Helmantel 2002: interactions in the Dutch adpositional domain

Helmantel's dissertation sorts the core Dutch adpositions by the path specification in their denotation. A narrow locative, in, op, achter, denotes a location with no path; a point locative, naar, tot, van, denotes a point on a path and is inherently directional; an extended locative, door, langs, om, denotes a location with extension along a path. Five distributional tests separate the three classes, and the classification has a syntactic correlate. Directionality sits in a functional projection above the adposition, the directionality phrase, whose head the adposition moves to. An inherently directional adposition checks the directionality itself and leaves its complement where the adposition selects it, which is the prepositional order; any other adposition in a directional phrase moves its complement to the specifier of the directionality phrase as well, which is the postpositional order. The postpositional order is thus derived from the prepositional one, never the reverse, and the adpositions with a postpositional use are a subset of the prepositions.

The complement in the specifier of the directionality phrase receives a path interpretation, and that specifier is the one position from which an element leaves the phrase, Van Riemsdijk's escape hatch. So the complement of a postpositional phrase is interpreted as the path travelled, is extractable, and cannot be a bare mass noun, while the complement of a prepositional phrase is a location, stays inside the phrase, and is unrestricted.

The classification is checked against the Dutch adposition fragment: the point locatives are the grammar's inherently directional prepositions and have no postpositional use, the narrow locatives are locational before their complement, and the grammar reads the path a narrow locative's postposition denotes as a goal and an extended locative's as a route or a source, which is the difference the length-modification test tracks. The two core adpositions the classification leaves out, met and zonder, are the fragment's non-spatial ones.

Main definitions

• narrowLocatives, pointLocatives, extendedLocatives: the classification of the core adpositions, over the fragment's entries.
• DPRaises, linearization: the complement's movement to the specifier of the directionality phrase, and the order of the adposition and its complement that results.

Main results

• linearization_eq_post_iff, linearization_eq_pre_of_inherent: the postpositional order is a directional phrase whose adposition is not inherently directional.
• dpRaises_iff_linearization_eq_post: the complement is in the escape hatch, extractable and read as a path, exactly in the postpositional order.
• pointLocative_linearization, pointLocative_directional, narrowLocative_locational: the point locatives are the inherently directional prepositions and are never postpositional.
• narrowLocative_direction_post, extendedLocative_direction_post: the class predicts the path the postpositional use denotes.

Implementation notes

• The classes are the dissertation's lists of core adpositions, as lists of fragment entries; the grammar's over 'across' is the one the dissertation classifies. The remaining, younger adpositions are left unclassified, as the dissertation leaves them.
• The directionality phrase is modelled by two parameters, whether it is projected and whether the adposition is inherently directional; the adposition's own movement to its head, the dimensionality requirement on the complement and its consequences for mass nouns, and the complex adpositional phrases of the second half of the dissertation are described here and not formalized.

References

• M. Helmantel, Interactions in the Dutch Adpositional Domain (2002)
• H. van Riemsdijk, A Case Study in Syntactic Markedness: The Binding Nature of Prepositional Phrases (1978)
• R. S. Kayne, The Antisymmetry of Syntax (1994)

The classification of the core adpositions

def Helmantel2002.narrowLocatives : List Dutch.Adposition

The narrow locative adpositions, whose denotation has no path specification.

Equations

• One or more equations did not get rendered due to their size.

def Helmantel2002.pointLocatives : List Dutch.Adposition

The point locative adpositions, whose complement is a point on a path, are the inherently directional adpositions.

Equations

• Helmantel2002.pointLocatives = [Dutch.Adpositions.naar, Dutch.Adpositions.tot, Dutch.Adpositions.van]

def Helmantel2002.extendedLocatives : List Dutch.Adposition

The extended locative adpositions, whose complement extends along a path.

