topics: |  cognitive | language | spatial

Many objects are associated with an "axis" - e.g. N/S (global) or
Front/Back (local, functional).  When such an object acts
as a spatial reference ("landmark" or "ground") for a located object
("trajector" or "figure"), then the reference is often based on this axis,
e.g. in front of the Post Office, or W of the Post office.   However,
sometimes one may say encode motions in terms of small vector fragments, with
location constraints such as "from X to Y past Z".  See
the study by Bohnemeyer below.

5: Jürgen Bohnemeyer: The Unique Vector Constraint

Presents the argument, based on a study of spatial descriptors across a
number of languages [examples are from Dutch, and
Yucatec Maya, which is mostly mono-clausal].  In all situations, primitive
motions are usually rectilinear fragments, what the author calls a vector
(start point, direction, distance).

Modality: Subjects are shown certain videos, involving changes of direction,
and produce descriptions such as:

Dutch1: The little ball rolls from the square along a track past the little
house to the little triangle

Dutch2: A red round thing starts from the blue thing on the left, then rolls
to the right across a track; but that actually looks a bit like a street,
because behind it there's a house.  It stops at a green triangle.

he notes that Dutch speakers prefer not to mention
more than two Ground objects per clause.

Yucatec:
But this time, I saw a blue thing, it remains at the end where the red thing
left, [the red thing] went rolling, then it passes by a thing which is also
red, then it arrives at the blue [i.e. green] triangle.

* Sally walked out of the library from the reception to the entrance.
[is ungrammatical because the source role is assigned twice - this violates
the AUC]

Argument Uniqueness Constraint AUC: no two structural arguments or adjuncts
of the same clause can be assigned the same semantic role.
known as "theta criterion" in GB (Government-Binding theory) or "biuniqueness
condition" in LFG

Originally proposed by Fillmore (1968):

    The sentence in its basic structure consists of a verb and one of more
    noun phrases, each associated with the verb in a particular case
    relationship.  The 'explanatory' use of this framework resides in the
    necessary claim that, although there can be compound instances of a
    single case (through noun phrase conjunction), each case relationship
    occurs only once in a simple sentence. p.21

In this paper, he poses a Uniqueness Vector Constraint as a general purpose
constraint across all languages, that spatial elements can only describe a
single direction.  This is used to explain examples like:


(3a) Sally walked north away from her house.
(3b) Sally walked away from her house and then north.

(3a) can only be describing a single direction (that is, a unique direction
vector) whereas (3b) can be used to describe a change in direction (that is,
two distinct direction vectors).

[NOTE: Some thoughts on whether this is true.  e.g.

I walked away from the CC towards the auditorium.

I guess what JB would say is that away codes only for change in distance,
change in orientation is coded by "towards X" so together they define a
vector and there is no conflict.

but
*? I walked north from the CC towards the auditorium.

but this violates AUC and not UVC
]

X moved away from A towards B [indicates linear motion]
X moved away from A and then towards B [indicates linear motion]

Jackendoff 1983:163: three types of paths, all defined w.r.t. referential
rounds:
 - bounded paths - define beg or end - assigned source and goal roles
 - routes - Grounds lie on path between source and goal
   encoded by: via, past, through, across, over, and along
 - directions - do not lie on path, but wouild if the path were extended some
   unspecified distance [p. 164]
   encoded by: only two path functions: towards, and away from.

diagnostic of direction spec is that they do not entail location change.
thus motion clauses specifying only direction are atelic.

[telicity is the property of a verb or verb phrase that presents an action or
event as being complete in some sense. A verb or verb phrase with this
property is said to be telic, while a verb or verb phrase that presents an
action or event as being incomplete is said to be atelic.]

