since a nonfinite clause has no probe and a PP, a strong pronoun or absolutive displacement leaves no second goal, the absence of the effects there follows without the caveats a Person Licensing Condition needs.

Implementation notes #

Goals are position-indexed so that two DPs with the same features stay distinct, and a segment's Agree is the relativized search of the probe substrate over that list, so the two-goal characterization of gluttony rests on the substrate's search. Person geometries are the branching geometry of the cyclic-Agree substrate and number the two-segment geometry of the paper; the model pairs a number probe with every person probe, one direction of the paper's probe-specification hierarchy. A K-encapsulated dative exposes its person node and no number: the paper leaves the dative's number open in a footnote and says a quirky DP externally bears at most a person feature, and the choice is what puts the nominative's number in the context the paper's diagrams caption. The crash of a gluttonous clitic-doubling probe is taken as the paper argues it, from its cliticization requirement, binary Merge and a Markovian derivation, rather than derived. A paradigm holds the forms the paper glosses, with German present bin added since the past-tense improvement the paper reports presupposes it, and is undefined in number contexts the paper does not gloss, so that an unglossed cell cannot converge by accident; the item a value demands is the score selection of the exponence substrate with the segment count as specificity, and a value demanding no item, the Kichean singular, competes with nothing. The person-case-constraint grammars of the substrate parametrize the descriptive table the probes derive; the Ultrastrong probe parts from that parametrization at 2 > 2 and the Me-First probe from the table itself at 1 > 1, a cell the paper does not remark on. The comparison with the Person Licensing Condition is the paper's own argument from probeless clauses, and the restricted condition keeps the escape through a Case-valuing head that the substrate formalization of the original condition has. Examples the paper records without an account, the Icelandic copulas, default agreement, participle agreement and the expletive, carry no configuration and enter no theorem.

TODO #

References #

Goals and their visible geometries #

A goal DP may sit in the K(ase) shell that encapsulates a dative, so that only its person node is visible from outside, as with Basque and Icelandic datives (§3.4.1).

  • person : Person

    The DP's person.

  • plural : Bool

    Whether the DP is plural.

  • encapsulated : Bool

    Whether a K shell hides everything but the person node.

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    def CoonKeine2021.instDecidableEqGoal.decEq (x✝ x✝¹ : Goal) :
    Decidable (x✝ = x✝¹)
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      def CoonKeine2021.instReprGoal.repr :
      Goal → ℕ → Std.Format
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        A φ-transparent goal.

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          A φ-transparent plural goal.

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            A K-encapsulated dative goal.

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              A goal exposes the person segments of its geometry under (11), or its person node alone.

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                Number geometry (12).

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                    The number segments a goal exposes; an encapsulated goal exposes none.

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                      A goal read as a nominal of [BR03] has its Case valued and its person licensed by its own head when it is an encapsulated dative, and neither when it is transparent.

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                        Segment-based Agree and gluttony (14)–(16) #

                        def CoonKeine2021.segmentProbe {σ : Type u_1} [DecidableEq σ] (geo : Goal → List σ) (s : σ) :

                        A probe segment is the relativized probe over position-indexed goals that sees the goals whose geometry bears it.

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                          def CoonKeine2021.segmentAgree {σ : Type u_1} [DecidableEq σ] (geo : Goal → List σ) (s : σ) (goals : List Goal) :
                          Option (Goal × ℕ)

                          Agree (14) for one probe segment finds the closest accessible goal whose geometry bears it.

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                            def CoonKeine2021.agreed {σ : Type u_1} [DecidableEq σ] (geo : Goal → List σ) (P : List σ) (goals : List Goal) :
                            List (Goal × ℕ)

                            The goals some segment of the probe has agreed with.

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                              def CoonKeine2021.Gluttonous {σ : Type u_1} [DecidableEq σ] (geo : Goal → List σ) (P : List σ) (goals : List Goal) :

                              Feature gluttony (16) is the probe's having agreed with more than one DP.

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                                instance CoonKeine2021.instDecidableGluttonous {σ : Type u_1} [DecidableEq σ] (geo : Goal → List σ) (P : List σ) (goals : List Goal) :
                                Decidable (Gluttonous geo P goals)
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                                def CoonKeine2021.values {σ : Type u_1} [DecidableEq σ] (geo : Goal → List σ) (P : List σ) (goals : List Goal) :
                                List (List σ)

                                The values the probe carries after Agree, one whole geometry per agreed goal ((16), (58)).

