Analyzing directionality: From paths to locations
Sander Lestrade
Research group Sprachkontakt und Sprachvergleich &SFB/TR 8 Spatial Cognition, University of Bremen, Germany

Abstract. This paper proposes an alternative to the currently prevalent
analysis of directionality in terms of paths. It is argued that directionality
should be understood as the temporal specification of locative modification in its stead. The proposal is compatible with both geometric andfunctional representations of space, is corroborated with typological findings, and meets the requirements for the careful development of a spatial
ontology.
Keywords: directionality, locations, paths, event structure, motion

1

Against paths as the primitives of directionality

Spatial expressions are predicates that map a thing or event onto a location.1
This location is specified by the configuration function in terms of a (geometrically or functionally defined) region with respect to a ground. In The ball isunder the table., the ball is said to be in the location specified by under the table.
The predication of locations often is temporarily restricted (cf. [9]). Generally,an object is mapped to some region for a restricted interval of time only as its
position may change at a later stage. In the present proposal, this change ofconfiguration is the realm of the directionality function.
In the currently prevalent analysis of directionality, viz. the one by Jackendoff ([7]), directionality is a function that refers to ordered stretches of space,so-called paths. For example, the FROM path off refers to a path that has an
ON configuration as its starting point. The first and most important objection
to the analysis of Jackendoff concerns the methodology in the collection of thedata that is said to constitute the directionality domain [7, 168–169]. There isno independent evidence that the used examples actually are examples of thesame phenomenon, i.e. of directionality. Indeed, some of Jackendoff’s directionality expressions probably express something completely different. For example,TOWARD is said to belong to the type of paths called directions, which, unlike
a bounded path such as TO, does not include (the region with respect to) thereference object but would do so if the path were extended by some unspecified
distance. In a non-trivial sense, we probably only want to allow for extensions
in approximately the same direction (otherwise, any direction could be turned
1Thanks to John Bateman, Carl Schultz, Thora Tenbrink, and two anonymous reviewers for valuable comments and discussion.

into a TO path). Now, imagine an enclosure around point A with an opening
at its south side and point B to its north. Because of the enclosure, one canonly go from A to B going southwards, through the opening. To go from Atoward B, however, one should go north. Crucially, the TOWARD path in thissituation cannot be extended in the same direction to become a bounded to B
path. Thus, instead of directionality, toward rather seems to expresses orientation. When modifying a motion event with this expression, the moving object ofcourse ends up closer to the ground. And by continuing along this direction, onewill generally end up at this ground too. But this need not be, as this example
shows.
As a second objection, the path reference that is assumed by Jackendoff
may follow from world knowledge instead of being part of the lexical semantics
of directionality (cf. the procedure for the development of a spatial ontology
in [1] and the principle of conceptual abstraction in [16, 595]). We know thatit takes a path from A to B to go from A to B as we cannot but traverse
all points in between when going there. Crucially, however, such paths are notnecessarily what is referred to by directionality expressions. In fact, directionality
expressions are probably better analyzed as predicates (cf. [16], [17]).
Finally, if directional PPs referred to paths, it should be possible to combine
an expression of duration with the continuation along such a path. But this is
not possible with Goal directionality as illustrated by the ungrammaticality of
He is walking into the building (*for hours). (cf. also [18]). Note that this is
not due to the semantics of the verb to walk : If explicit reference is made to apath, by substituting through for into in the example, it is possible to use anexpression of duration. Thus, the contrast between these sentences shows that(Goal) directionality is probably not about paths.