Equations

• One or more equations did not get rendered due to their size.

theorem Helmantel2002.classes_spatial (a : Dutch.Adposition) : a ∈ narrowLocatives ++ pointLocatives ++ extendedLocatives → a.IsSpatial

The classified adpositions are the spatial ones.

theorem Helmantel2002.met_zonder_not_spatial : ¬Dutch.Adpositions.met.IsSpatial ∧ ¬Dutch.Adpositions.zonder.IsSpatial

The two core adpositions that do not fit the classification are non-spatial.

theorem Helmantel2002.pointLocative_directional (a : Dutch.Adposition) : a ∈ pointLocatives → a.direction Adposition.Linearization.pre ≠ Spatial.Path.Direction.place

A point locative is one of the grammar's directional prepositions.

theorem Helmantel2002.narrowLocative_locational (a : Dutch.Adposition) : a ∈ narrowLocatives → a.direction Adposition.Linearization.pre = Spatial.Path.Direction.place

A narrow locative is locational before its complement.

theorem Helmantel2002.pointLocative_linearization (a : Dutch.Adposition) : a ∈ pointLocatives → a.linearization = {Adposition.Linearization.pre}

A point locative is a preposition only: an inherently directional adposition checks the directionality itself and never raises its complement.

theorem Helmantel2002.narrowLocative_direction_post (a : Dutch.Adposition) : a ∈ narrowLocatives → a.IsPostposition → a.direction Adposition.Linearization.post = Spatial.Path.Direction.goal

The postposition of a narrow locative denotes a goal path, de berg op 'up the mountain': the complement is read as the path and the location the preposition denotes as its endpoint, which is why a length modifier can measure it.

theorem Helmantel2002.extendedLocative_direction_post (a : Dutch.Adposition) : a ∈ extendedLocatives → a.IsPostposition → a.direction Adposition.Linearization.post ≠ Spatial.Path.Direction.goal

The postposition of an extended locative denotes a route or a source path, het bos door 'through the woods', never a goal: the complement already extends along the path.

The directionality phrase

def Helmantel2002.DPRaises (dirP inherent : Prop) : Prop

The complement moves to the specifier of the directionality phrase when the phrase is projected and the adposition is not inherently directional; an inherently directional adposition checks the directionality by moving to the head alone and leaves its complement in place.

Equations

• Helmantel2002.DPRaises dirP inherent = (dirP ∧ ¬inherent)

@[instance_reducible]

instance Helmantel2002.instDecidableDPRaises (dirP inherent : Prop) [Decidable dirP] [Decidable inherent] : Decidable (DPRaises dirP inherent)

Equations

• Helmantel2002.instDecidableDPRaises dirP inherent = { decide := decide dirP && decide ¬inherent, reflects_decide := ⋯ }

def Helmantel2002.linearization (dirP inherent : Prop) [Decidable dirP] [Decidable inherent] : Adposition.Linearization

The adposition follows its complement when the complement has raised, and precedes it otherwise.

Equations

• Helmantel2002.linearization dirP inherent = if Helmantel2002.DPRaises dirP inherent then Adposition.Linearization.post else Adposition.Linearization.pre

theorem Helmantel2002.linearization_eq_post_iff {dirP inherent : Prop} [Decidable dirP] [Decidable inherent] : linearization dirP inherent = Adposition.Linearization.post ↔ dirP ∧ ¬inherent

The postpositional order is a directional phrase whose adposition is not inherently directional, so the postpositional order is derived from the prepositional one and the postpositions are a subset of the prepositions.

theorem Helmantel2002.linearization_eq_pre_of_inherent {dirP inherent : Prop} [Decidable dirP] [Decidable inherent] (h : inherent) : linearization dirP inherent = Adposition.Linearization.pre

An inherently directional adposition is a preposition.

theorem Helmantel2002.dirP_of_linearization_eq_post {dirP inherent : Prop} [Decidable dirP] [Decidable inherent] (h : linearization dirP inherent = Adposition.Linearization.post) : dirP

A phrase in the postpositional order is directional.

theorem Helmantel2002.dpRaises_iff_linearization_eq_post {dirP inherent : Prop} [Decidable dirP] [Decidable inherent] : DPRaises dirP inherent ↔ linearization dirP inherent = Adposition.Linearization.post

The complement sits in the specifier of the directionality phrase exactly in the postpositional order. That specifier is the one position from which an element leaves the phrase, the escape hatch Van Riemsdijk's Head Constraint allows, and the position in which the complement is read as the path travelled; so the complement of a postpositional phrase is extractable and a path, and the complement of a prepositional phrase is neither.