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                                  theorem CoonKeine2021.mem_agreed {σ : Type u_1} [DecidableEq σ] {geo : Goal → List σ} {P : List σ} {goals : List Goal} {t : Goal × ℕ} :
                                  t ∈ agreed geo P goals ↔ t ∈ goals.zipIdx ∧ ∃ s ∈ P, segmentAgree geo s goals = some t
                                  theorem CoonKeine2021.segmentAgree_pair {σ : Type u_1} [DecidableEq σ] {geo : Goal → List σ} {s : σ} {hi lo : Goal} :
                                  segmentAgree geo s [hi, lo] = if s ∈ geo hi then some (hi, 0) else if s ∈ geo lo then some (lo, 1) else none

                                  Agree over two goals finds the higher if it bears the segment, else the lower if it does.

                                  theorem CoonKeine2021.segmentAgree_pair_eq_higher_iff {σ : Type u_1} [DecidableEq σ] {geo : Goal → List σ} {s : σ} {hi lo : Goal} :
                                  segmentAgree geo s [hi, lo] = some (hi, 0) ↔ s ∈ geo hi
                                  theorem CoonKeine2021.segmentAgree_pair_eq_lower_iff {σ : Type u_1} [DecidableEq σ] {geo : Goal → List σ} {s : σ} {hi lo : Goal} :
                                  segmentAgree geo s [hi, lo] = some (lo, 1) ↔ s ∉ geo hi ∧ s ∈ geo lo
                                  theorem CoonKeine2021.gluttonous_pair_iff {σ : Type u_1} [DecidableEq σ] {geo : Goal → List σ} {P : List σ} {hi lo : Goal} :
                                  Gluttonous geo P [hi, lo] ↔ (∃ s ∈ P, s ∈ geo hi) ∧ ∃ s ∈ P, s ∉ geo hi ∧ s ∈ geo lo

                                  Gluttony over two goals is an inverse configuration, in which some segment finds the higher goal and some segment the higher goal lacks finds the lower.

                                  theorem CoonKeine2021.not_gluttonous_of_subset {σ : Type u_1} [DecidableEq σ] {geo : Goal → List σ} {P : List σ} {hi lo : Goal} (h : geo lo ⊆ geo hi) :
                                  ¬Gluttonous geo P [hi, lo]

                                  Gluttony arises only in inverse configurations, so when the lower goal bears no segment the higher lacks, no probe gluttons over them.

                                  theorem CoonKeine2021.not_gluttonous_of_length_le_one {σ : Type u_1} [DecidableEq σ] {geo : Goal → List σ} {P : List σ} {goals : List Goal} (h : goals.length ≤ 1) :
                                  ¬Gluttonous geo P goals

                                  A probe over at most one goal never gluttons, as in the repairs of §3.5 and with the multiply agreed-with DP of (86).

                                  theorem CoonKeine2021.not_gluttonous_singleton {σ : Type u_1} [DecidableEq σ] {geo : Goal → List σ} {goals : List Goal} {s : σ} :
                                  ¬Gluttonous geo [s] goals

                                  A single-segment probe never gluttons (fn. 21).

                                  Gluttony over a higher goal transfers to a bare 3rd person one, since whichever segment reached the lower goal past the higher reaches it past a lone person node.

                                  The Person Case Constraint from probe articulation (§3) #

                                  The PCC configuration is a clitic-doubling probe over IO > DO, the IO optionally K-encapsulated. By (30) each agreed-with DP must cliticize, which a gluttonous probe cannot satisfy, so gluttony is the violation.

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                                    The probe [uPERS [uPART]] of (39a) yields the Weak PCC, and is the person probe of German and Icelandic T ((55), (79)).

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                                      The probe [uPERS [uPART [uSPKR]]] of (39b) yields the Ultrastrong PCC.

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                                        The probe [uPERS [uSPKR]] of (39c) yields the Me-First PCC, with a missing intermediate segment.

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                                          The probe [uPERS [uPART [uSPKR] [uADDR]]] of fn. 22 (i) yields the Strong PCC over transparent datives, and Slovenian's reversible Strong PCC (fn. 26).

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                                            The Weak PCC (22) bans *3 > 1/2.

                                            Datives that expose their person node alone yield the Strong PCC, *1/2/3 > 1/2 (§3.4.1).

                                            The Ultrastrong PCC (39b) has the Weak bans and *2 > 1.

                                            The Me-First probe (39c) bans a 1st person direct object under a 2nd or 3rd person indirect object; the 1 > 1 cell of table 1 is beyond it.

                                            The branching probe over transparent datives bans every distinct-person cluster with a 1st or 2nd person direct object.