2Directionality in terms of locations

A more careful procedure than the one used by [7] can be followed in the collection of the data. It has been observed that more grammatical means of expression
tend to make less idiosyncratic meaning distinctions ([14, 178], [6, 178], [1, 1035]).
Also, it has been found that spatial cases primarily express directionality ([8],[13], [2]). Finally, cross-linguistic agreement is said to suggest relative uniformity
in the way people conceptualize a domain [4]. So not only can we indeed expect
directionality distinctions to be expressed by spatial case systems, also, we canexpect whatever directionality distinctions that are made by spatial case to beof a more fundamental, conceptual type, especially when they show up in language after language. In a cross-linguistic study of spatial case inventories that isthus motivated, Lestrade [10] identifies three basic distinctions of directionality:Place, Goal, and Source.
This kernel of directionality could be described in terms of paths, but, arguably, it is preferable to use locations only as we need these anyway for theconfiguration function. Then, Goal and Source directionality denote a change oflocation, and Place denotes an absence of such a change. To define Goal andSource, we need some ordered dimension: Goal directionality denotes a change
into some location, Source does the opposite.
An ordered dimension can be provided for free by the extended event structure of the verb. Pustejovsky ([12]) argues that Davidsonian event arguments
may have internal structure. For our present purposes, only the structure inwhich there is a strict partial order between the two subevents is relevant:
(1)a.
b.

[e3 e1 <α e2 ] =def <α ({e1 , e2 }, e3 )
∀e1 , e2 , e3 [<α ({e1 , e2 }, e3 ) ↔ e1  e3 ∧ e2  e3 ∧ e1 < e2 ∧∀e[e  e3 → e = e1 ∨ e = e2 ]]In this definition, event e3 is a complex event structure that consists of twosubevents, e1 and e2 , where e1 and e2 are temporally ordered such that each isa logical part of e3 , the first subevent precedes the second, and there is no otherevent that is part of e3 [12, 69]. For example, the verb build is analyzed into adevelopment process and a resulting state.
Pustejovsky [12, 74] explicitly allows for adverbial phrases to take scope overboth the entire event and over individual subevents. Thus, we have three logicalpossibilities for spatial modification of motion verbs, which nicely corresponds
to the empirically established kernel: the spatial modification of the entire event
is called Place directionality (note the different use of this term here from theone by Jackendoff in the above); the modification of the first subevent is called
Source, and the modification of the second subevent is called Goal. For example,depending on the type of directionality that is imposed by the spatial modifier
and assuming the structure in (1), a walking event e3 of subject x modified bylocation y can be decomposed as follows: [walk(e3 , x) ∧ loc(e3 , x, y)] for Place,[walk(e1 , x) ∧ loc(e2 , x, y)] for Goal, and [loc(e1 , x, y) ∧ walk(e2 , x)] for Source.
In principle, the explicit spatial modification of one subevent by location ydoes not exclude the additional implicit modification of the second subevent by
this same location. Following a suggestion of Hendriks et al. [5, chapter 8], we
can ensure a change of location in a system of pragmatic contrasts (cf. also [15]):The speaker would have modified the whole event if the location had scope over
the whole event, so if she only modifies the first subevent, we know that thelocative function does not apply to the second one by pragmatic implicature.
By only using existing structures that have been established independently
from present purposes, the proposal meets the criterion of Bateman et al. [1]to exclude the contribution of world knowledge in the development of a spatialontology. Also, the account straightforwardly accounts for syncretism patterns indirectionality systems. It has been observed that such syncretisms occur between
Place and Source, between Place and Goal, or between all three distinctions, but
not between Source and Goal to the exclusion of Place (cf. [2], [10], [11]). Thisnaturally follows from the present proposal: If a language has a special marker
for the spatial modification of the first subevent, the second subevent and theentire event will be treated uniformly as its complement (and the other wayaround), but taking together the two subevents would render the entire event(cf. (1-b)) and therefore could not be distinguished from it. Finally, the temporal
specification of a spatial modification does not impose any specific ontologicalcategory to this modification and is thus compatible with both geometrical andfunctional representations of space [3].
In conclusion, it was argued that directionality is best analyzed as the locative modification of an extended event structure. This accounts for the empirically established kernel of directionality, correctly predicts attested syncretism
patterns, and does not stipulate any additional machinery.

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