[Q. what about "around" - "the car drove around" - clearly atelic, but not
a route, nor a direction.  "the car drove around the building" is also not a
route by Jackendoff definition - Ground is not between source and goal. ]

Jackendoff:1983, Semantics and Cognition, MIT Press

much of the linguistic data covered here can be found in:
http://www.mpi.nl/world/persons/private/bohnem/vecjbnew.pdf

Contents

1. The representation of direction in language and space
2. Spatial language and spatial cognition: the roles of axial and vector
3. Vectors across spatial domains: from place to size, orientation, shape and
   parts
4. Vector grammar, places, and the functional role of the spatial
   prepositions in English
5. Constraints on motion event coding: vectors or path shapes?
6. Defining spatial relations: reconciling axis and vector representations
7. Places: points, paths, and portions
8. Ontological problems for the semantics of spatial expressions in natural
   language
9. Change of orientation
10. Memory for locations relative to objects: axes and the categorization of
   regions
11. How Finnish postpositions see the axis system
12. Directions from shape: how spatial features determine reference axis
   categorization
13. Spatial prepositions, spatial templates, and 'semantic' versus
   'pragmatic' visual representations

Other reviews

http://www.sil.org/silebr/silebr2006-002
Reviewed by Steve Nicolle

The contributions in this volume can be broadly divided into those which
favour the use of VECTORS to represent direction, and those which favour an
AXIS-based approach.

AXIS:

According to the axis-based approach, the object which
is located (termed the figure) is described or understood relative to an
axis, such as front-back or north-south. The nature of the axis depends on
the context, and is either projected onto the object relative to which the
figure is located (the referent or ground) or is based on intrinsic
properties of the referent, such as its function or shape (compare in front
of the tree, in which a front-back axis is projected onto the referent based,
say, on the viewer’s perspective, with in front of the television, which
indicates that the figure is located on a front-back axis relative to the
television screen, and additionally that the figure may be oriented so as to
be facing the screen). In contrast, a vector is a line originating at a known
location, typically (some part of) the referent, and ending at another
location, typically the location of the figure. In contrast to axes, vectors
represent both direction and distance, and a referent may be the source of an
infinite number of potential vectors. An expression such as in front of is
associated with a set of vectors of varying degrees of acceptability, rather
than with proximity to the front part of a front-back axis. Changes in the
position and direction of a moving figure (a path) can be represented as “an
ordered sequence of places and the direction vectors between them” (John
O’Keefe, p.70).

VECTOR:

The vector-based approach is adopted by the two more linguistically oriented
chapters which I discuss in some detail below. First, Joost Zwarts (‘Vectors
across Spatial Domains’) suggests that the domains of place, size,
orientation, shape, and spatial parts can all be described in terms of
vectors, without the need for distinct ontological categories or primitives
for each domain. This, he claims, is why the same measure phrases are used
with different domains:

	(1a)  	The stone was twelve inches deep. [place]
	(1b)  	The rope was twelve inches long. [size]

These descriptions can both be formalised in terms of vectors as follows,
where place(x,v,y) means ‘x is placed at vector v, and vector v is placed at
y’, axis(x,v) means ‘x has an axis v’ (that is, v connects one end of x with
the opposite end) and |v| means ‘the length of vector v’:

	(2a) x is twelve inches deep: there is a downward v such that
	     place(x,v,y) and |v|=12in
	(2b) x is twelve inches long: there is a v such that axis(x,v)
	     and |v|=12in

Jürgen Bohnemeyer (“The Unique Vector Constraint”) makes the interesting
universal claim that “all direction specifications in a single simple clause
must denote the same direction vector” (86). This is illustrated by the
following example.

(3a) Sally walked north away from her house.
(3b) Sally walked away from her house and then north.

(3a) can only be describing a single direction (that is, a unique direction
vector) whereas (3b) can be used to describe a change in direction (that is,
two distinct direction vectors). A direction vector is defined as a vector
(or set of vectors) which determines the orientation or direction of motion
of a figure with respect to a ground during a particular time interval; a
single direction vector can therefore describe a change of direction, as in
the following examples from English and Ewe:

	(4a) Sally went around the corner to the kiosk.
	(4b) *Sally went around the corner north.

(4b) is unacceptable because two direction vectors, ‘around the corner’ and
‘north’, have been combined in a single simple clause.