                                            theorem CoonKeine2021.direct_never_banned (P : Minimalist.Probe.Articulation) (b : Bool) (io : Person) :
                                            ¬PCCViolation P b { high := io, low := Person.third }

                                            No probe bans a direct or balanced configuration (§3.4.2), since a 3rd person direct object exposes nothing the indirect object lacks.

                                            A probe rooted in [uPERS] that bans a cluster bans its direct object under a 3rd person indirect object (§3.4.2), so a ban on [PART] > [PART] entails the ban on 3 > [PART].

                                            The Weak and Strong probes against the descriptive typology of table 1 as [PZ18] parametrize it, cell for cell.

                                            Against that parametrization the Ultrastrong probe bans every cell but 2 > 2, on which table 1 is silent, P-Uniqueness bans it, and the probe, matched throughout by the indirect object, permits it.

                                            The Me-First probe matches the typology in every cell but 1 > 1, which table 1 bans and the probe, whose [uSPKR] the indirect object matches, permits.

                                            In the Reverse PCC (44)–(45) and its diagnosis (fn. 26), the branching probe over transparent goals bans the lower [PART] DP whichever object it is, while a dative exposing its person node alone cannot be banned when it is the lower one, so Slovenian's Strong PCC is the branching probe.

                                            Against licensing (§2.3) #

                                            The Person Licensing Condition of [Pre11b], (9), is the condition of [BR03] restricted to clauses with a φ-probing head F?.

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                                              Basque (10) is the paper's argument against the original condition. The 3DAT > 1ABS cluster is gluttonous in a finite clause and has no probe to glutton in a nonfinite one, whereas the original condition leaves the 1st person object unlicensed in both and needs the restriction of (9) to exempt the probeless clause.

                                              Number and clitic doubling (§3.4.3, §4.1.3) #

                                              The articulated number probe [uNUM [uPL]] of (23) and (55) comes paired with a person probe, since the probe-specification hierarchy (40) makes a number probe entail a person one.

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                                                Clitic doubling removes the doubled DP from later probing (§3.2), which fixes what the number probe sees after the person probe.

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                                                  There is no Number Case Constraint ((40)–(42)). Over two clitic-doubled objects the person probe, rooted in [uPERS], doubles the higher one, so the number probe sees one goal.

                                                  With a third accessible DP (43), the number probe sees two goals after doubling and gluttons over SG > PL.

                                                  German copulas double nothing, so the number probe sees both nominatives (67), with gluttony in SG > PL (64) but not in PL > SG.

                                                  Gluttony and Vocabulary insertion (§4, §5.2) #

                                                  structure CoonKeine2021.VI (σ : Type u_1) :
                                                  Type u_1

                                                  A Vocabulary item for an agreement head.

                                                  • spec : List σ

                                                    The geometry the item is specified for; [] is the elsewhere item.

                                                  • exponent : String

                                                    The form inserted.

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                                                    instance CoonKeine2021.instDecidableEqVI {σ✝ : Type u_1} [DecidableEq σ✝] :
                                                    DecidableEq (VI σ✝)
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                                                    def CoonKeine2021.instDecidableEqVI.decEq {σ✝ : Type u_1} [DecidableEq σ✝] (x✝ x✝¹ : VI σ✝) :
                                                    Decidable (x✝ = x✝¹)
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                                                      instance CoonKeine2021.instReprVI {σ✝ : Type u_1} [Repr σ✝] :
                                                      Repr (VI σ✝)
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                                                      def CoonKeine2021.instReprVI.repr {σ✝ : Type u_1} [Repr σ✝] :
                                                      VI σ✝ → ℕ → Std.Format
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                                                        instance CoonKeine2021.instRuleVIListString {σ : Type u_1} :
                                                        Morphology.Exponence.Rule (VI σ) (List σ) String

                                                        An item applies to a value when its specification is a subset of the value.

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                                                        abbrev CoonKeine2021.demand {σ : Type u_1} [DecidableEq σ] (vocab : Morphology.Exponence.RuleSet (VI σ)) (value : List σ) :
                                                        Option (VI σ)

                                                        A value demands the most specific applicable item.

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                                                          def CoonKeine2021.Resolvable {σ : Type u_1} [DecidableEq σ] (vocab : Morphology.Exponence.RuleSet (VI σ)) (vals : List (List σ)) :

                                                          The values a probe carries are resolvable when the items they demand are all the same one (85); a value that demands no item, as in (88), competes with nothing.

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                                                            instance CoonKeine2021.instDecidableResolvable {σ : Type u_1} [DecidableEq σ] (vocab : Morphology.Exponence.RuleSet (VI σ)) (vals : List (List σ)) :
                                                            Decidable (Resolvable vocab vals)
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                                                            def CoonKeine2021.realization {σ : Type u_1} [DecidableEq σ] (vocab : Morphology.Exponence.RuleSet (VI σ)) (vals : List (List σ)) :
                                                            Option String

                                                            The exponent inserted for resolvable values.

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                                                              The paper realizes gluttonous probes in these paradigms, each holding the forms it glosses, the Icelandic past mediopassive (81), líka and þykja of (76b) and (78), the German present and past copula ((51), (52), fn. 32), the Hindi-Urdu present and past copula ((68), (69), fn. 34) and the Brazilian Portuguese copula (70).

                                                              • icelandicMediopassivePast : Paradigm

                                                                Icelandic past mediopassive, (81).

                                                              • icelandicLikaPast : Paradigm

                                                                Icelandic líka 'like' in the past, (73) and (76b).

                                                              • icelandicThykjaPresent : Paradigm

                                                                Icelandic þykja 'think' in the present, (78).

                                                              • germanPresent : Paradigm

                                                                German present copula, (51)–(52).

                                                              • germanPast : Paradigm

                                                                German past copula, fn. 32.

                                                              • hindiPresent : Paradigm

                                                                Hindi-Urdu present copula, (68)–(69).

                                                              • hindiPast : Paradigm

                                                                Hindi-Urdu past copula, fn. 34.

                                                              • portuguesePresent : Paradigm

                                                                Brazilian Portuguese present copula, (70).

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                                                                def CoonKeine2021.instReprParadigm.repr :
                                                                Paradigm → ℕ → Std.Format
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                                                                  The person items of a paradigm in the context of the number probe's value (82), undefined where the paper glosses no forms.

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                                                                    The number items of a paradigm, where the paper gives them.

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                                                                    • x✝.number = []
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                                                                      The number context of person insertion is that the number probe's first value is plural.

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                                                                        After Agree a probe either cliticizes what it agreed with (30) or undergoes Vocabulary insertion in a paradigm.

                                                                        • cliticize : Aftermath

                                                                          Each agreed-with DP cliticizes onto the probe's host.

                                                                        • realize (paradigm : Paradigm) : Aftermath

                                                                          The probe is realized by one item of the paradigm.

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                                                                            A person probe converges over its goals when a clitic-doubling probe does not glutton, and when an agreement probe's person and number demands are resolvable in a glossed number context.

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                                                                              instance CoonKeine2021.instDecidableConverges (a : Aftermath) (P : Minimalist.Probe.Articulation) (goals : List Goal) :
                                                                              Decidable (a.Converges P goals)
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                                                                              In Icelandic dative-nominative agreement (76)–(85) in the past mediopassive, a 1st person plural nominative crashes on -ust against -umst (83), a 2nd person plural one converges on -ust (85), and in the singular, where every cell is -ist, the restriction is lifted.

                                                                              Kichean Agent Focus number agreement (88) has one item, realizing plural.

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                                                                                def CoonKeine2021.kicheanGoals (s o : Bool) :
                                                                                List Goal

                                                                                Two 3rd person goals of the given numbers, the cells of (88).

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                                                                                  In omnivorous number (§5.2), with no singular item, a number probe gluttonous over SG > PL converges on the plural item, and the table of (88) follows.

                                                                                  The paper's examples #

                                                                                  A configuration the paper assigns an example.

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                                                                                    def CoonKeine2021.instDecidableEqConfig.decEq (x✝ x✝¹ : Config) :
                                                                                    Decidable (x✝ = x✝¹)
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                                                                                      The configuration converges.

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                                                                                          def CoonKeine2021.paradigms :
                                                                                          List (String × Paradigm)
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                                                                                            def CoonKeine2021.rowGoal (row : Datum) (k : String) :
                                                                                            Option (List Goal)

                                                                                            The goal a row's higher or lower features describe, absent when shielded from the probe.

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                                                                                              The configuration of a row that the paper analyses.

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                                                                                                A row counts as grammatical when the paper judges it acceptable or marginal. Its ? examples, (77) and fn. 32, it calls quite acceptable and much improved, while *? and ?? carry its star.

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                                                                                                  theorem CoonKeine2021.analysed_rows (row : Datum) :
                                                                                                  row ∈ Examples.all → (row.feature? "aftermath").isSome = true → ∃ c ∈ Config.ofRow row, Grammatical row ↔ c.Converges

                                                                                                  Every analysed example is grammatical exactly when its configuration converges.