The vector-based approach to encoding direction is also adopted by John
O’Keefe (“Vector Grammar, Places and the Functional Role of the Spatial
Prepositions in English”). O’Keefe shows how the hippocampus, which in humans
processes both spatial information and language, in rats is exclusively
devoted to processing spatial information. From this basis, he argues that
the spatial senses of prepositions constitute their basic meanings, with
other senses being derived by metaphorical extension. Two other contributions
combine a vector and an axis approach.

Laura Carlson, Terry Regier and Eric
Covey (“Defining Spatial Relations: Reconciling Axis and Vector
Representations”) argue that both axis and vector representations are needed
to define spatial relations, with axes underlying reference frames (which are
imposed on reference objects so as to define orientation, direction and
scale) and vectors underlying spatial templates, which operate across
reference frames and define general concepts such as above used independently
of specific objects.

Rik Eshuis (“Memory for Locations Relative to Objects:
Axes and the Categorization of Regions”) comes to a similar conclusion based
on experimental evidence.

Barbara Tversky (‘Places: Points, Planes, Paths, and Portions’) presents
evidence that, when people express location, landmarks are preferred over
directions and distances, which suggests that vector representations (which
are predicated on direction and distance) may not in fact be the most useful
way of describing locations. Three other contributions prefer axis-based
approaches over a vector-based approach. Barbara Landau (“Axes and Direction
in Spatial Language and Spatial Cognition”) shows that people are better at
recognising and remembering direction when it is close to vertical or
horizontal axes, with the vertical axis being more salient than the
horizontal.

Similar results were obtained by Emile van der Zee & Rik Eshuis
(“Directions from Shape: How Spatial Features Determine Reference Axis
Categorization”) from experiments in which Dutch participants were asked to
place dots in locations described as voor ‘in front of’, achter ‘behind’,
links van ‘to the left of’ and rechts van ‘to the right of’ variously shaped
reference objects.

Axis representations were also used by Urpo Nikkanne (“Finnish
Postpositions”), although the major interest of this chapter for me lies in
the linguistic data itself. In Finnish, some postpositions meaning ‘behind’
or ‘in front of’ can only be used when referring to two or more moving
objects:

(6a)  	Buick on Volvon perassa / jaljessa  (following behind)
(6b)  	Buick on Volvon takana (behind)

In a footnote at the end of his chapter, Nikanne notes that “this fact of
Finnish postpositions has not been pointed out in the Finnish grammatical
literature… Possibly we Finnish grammarians see our own language through the
Germanic/Romance grammatical tradition, without noticing it” (208). If this
is the case with a well-documented language such as Finnish, how much more
likely is it that similar facts have been overlooked in other less
well-documented languages?

Finally, three contributions eschew the use of vectors and axes
altogether. Pierre Gambaratto & Philippe Muller (‘Ontological Problems for
the Semantics of Spatial Expressions in Natural Language’) and Hedda
Schmidtke et al. (‘Change of Orientation’) aim to formalise natural language
expressions (such as the German expressions for turn
right/round/off/clockwise) using the apparatus of formal logic, and

In the final chapter of the volume, Kenny Coventry (‘Spatial Prepositions,
Spatial Templates, and ‘Semantic’ versus ‘Pragmatic’ Visual Representations’)
emphasises the importance of the function of the figure and the ground when
describing a spatial relation.

References

Levinson, S. 2003. Space in language and cognition: Explorations in cognitive
diversity. Cambridge: Cambridge University Press.

Levinson, S. C. & Wilkins, D. (eds.) 2006. Grammars of space. Cambridge:
Cambridge University Press.

Shay, E. & Seibert, U (eds.) 2003. Motion, direction and location in
languages: In honor of Zygmunt Frajzyngier. (TSL, 56.) Amsterdam: Benjamins.

van der Zee, E. 1996. Spatial knowledge and spatial language: A theoretical
and empirical investigation. Utrecht: ISOR Publications.